{"id":31852,"date":"2026-09-10T15:06:32","date_gmt":"2026-09-10T09:36:32","guid":{"rendered":"https:\/\/mycbseguide.com\/blog\/?p=31852"},"modified":"2026-09-10T15:10:36","modified_gmt":"2026-09-10T09:40:36","slug":"large-numbers-around-us-ncert-solutions-class-7-maths-ganita-prakash","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/large-numbers-around-us-ncert-solutions-class-7-maths-ganita-prakash\/","title":{"rendered":"Large Numbers Around Us – NCERT Solutions Class 7 Maths (Ganita Prakash)"},"content":{"rendered":"\n

Large Numbers Around Us<\/strong><\/strong> – NCERT Solutions Class 7 Maths (Ganita Prakash) includes all the questions with solutions given in the NCERT Class 7 Maths (Ganita Prakash).<\/p>\n\n\n\n

NCERT Solutions Class 7<\/h2>\n\n\nEnglish Poorvi<\/a>\n\n\nHindi Malhar<\/a>\n\n\nMaths Ganita Prakash<\/a>\n\n\nScience Curiosity<\/a>\n\n\nSocial Exploring Society<\/a>\n\n\n\n

Large Numbers Around Us<\/strong><\/strong> \u2013 NCERT Solutions<\/h2>\n\n\n\n
\n\n\n\n

Q.1: What if we ate 2 varieties of rice every day? Would we then be able to eat 1 lakh varieties of rice in 100 years?<\/p>\n\n\n\n

Solution:<\/p>\n\n\n\n

Days in a year =365=365
Rice varieties eaten per day =2=2
Rice varieties eaten in a year =2\u00d7365=730=2\u00d7365=730
Rice varieties eaten in 100 years =730\u00d7100=73,000=730\u00d7100=73,000 varieties.
No, we can eat only 73,000 varieties in 100 years, not 1 lakh.<\/p>\n\n\n\n

\n\n\n\n

Q.2: What if a person ate 3 varieties of rice every day? Will they be able to taste all the lakh varieties in a 100 year lifetime? Find out.<\/p>\n\n\n\n

Solution:<\/p>\n\n\n\n

Days in a year =365=365
Rice varieties eaten per day =3=3
Rice varieties eaten in a year =3\u00d7365=1095=3\u00d7365=1095
Rice varieties eaten in 100 years =1095\u00d7100=1,09,500=1095\u00d7100=1,09,500 varieties.
Yes, they can eat all 1 lakh varieties in 100 years.<\/p>\n\n\n\n

\n\n\n\n

Q.3: Estu said, “We know how many days there are in a year – 365, if we ignore leap years. If we live for yy years, the number of days in our lifetime will be 365\u00d7y365\u00d7y.”<\/p>\n\n\n\n

Solution:<\/p>\n\n\n\n

Assume we live for 95 years, i.e. y=95y=95.
Number of days in our lifetime =365\u00d795=34,675=365\u00d795=34,675
Difference between 1,00,0001,00,000 and 34,675=1,00,000\u221234,675=65,32534,675=1,00,000\u221234,675=65,325.<\/p>\n\n\n\n

\n\n\n\n

Q.4: Look at the picture on the right. Somu is 1 metre tall. If each floor is about four times his height, what is the approximate height of the building?
<\/p>\n\n\n\n

Solution:<\/p>\n\n\n\n

Somu’s height = 1 metre
Height of each floor =4\u00d71=4=4\u00d71=4 metres
Number of floors in the building =10=10
Height of the building =10\u00d74=40=10\u00d74=40 metres.<\/p>\n\n\n\n

\n\n\n\n

Q.5: Which is taller – The Statue of Unity or this building? How much taller? ________ m.
<\/p>\n\n\n\n

Solution:<\/p>\n\n\n\n

Height of The Statue of Unity = 180 m
Height of Somu’s building =40 m=40 m
Since, 180\u221240=140 m180\u221240=140 m
The Statue of Unity is 140 m taller than the building.<\/p>\n\n\n\n

\n\n\n\n

Q.6: How much taller is the Kunchikal waterfall than Somu’s building? ________ m.
<\/p>\n\n\n\n

Solution:<\/p>\n\n\n\n

Height of the Kunchikal waterfall =450 m=450 m
Height of Somu’s building =40 m=40 m
Since 450\u221240=410 m450\u221240=410 m
The Kunchikal waterfall is 410 m taller than Somu’s building.<\/p>\n\n\n\n

\n\n\n\n

Q.7: How many floors should Somu\u2019s building have to be as high as the waterfall?
<\/p>\n\n\n\n

Solution:<\/p>\n\n\n\n

Height of each floor in the building =4 m=4 m
Height of the waterfall =450 m=450 m
Number of floors required =450\u00f74=112.5=450\u00f74=112.5
So, Somu’s building should have at least 113 floors to be as high as the waterfall.<\/p>\n\n\n\n

\n\n\n\n

Q.8: How do you view a lakh – is a lakh big or small?<\/p>\n\n\n\n

Solution:<\/p>\n\n\n\n

A lakh can seem big or small depending on the context and what it’s being compared to. For instance, a crowd of 1 lakh people at an event or protest is massive, but in terms of city population, 1 lakh might be considered a small town.<\/p>\n\n\n\n

\n\n\n\n

Q.9: Write each of the numbers given below in words:<\/p>\n\n\n\n

    \n
  1. 3,00,6003,00,600<\/li>\n\n\n\n
  2. 5,04,0855,04,085<\/li>\n\n\n\n
  3. 27,30,00027,30,000<\/li>\n\n\n\n
  4. 70,53,13870,53,138<\/li>\n<\/ol>\n\n\n\n

    Solution:<\/p>\n\n\n\n

    3,00,6003,00,600 – Three lakh six hundred.
    5,04,085 – Five lakh four thousand eighty five.
    27,30,000 – Twenty seven lakh thirty thousand.
    70,53,13870,53,138 – Seventy lakh fifty three thousand one hundred and thirty eight.<\/p>\n\n\n\n

    \n\n\n\n

    Q.10: Write the corresponding number in the Indian place value system for each of the following:<\/p>\n\n\n\n

      \n
    1. One lakh twenty three thousand four hundred and fifty six<\/li>\n\n\n\n
    2. Four lakh seven thousand seven hundred and four<\/li>\n\n\n\n
    3. Fifty lakhs five thousand and fifty<\/li>\n\n\n\n
    4. Ten lakhs two hundred and thirty five<\/li>\n<\/ol>\n\n\n\n

      Solution:<\/p>\n\n\n\n

        \n
      1. One lakh twenty three thousand four hundred and fifty six \u22121,23,456\u22121,23,456.<\/li>\n\n\n\n
      2. Four lakh seven thousand seven hundred and four – 4,07,704.<\/li>\n\n\n\n
      3. Fifty lakhs five thousand and fifty – 50,05,050.<\/li>\n\n\n\n
      4. Ten lakhs two hundred and thirty five – 10,02,03510,02,035.<\/li>\n<\/ol>\n\n\n\n
        \n\n\n\n

        Q.11: The Thoughtful Thousands only has a +1000 button. How many times should it be pressed to show:<\/p>\n\n\n\n

          \n
        1. Three thousand? 3 times<\/li>\n\n\n\n
        2. 10,000? ________<\/li>\n\n\n\n
        3. Fifty three thousand? ________<\/li>\n\n\n\n
        4. 90,000? ________<\/li>\n\n\n\n
        5. One Lakh? ________<\/li>\n\n\n\n
        6. ________? 153 times<\/li>\n\n\n\n
        7. How many thousands are required to make one lakh?<\/li>\n<\/ol>\n\n\n\n

          Solution:<\/p>\n\n\n\n

            \n
          1. 10 times (\u223510,000\u00f71000=10)10 times (\u223510,000\u00f71000=10)<\/li>\n\n\n\n
          2. 53 times (\u223553,000\u00f71000=53)53 times (\u223553,000\u00f71000=53)<\/li>\n\n\n\n
          3. 90 times (\u223590,000\u00f71000=90)90 times (\u223590,000\u00f71000=90)<\/li>\n\n\n\n
          4. 100 times (\u22351,00,000\u00f71000=100)100 times (\u22351,00,000\u00f71000=100)<\/li>\n\n\n\n
          5. 1,53,000(\u2235153\u00d71000=1,53,000)1,53,000(\u2235153\u00d71000=1,53,000)<\/li>\n\n\n\n
          6. 1,00,000\u00f71000=100.1,00,000\u00f71000=100.
            \u2234\u2234 100 thousands make one lakh.<\/li>\n<\/ol>\n\n\n\n
            \n\n\n\n

            Q.12: The Tedious Tens only has a +10 button. How many times should it be pressed to show:<\/p>\n\n\n\n

              \n
            1. Five hundred?<\/li>\n\n\n\n
            2. 780? ________<\/li>\n\n\n\n
            3. 1000? ________<\/li>\n\n\n\n
            4. 3700? ________<\/li>\n\n\n\n
            5. 10,000? ________<\/li>\n\n\n\n
            6. One lakh? ________<\/li>\n\n\n\n
            7. ________? 435 times<\/li>\n<\/ol>\n\n\n\n

              Solution:<\/p>\n\n\n\n

                \n
              1. 50 times (\u2235500\u00f710=50)50 times (\u2235500\u00f710=50)<\/li>\n\n\n\n
              2. 78 times (\u2235780\u00f710=78)78 times (\u2235780\u00f710=78)<\/li>\n\n\n\n
              3. 100 times (\u22351000\u00f710=100)100 times (\u22351000\u00f710=100)<\/li>\n\n\n\n
              4. 370 times (\u22353700\u00f710=370)370 times (\u22353700\u00f710=370)<\/li>\n\n\n\n
              5. 1000 times (\u223510,000\u00f710=1,000)1000 times (\u223510,000\u00f710=1,000)<\/li>\n\n\n\n
              6. 10000 times (\u22351,00,00\u00f710=10,000)10000 times (\u22351,00,00\u00f710=10,000)<\/li>\n\n\n\n
              7. 4350(\u2235435\u00d710=4350)4350(\u2235435\u00d710=4350)<\/li>\n<\/ol>\n\n\n\n
                \n\n\n\n

                Q.13: The Handy Hundreds only has a +100 button. How many times should it be pressed to show:<\/p>\n\n\n\n

                  \n
                1. Four hundred? ________ times<\/li>\n\n\n\n
                2. 3,700? ________<\/li>\n\n\n\n
                3. 10,000? ________<\/li>\n\n\n\n
                4. Fifty three thousand? ________<\/li>\n\n\n\n
                5. 90,000? ________<\/li>\n\n\n\n
                6. 97,600? ________<\/li>\n\n\n\n
                7. 1,00,000? ________<\/li>\n\n\n\n
                8. ________? 582 times<\/li>\n\n\n\n
                9. How many hundreds are required to make ten thousand?<\/li>\n\n\n\n
                10. How many hundreds are required to make one lakh?<\/li>\n\n\n\n
                11. Handy Hundreds says, \u201cThere are some numbers which Tedious Tens and Thoughtful Thousands can\u2019t show but I can.\u201d Is this statement true? Think and explore.<\/li>\n<\/ol>\n\n\n\n

                  Solution:<\/p>\n\n\n\n

                    \n
                  1. 4 times (\u2235400\u00f7100=4)4 times (\u2235400\u00f7100=4)<\/li>\n\n\n\n
                  2. 37 times (\u22353700\u00f7100=37)37 times (\u22353700\u00f7100=37)<\/li>\n\n\n\n
                  3. 100 times (\u223510,000\u00f7100=100)100 times (\u223510,000\u00f7100=100)<\/li>\n\n\n\n
                  4. 530 times (\u223553,000\u00f7100=530)530 times (\u223553,000\u00f7100=530)<\/li>\n\n\n\n
                  5. 900 times (\u223590,000\u00f7100=900)900 times (\u223590,000\u00f7100=900)<\/li>\n\n\n\n
                  6. 976 times (\u223597,600\u00f7100=976)976 times (\u223597,600\u00f7100=976) + 1000 times (\u22351,00,000\u00f7100=1,000)1000 times (\u22351,00,000\u00f7100=1,000)<\/li>\n\n\n\n
                  7. 58,200(\u2235582\u00d7100=58,200)58,200(\u2235582\u00d7100=58,200)<\/li>\n\n\n\n
                  8. 10,000100=100 hundreds 10,000100=100 hundreds 
                    100 hundreds make ten thousand.<\/li>\n\n\n\n
                  9. 1,00,000100=1000 hundreds 1,00,000100=1000 hundreds <\/li>\n\n\n\n
                  10. 100 hundreds make one lakh.<\/li>\n\n\n\n
                  11. Handy Hundreds’ statement is true <\/strong>compared to Thoughtful Thousands because Thoughtful Thousands can\u2019t show multiples of 100 or 10. However, Handy Hundreds’ statement is false <\/strong>compared to Tedious Tens because Tedious Tens can reach any multiple of 100, although it would take many steps.<\/li>\n<\/ol>\n\n\n\n
                    \n\n\n\n

                    Q.14: Creative Chitti is a different kind of calculator. It has the following buttons: +1,+10,+100+1,+10,+100, +1000,+10000,+100000+1000,+10000,+100000 and +1000000. It always has multiple ways of doing things. “How so?”, you might ask. To get the number 321, it presses +10 thirty two times and +1 once. Will it get 321? Alternatively, it can press +100 two times and +10 twelve times and +1 once.
                    <\/p>\n\n\n\n

                    Solution:<\/p>\n\n\n\n

                    First method:<\/strong>
                    Press +10,32+10,32 times \u219232\u00d710=320\u219232\u00d710=320
                    Press +1 once \u21921\u21921
                    On Adding, 320 + 1 = 321
                    Yes, Chitti reaches 321 this way.
                    Second method:<\/strong>
                    Press +100,2+100,2 times \u21922\u00d7100=200\u21922\u00d7100=200
                    Press + 10, 12times \u219212\u00d710=120\u219212\u00d710=120
                    Press +1 once \u21921\u21921
                    On adding, 200+120+1=321200+120+1=321
                    Again, Chitti reaches 321.<\/p>\n\n\n\n

                    \n\n\n\n

                    Q.15: Two of the many different ways to get 5072 are shown below: These two ways can be expressed as:<\/p>\n\n\n\n

                      \n
                    1. (50\u00d7100)+(7\u00d710)+(2\u00d71)=5072(50\u00d7100)+(7\u00d710)+(2\u00d71)=5072<\/li>\n\n\n\n
                    2. (3\u00d71000)+(20\u00d7100)+(72\u00d71)=5072(3\u00d71000)+(20\u00d7100)+(72\u00d71)=5072<\/li>\n<\/ol>\n\n\n\n

                      Find a different way to get 5072 and write an expression for the same.
                      <\/p>\n\n\n\n

                      Solution:<\/p>\n\n\n\n

                      (5\u00d71000)+(0\u00d7100)(5\u00d71000)+(0\u00d7100) +(7\u00d710)+(2\u00d71)=5072+(7\u00d710)+(2\u00d71)=5072<\/p>\n\n\n\n

                      \n\n\n\n

                      Q.16: Think and share situations where it is appropriate to<\/p>\n\n\n\n

                        \n
                      1. round up and<\/li>\n\n\n\n
                      2. round down.<\/li>\n<\/ol>\n\n\n\n

                        Solution:<\/p>\n\n\n\n

                          \n
                        1. Round Up:
                          Buying food for a group or occasion. Buying materials so you don\u2019t run short.<\/li>\n\n\n\n
                        2. Round Down:
                          Shopkeeper saying lesser prices to attract buyers. Estimating fuel left to drive more carefully. Estimating remaining time to a meeting (e.g., saying 10 minutes left when it\u2019s 12 minutes) to create urgency and avoid being late<\/li>\n<\/ol>\n\n\n\n
                          \n\n\n\n

                          Q.17: Think and share situations where it is appropriate to<\/p>\n\n\n\n

                            \n
                          1. either rounding up or rounding down is okay and<\/li>\n\n\n\n
                          2. when exact numbers are needed.<\/li>\n<\/ol>\n\n\n\n

                            Solution:<\/p>\n\n\n\n

                              \n
                            1. Either is Okay:
                              Casual talks. Distance estimation between places.
                              Telling academic results.<\/li>\n\n\n\n
                            2. Exact Numbers Needed:
                              Handling money (bank balance, salary, tax).
                              Doing science experiments or engineering work.
                              Dialling emergency numbers (like 100 for the police)<\/li>\n<\/ol>\n\n\n\n
                              \n\n\n\n

                              Q.18: Write the five nearest neighbours for these numbers:<\/p>\n\n\n\n

                                \n
                              1. 3,87,69,957<\/li>\n\n\n\n
                              2. 29,05,32,481<\/li>\n<\/ol>\n\n\n\n

                                Solution:<\/p>\n\n\n\n

                                  \n
                                1. 3,87,69,957 Nearest thousand 3,87,70,0003,87,70,000 Nearest ten thousand 3,87,70,0003,87,70,000 Nearest lakh 3,88,00,0003,88,00,000 Nearest ten lakh 3,90,00,0003,90,00,000 Nearest crore 4,00,00,0004,00,00,000<\/li>\n\n\n\n
                                2. 29,05,32,481 Nearest thousand 29,05,32,00029,05,32,000 Nearest ten thousand 29,05,30,00029,05,30,000 Nearest lakh 29,05,00,00029,05,00,000 Nearest ten lakh 29,10,00,00029,10,00,000 Nearest crore 29,00,00,00029,00,00,000<\/li>\n<\/ol>\n\n\n\n
                                  \n\n\n\n

                                  Q.19: I have a number for which all five nearest neighbours are 5,00,00,000. What could the number be? How many such numbers are there?<\/p>\n\n\n\n

                                  Solution:<\/p>\n\n\n\n

                                  A number between 4,99,99,500 and 5,00,00,499 (inclusive of the first, exclusive of the second) rounds to 5,00,00,000 at all five levels. There are 1000 such numbers.<\/p>\n\n\n\n

                                  \n\n\n\n

                                  Q.20: From the information given in the table, answer the following questions by approximation:<\/p>\n\n\n\n

                                    \n
                                  1. What is your general observation about this data? Share it with the class.<\/li>\n\n\n\n
                                  2. What is an appropriate title for the above table?<\/li>\n\n\n\n
                                  3. How much is the population of Pune in 2011? Approximately, by how much has it increased compared to 2001?<\/li>\n\n\n\n
                                  4. Which city\u2019s population increased the most between 2001 and 2011?<\/li>\n\n\n\n
                                  5. Are there cities whose population has almost doubled? Which are they?<\/li>\n\n\n\n
                                  6. By what number should we multiply Patna\u2019s population to get a number\/population close to that of Mumbai?<\/li>\n<\/ol>\n\n\n\n
                                    Rank<\/strong><\/td>City<\/strong><\/td>Population (2011)<\/strong><\/td>Population (2001)<\/strong><\/td><\/tr>
                                    1<\/td>Mumbai<\/td>1,24,42,373<\/td>1,19,78,450<\/td><\/tr>
                                    2<\/td>New Delhi<\/td>1,10,07,835<\/td>98,79,172<\/td><\/tr>
                                    3<\/td>Bengaluru<\/td>84,25,970<\/td>43,01,326<\/td><\/tr>
                                    4<\/td>Hyderabad<\/td>68,09,970<\/td>36,37,483<\/td><\/tr>
                                    5<\/td>Ahmedabad<\/td>55,70,585<\/td>35,20,085<\/td><\/tr>
                                    6<\/td>Chennai<\/td>46,81,087<\/td>43,43,645<\/td><\/tr>
                                    7<\/td>Kolkata<\/td>44,86,679<\/td>45,72,876<\/td><\/tr>
                                    8<\/td>Surat<\/td>44,67,797<\/td>24,33,835<\/td><\/tr>
                                    9<\/td>Vadodara<\/td>35,52,371<\/td>16,90,000<\/td><\/tr>
                                    10<\/td>Pune<\/td>31,15,431<\/td>25,38,473<\/td><\/tr>
                                    11<\/td>Jaipur<\/td>30,46,163<\/td>23,22,575<\/td><\/tr>
                                    12<\/td>Lucknow<\/td>28,15,601<\/td>21,85,927<\/td><\/tr>
                                    13<\/td>Kanpur<\/td>27,67,031<\/td>25,51,337<\/td><\/tr>
                                    14<\/td>Nagpur<\/td>24,05,665<\/td>20,52,066<\/td><\/tr>
                                    15<\/td>Indore<\/td>19,60,631<\/td>14,74,968<\/td><\/tr>
                                    16<\/td>Thane<\/td>18,18,872<\/td>12,62,551<\/td><\/tr>
                                    17<\/td>Bhopal<\/td>17,98,218<\/td>14,37,354<\/td><\/tr>
                                    18<\/td>Visakhapatnam<\/td>17,28,128<\/td>13,45,938<\/td><\/tr>
                                    19<\/td>Pimpri-Chinchwad<\/td>17,27,692<\/td>10,12,472<\/td><\/tr>
                                    20<\/td>Patna<\/td>16,84,222<\/td>13,66,444<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

                                    Solution:<\/p>\n\n\n\n

                                      \n
                                    1. Most cities have seen a significant rise in pollution from 2001 to 2011 with a few cities like Surat, Vadodara almost doubling their population. Some cities like Kolkata have shown very little growth.<\/li>\n\n\n\n
                                    2. Population of major Indian cities in 2001 and 2011.<\/li>\n\n\n\n
                                    3. Pune’s population in 2011=31,15,4312011=31,15,431.
                                      Pune’s population in 2001=25,38,4732001=25,38,473.
                                      Increase in population =3,115,431\u22122,538,473=3,115,431\u22122,538,473
                                      =576,958.=576,958.
                                      Approximately, the population increased by about 5.8 lakhs or nearly 6 lakhs.<\/li>\n\n\n\n
                                    4. Population increase of some cities:
                                      Bengaluru: 84,25,970\u221243,01,326=41,24,64484,25,970\u221243,01,326=41,24,644
                                      Hyderabad: 68,09,970\u221236,37,483=31,72,48768,09,970\u221236,37,483=31,72,487
                                      Ahmedabad: 55,70,585\u221235,20,085=20,50,50055,70,585\u221235,20,085=20,50,500
                                      Surat: 44,67,797\u221224,33,835=20,33,96244,67,797\u221224,33,835=20,33,962
                                      Vadodara: 35,52,371\u221216,90,000=18,62,37135,52,371\u221216,90,000=18,62,371
                                      Bengaluru had the highest population increase: 41,24,644.<\/li>\n\n\n\n
                                    5. Yes, several cities nearly doubled their population. They are:\n
                                        \n
                                      1. Bengaluru
                                         2001: 43,01,326 \u2192 2011: 84,25,970 2001: 43,01,326 \u2192 2011: 84,25,970<\/li>\n\n\n\n
                                      2. Hyderabad
                                        2001:36,37,483\u21922011:68,09,9702001:36,37,483\u21922011:68,09,970<\/li>\n\n\n\n
                                      3. Surat
                                        2001:24,33,835\u21922011:44,67,7972001:24,33,835\u21922011:44,67,797<\/li>\n\n\n\n
                                      4. Vadodara
                                        2001:16,90,000\u21922011:35,52,3712001:16,90,000\u21922011:35,52,371<\/li>\n<\/ol>\n<\/li>\n\n\n\n
                                      5. Mumbai (2011): 1,24,42,3731,24,42,373
                                        Patna (2011): 16,84,222
                                         Multiplier =1,24,42,37316,84,222=7.39 Multiplier =1,24,42,37316,84,222=7.39
                                        Therefore, we should multiply Patna\u2019s population by 7.39 to get a number close to that of Mumbai.<\/li>\n<\/ol>\n\n\n\n
                                        \n\n\n\n

                                        Q.21: Using the meaning of multiplication and division, can you explain why multiplying by 5 is the same as dividing by 2 and multiplying by 10?<\/p>\n\n\n\n

                                        Solution:<\/p>\n\n\n\n

                                        Multiplying by 5 is the same as multiplying by 10 and then dividing by 2 because 102=10\u00f722\u00f72=5102=10\u00f722\u00f72=5.<\/p>\n\n\n\n

                                        \n\n\n\n

                                        Q.22: Observe the number of digits in the two numbers being multiplied and their product in each case. Is there any connection between the numbers being multiplied and the number of digits in their product?<\/p>\n\n\n\n

                                        Solution:<\/p>\n\n\n\n

                                        The number of digits in the product becomes twice, one less than twice, or one more than twice compared to the number of digits in the in the multiplied numbers.<\/p>\n\n\n\n

                                        \n\n\n\n

                                        Q.23: Roxie says that the product of two 2-digit numbers can only be a 3- or a 4-digit number. Is she correct?<\/p>\n\n\n\n

                                        Solution:<\/p>\n\n\n\n

                                        Yes, she is correct. Because, product of smallest two 2-digit numbers = 10 \u00d7\u00d7 10 = 100 (3-digit number) And the product of the largest two 3-digit numbers = 99 \u00d7\u00d7 99 = 9801 (4-digit number).<\/p>\n\n\n\n

                                        \n\n\n\n

                                        Q.24: Should we try all possible multiplications with 2-digit numbers to tell whether Roxie\u2019s claim is true? Or is there a better way to find out?<\/p>\n\n\n\n

                                        Solution:<\/p>\n\n\n\n

                                        No, we don\u2019t need to do all possible multiplications, check extremes: 10 \u00d7\u00d7 10 and 99 \u00d7\u00d7 99 give the minimum and maximum digits possible.<\/p>\n\n\n\n

                                        \n\n\n\n

                                        Q.25: Can multiplying a 3-digit number with another 3-digit number give a 4-digit number?<\/p>\n\n\n\n

                                        Solution:<\/p>\n\n\n\n

                                        Product of smallest two 3-digit numbers = 100 \u00d7\u00d7 100 = 10,000 (4-digit number)
                                        Product of largest two 3-digit numbers = 999 \u00d7\u00d7 999 = 9,98,001 (5-digit number)
                                        Therefore, a 4-digit number can\u2019t be obtained by multiplying two 3-digit numbers.<\/p>\n\n\n\n

                                        \n\n\n\n

                                        Q.26: Can multiplying a 4-digit number with a 2-digit number give a 5-digit number?<\/p>\n\n\n\n

                                        Solution:<\/p>\n\n\n\n

                                        Product of smallest 4-difit number and a 2-digit number = 1,000 \u00d7\u00d7 10 = 10,000 (4-digit number)
                                        Product of largest 4-digit number and a 2-digit number = 9,999 \u00d7\u00d7 99 = 9,89,901 (5-digit number)
                                        Yes, it is possible.<\/p>\n\n\n\n

                                        \n\n\n\n

                                        Q.27: Observe the multiplication statements below. Do you notice any patterns? See if this pattern extends for other numbers as well.<\/p>\n\n\n\n

                                        Solution:<\/p>\n\n\n\n

                                        1\u00d71-digit =1 or 2 digits 1\u00d71-digit =1 or 2 digits 
                                        2\u00d71-digit =2 or 3 digits 2\u00d71-digit =2 or 3 digits 
                                        2\u00d72-digit =3 or 4 digits 2\u00d72-digit =3 or 4 digits 
                                        3 \u00d7\u00d7 3-digit = 5 or 6 digits
                                        5 \u00d7\u00d7 5-digit = 9 – 10 digits (Min = 5 + 5 – 1, Max = 5 + 5)
                                        8 \u00d7\u00d7 3-digit = 10 – 11 digits (Min = 8 + 3 – 1, Max = 8 + 3)
                                        12 \u00d7\u00d7 13-digit = 24 – 25 digits (Min = 12 + 13 – 1, Max = 12 + 13)<\/p>\n\n\n\n

                                        \n\n\n\n

                                        Q.28: 1250 \u00d7\u00d7 380 ________ is the number of k\u012brtanas composed by Purandarad\u0101sa according to legends.<\/p>\n\n\n\n

                                        Solution:<\/p>\n\n\n\n

                                         Kirtanas =1250\u00d7380 Kirtanas =1250\u00d7380
                                        =(125\u00d710)\u00d7(38\u00d710)=(125\u00d710)\u00d7(38\u00d710)
                                        =125\u00d738\u00d710\u00d710=125\u00d738\u00d710\u00d710
                                        =4,750\u00d7100=4,750\u00d7100
                                        =4,75,000=4,75,000<\/p>\n\n\n\n

                                        \n\n\n\n

                                        Q.29: 2100 \u00d7\u00d7 70,000 ________ is the approximate distance in kilometers, between the Earth and the Sun.<\/p>\n\n\n\n

                                        Solution:<\/p>\n\n\n\n

                                         Distance =2100\u00d770,000 Distance =2100\u00d770,000
                                        =(21\u00d71,000)\u00d7(7\u00d710,000)=(21\u00d71,000)\u00d7(7\u00d710,000)
                                        =21\u00d77\u00d71,000\u00d710,000=21\u00d77\u00d71,000\u00d710,000
                                        =147\u00d71,00,00,000=147\u00d71,00,00,000
                                        =1,47,00,00,000 km=1,47,00,00,000 km<\/p>\n\n\n\n

                                        \n\n\n\n

                                        Q.30: 6400 \u00d7\u00d7 62,500 ________ is the average number of litres of water the Amazon river discharges into the Atlantic Ocean every second.<\/p>\n\n\n\n

                                        Solution:<\/p>\n\n\n\n

                                         Average =6,400\u00d762,500 Average =6,400\u00d762,500
                                        =(64\u00d7100)\u00d7(625\u00d7100)=(64\u00d7100)\u00d7(625\u00d7100)
                                        =64\u00d7625\u00d7100\u00d7100=64\u00d7625\u00d7100\u00d7100
                                        =40,000\u00d710,000=40,000\u00d710,000
                                        =40,00,00,000 litres =40,00,00,000 litres <\/p>\n\n\n\n

                                        \n\n\n\n

                                        Q.31: 13,95,000 \u00f7\u00f7 150 ________ is the distance (in kms) of the longest single-train journey in the world.<\/p>\n\n\n\n

                                        Solution:<\/p>\n\n\n\n

                                        Distance =13,95,000150=9300 km=13,95,000150=9300 km.<\/p>\n\n\n\n

                                        \n\n\n\n

                                        Q.32: Adult blue whales can weigh more than 10,50,00,000 \u00f7\u00f7 700 ________ kilograms.<\/p>\n\n\n\n

                                        Solution:<\/p>\n\n\n\n

                                        Weight =10,50,00,000700=1,50,000 kg=10,50,00,000700=1,50,000 kg.<\/p>\n\n\n\n

                                        \n\n\n\n

                                        Q.33: 52,00,00,00,000 \u00f7\u00f7 130 ________ was the weight, in tonnes, of global plastic waste generated in the year 2021.<\/p>\n\n\n\n

                                        Solution:<\/p>\n\n\n\n

                                        Weight ((in tonnes)=52,00,00,00,000130=40,00,00,000)=52,00,00,00,000130=40,00,00,000.<\/p>\n\n\n\n

                                        \n\n\n\n

                                        Q.34: The RMS Titanic ship carried about 2500 passengers. Can the population of Mumbai fit into 5000 such ships?<\/p>\n\n\n\n

                                        Solution:<\/p>\n\n\n\n

                                        Passengers in one ship =2500=2500
                                        Passengers in 5000 ships =5000\u00d72500=5000\u00d72500
                                        =1,25,00,000.=1,25,00,000.
                                        Population of Mumbai =1,24,00,00=1,24,00,00
                                        Therefore, the population of Mumbai can easily fit into 500 such ships.<\/p>\n\n\n\n

                                        \n\n\n\n

                                        Q.35: Find out if you can reach the Sun in a lifetime, if you travel 1000 kilometers every day. (Distance between the Sun and the Earth from page 16 calculation = 147,000,000 km)<\/p>\n\n\n\n

                                        Solution:<\/p>\n\n\n\n

                                        Distance between the Sun and the Earth =14,70,00,000 km=14,70,00,000 km
                                        Distance travelled in one day =1000 km=1000 km
                                        Distance travelled in one year (365 days) =365\u00d71000=3,65,000 km=365\u00d71000=3,65,000 km
                                        Time (in years) to reach the Sun =14,70,00,0003,65,000=403=14,70,00,0003,65,000=403 years
                                        Since a man can’t live up to 403 years. So, you can’t reach the Sun in a lifetime.<\/p>\n\n\n\n

                                        \n\n\n\n

                                        Q.36: Make necessary reasonable assumptions and answer the questions below:<\/p>\n\n\n\n

                                          \n
                                        1. If a single sheet of paper weighs 5 grams, could you lift one lakh sheets of paper together at the same time?<\/li>\n\n\n\n
                                        2. If 250 babies are born every minute across the world, will a million babies be born in a day?<\/li>\n\n\n\n
                                        3. Can you count 1 million coins in a day? Assume you can count 1 coin every second.<\/li>\n<\/ol>\n\n\n\n

                                          Solution:<\/p>\n\n\n\n

                                            \n
                                          1. Weight of single sheet =5=5 grams
                                             Weight of 1 lakh sheets =1,00,000\u00d75 Weight of 1 lakh sheets =1,00,000\u00d75
                                            =5,00,000 grams =5,00,0001000=500 kg.=5,00,000 grams =5,00,0001000=500 kg.
                                            Since, a typical person can’t lift 500 kg.
                                            Therefore, you couldn\u2019t lift one lakh sheets of paper.<\/li>\n\n\n\n
                                          2. Babies born in a minute = 250 babies
                                            Babies born in an hour =250\u00d760=15,000=250\u00d760=15,000 babies
                                            Babies born in a day =15,000\u00d724=3,60,000=15,000\u00d724=3,60,000 babies
                                            Since,
                                            3,60,0003,60,000 is less than 1 million (10 lakh).
                                            Therefore, a million babies will not be born in a year.<\/li>\n\n\n\n
                                          3. Coins counted per sec = 1 coin
                                            Coins counted per minute =60=60 coins
                                            Coins counted per hour =60\u00d760=3,600=60\u00d760=3,600 coins
                                            Coins counted per day =3,600\u00d724=86,400=3,600\u00d724=86,400 coins
                                            Since,
                                            84,000 is much less than 1 million (10 lakh).
                                            Therefore, you can’t count 1 million coins in a day.<\/li>\n<\/ol>\n\n\n\n
                                            \n\n\n\n

                                            Q.37: According to the 2011 Census, the population of the town of Chintamani was about 75,000. How much less than one lakh is 75,000?<\/p>\n\n\n\n

                                            Solution:<\/p>\n\n\n\n

                                            Population of the town in 2011=75,0002011=75,000
                                            Since 1,00,000\u221275,000=25,0001,00,000\u221275,000=25,000
                                            75,000 is 25,000 less than one lakh.<\/p>\n\n\n\n

                                            \n\n\n\n

                                            Q.38: The estimated population of Chintamani in the year 2024 is 1,06,000. How much more than one lakh is 1,06,000?<\/p>\n\n\n\n

                                            Solution:<\/p>\n\n\n\n

                                            Population of town in 2024=1,06,0002024=1,06,000
                                            Since, 1,06,000\u22121,00,000=6,0001,06,000\u22121,00,000=6,000
                                            1,06,0001,06,000 is 6,000 more than one lakh.<\/p>\n\n\n\n

                                            \n\n\n\n

                                            Q.39: By how much did the population of Chintamani increase from 2011 to 2024?<\/p>\n\n\n\n

                                            Solution:<\/p>\n\n\n\n

                                            Increase in population from 2011 to 2024 = 1,06,000 – 75,000 = 31,000.<\/p>\n\n\n\n

                                            \n\n\n\n

                                            Q.40: For each number given below, write expressions for at least two different ways to obtain the number through button clicks. Think like Chitti and be creative.<\/p>\n\n\n\n

                                              \n
                                            1. 8300<\/li>\n\n\n\n
                                            2. 40629<\/li>\n\n\n\n
                                            3. 56354<\/li>\n\n\n\n
                                            4. 66666<\/li>\n\n\n\n
                                            5. 367813<\/li>\n<\/ol>\n\n\n\n

                                              Solution:<\/p>\n\n\n\n

                                                \n
                                              1. 8300
                                                (8\u00d71000)+(3\u00d7100)=8300(8\u00d71000)+(3\u00d7100)=8300
                                                (5\u00d71000)+(30\u00d7100)(5\u00d71000)+(30\u00d7100) +(30\u00d710)=8300+(30\u00d710)=8300<\/li>\n\n\n\n
                                              2. 40629
                                                (40\u00d71000)+(6\u00d7100)(40\u00d71000)+(6\u00d7100) +(2\u00d710)+(9\u00d71)=40629+(2\u00d710)+(9\u00d71)=40629
                                                (35\u00d71000)+(56\u00d7100)(35\u00d71000)+(56\u00d7100)+(2\u00d710)+(9\u00d71)=40629+(2\u00d710)+(9\u00d71)=40629<\/li>\n\n\n\n
                                              3. 56354
                                                (5\u00d710000)+(6\u00d71000)+(3\u00d7100)(5\u00d710000)+(6\u00d71000)+(3\u00d7100) +(5\u00d710)+(4\u00d71)=56354+(5\u00d710)+(4\u00d71)=56354
                                                (56\u00d71000)+(3\u00d7100)(56\u00d71000)+(3\u00d7100)+(5\u00d710)+(4\u00d71)=56354+(5\u00d710)+(4\u00d71)=56354<\/li>\n\n\n\n
                                              4. 66666
                                                (6\u00d710000)+(6\u00d71000)+(6\u00d7100)(6\u00d710000)+(6\u00d71000)+(6\u00d7100)+(6\u00d710)+(6\u00d71)=66666+(6\u00d710)+(6\u00d71)=66666
                                                (66\u00d71000)+(6\u00d7100)(66\u00d71000)+(6\u00d7100)+(6\u00d710)+(6\u00d71)=66666+(6\u00d710)+(6\u00d71)=66666<\/li>\n\n\n\n
                                              5. 367813
                                                (3\u00d7100000)+(6\u00d710000)(3\u00d7100000)+(6\u00d710000)+(7\u00d71000)+(8\u00d7100)+(7\u00d71000)+(8\u00d7100)+(1\u00d710)+(3\u00d71)=367813+(1\u00d710)+(3\u00d71)=367813
                                                (30\u00d710000)+(60\u00d71000)(30\u00d710000)+(60\u00d71000)+(70\u00d7100)+(81\u00d710)+(70\u00d7100)+(81\u00d710)+(3\u00d71)=367813+(3\u00d71)=367813<\/li>\n<\/ol>\n\n\n\n
                                                \n\n\n\n

                                                Q.41: Creative Chitti<\/strong> has some questions for you- <\/p>\n\n\n\n

                                                  \n
                                                1. You have to make exactly 30 button presses. What is the largest 3-digit number you can make? What is the smallest 3-digit number you can make?<\/li>\n\n\n\n
                                                2. 997 can be made using 25 clicks. Can you make 997 with a different number of clicks?<\/li>\n<\/ol>\n\n\n\n
                                                  \"\"\/<\/figure>\n\n\n\n

                                                  Solution:<\/p>\n\n\n\n

                                                    \n
                                                  1. Largest 3-digit number:
                                                    (9\u00d7100)+(8\u00d710)+(13\u00d71)=993(9\u00d7100)+(8\u00d710)+(13\u00d71)=993
                                                    Total clicks =9+8+13=30=9+8+13=30.
                                                    Therefore, 993 is the largest 3-digit number made with 30 clicks.
                                                    Smallest 3-digit number:
                                                    (8\u00d710)+(22\u00d71)=102(8\u00d710)+(22\u00d71)=102
                                                    Total clicks =8+22=30=8+22=30.
                                                    Therefore, 102 is the smallest 3-digit number made with 30 clicks.<\/li>\n\n\n\n
                                                  2. (8\u00d7100)+(19\u00d710)(8\u00d7100)+(19\u00d710)+(7\u00d71)=997+(7\u00d71)=997.
                                                    Total clicks =8+19+7=34=8+19+7=34.
                                                    Therefore, 997 can also be obtained in 34 clicks.<\/li>\n<\/ol>\n\n\n\n
                                                    \n\n\n\n

                                                    Q.42: Systematic Sippy is a different kind of calculator. It has the following buttons: +1, +10, +100, +1000, +10000, +100000. It wants to be used as minimally as possible.

                                                    How can we get the numbers (a) 5072, (b) 8300 using as few button clicks as possible?<\/p>\n\n\n\n

                                                    Solution:<\/p>\n\n\n\n

                                                      \n
                                                    1. 5072
                                                      (5\u00d71,000)+(7\u00d710)+(2\u00d71)(5\u00d71,000)+(7\u00d710)+(2\u00d71)
                                                       Total clicks =5+7+2=14 Total clicks =5+7+2=14
                                                      Yes, 5072 can be obtained in 14 button clicks.<\/li>\n\n\n\n
                                                    2. 8300
                                                      (8\u00d71,000)+(3\u00d7100)(8\u00d71,000)+(3\u00d7100)
                                                       Total clicks =8+3=11 Total clicks =8+3=11
                                                      8300 can be obtained in 11 button clicks.<\/li>\n<\/ol>\n\n\n\n
                                                      \n\n\n\n

                                                      Q.43: Is there another way to get 5072 using less than 23 button clicks? Write the expression for the same.
                                                      <\/p>\n\n\n\n

                                                      Solution:<\/p>\n\n\n\n

                                                      (5\u00d71,000)+(7\u00d710)+(2\u00d71)(5\u00d71,000)+(7\u00d710)+(2\u00d71)
                                                       Total clicks =5+7+2=14 Total clicks =5+7+2=14
                                                      Yes, 5072 can be obtained in less than 23 clicks i.e. 14 clicks.<\/p>\n\n\n\n

                                                      \n\n\n\n

                                                      Q.44: For the numbers in the previous exercise, find out how to get each number by making the smallest number of button clicks and write the expression.<\/p>\n\n\n\n

                                                        \n
                                                      1. 8300<\/li>\n\n\n\n
                                                      2. 40629<\/li>\n\n\n\n
                                                      3. 56354<\/li>\n\n\n\n
                                                      4. 66666<\/li>\n\n\n\n
                                                      5. 367813<\/li>\n<\/ol>\n\n\n\n

                                                        Solution:<\/p>\n\n\n\n

                                                          \n
                                                        1. 8300
                                                          (8\u00d71,000)+(3\u00d7100)=8300(8\u00d71,000)+(3\u00d7100)=8300
                                                          8300 can be obtained in 8+3=118+3=11 clicks.<\/li>\n\n\n\n
                                                        2. 40629
                                                          (4\u00d710,000)+(6\u00d7100)+(2\u00d710)+(9\u00d71)=40629(4\u00d710,000)+(6\u00d7100)+(2\u00d710)+(9\u00d71)=40629
                                                          40629 can be obtained in 4+6+2+9=214+6+2+9=21 clicks.<\/li>\n\n\n\n
                                                        3. 56354
                                                          (5\u00d710,000)+(6\u00d71,000)+(5\u00d710,000)+(6\u00d71,000)+(3\u00d7100)+(5\u00d710)+(4\u00d71)=56354(3\u00d7100)+(5\u00d710)+(4\u00d71)=56354
                                                          56354 can be obtained in 5+6+3+5+4=235+6+3+5+4=23 clicks.<\/li>\n\n\n\n
                                                        4. 66666
                                                          (6\u00d710,000)+(6\u00d71,000)+(6\u00d7100)+(6\u00d710)+(6\u00d71)=66666(6\u00d710,000)+(6\u00d71,000)+(6\u00d7100)+(6\u00d710)+(6\u00d71)=66666
                                                          66666 can be obtained in 6+6+6+6+6=306+6+6+6+6=30 clicks.<\/li>\n\n\n\n
                                                        5. 367813
                                                          (3\u00d71,00,000)+(6\u00d710,000)+(3\u00d71,00,000)+(6\u00d710,000)+(7\u00d71,000)+(8\u00d7100)+(1\u00d710)+(3\u00d71)=367813(7\u00d71,000)+(8\u00d7100)+(1\u00d710)+(3\u00d71)=367813
                                                          367813 can be obtained in 3+6+7+8+1+3=283+6+7+8+1+3=28 clicks.<\/li>\n<\/ol>\n\n\n\n
                                                          \n\n\n\n

                                                          Q.45: Do you see any connection between each number and the corresponding smallest number of button clicks?<\/p>\n\n\n\n

                                                          Solution:<\/p>\n\n\n\n

                                                          The smallest number of button clicks for each number is the sum of its digits.<\/p>\n\n\n\n

                                                          \n\n\n\n

                                                          Q.46: If you notice, the expressions for the least button clicks also give the Indian place value notation of the numbers. Think about why this is so.<\/p>\n\n\n\n

                                                          Solution:<\/p>\n\n\n\n

                                                          The Indian place value system helps in identifying and differentiating between numbers easily by grouping them into thousands, lakhs, crores, etc.<\/p>\n\n\n\n

                                                          \n\n\n\n

                                                          Q.47: How many zeros does a thousand lakh have?<\/p>\n\n\n\n

                                                          Solution:<\/p>\n\n\n\n

                                                          Thousand lakh = 1,000 \u00d7\u00d7 1,00,000 = 10,00,00,000 and it has 8 zeros.<\/p>\n\n\n\n

                                                          \n\n\n\n

                                                          Q.48: How many zeros does a hundred thousand have?<\/p>\n\n\n\n

                                                          Solution:<\/p>\n\n\n\n

                                                          Hundred thousand = 100 \u00d7\u00d7 1,000 = 1,00,000 and it has 5 zeros.<\/p>\n\n\n\n

                                                          \n\n\n\n

                                                          Q.49: Read the following numbers in Indian place value notation and write their number names in both the Indian and American systems:<\/p>\n\n\n\n

                                                            \n
                                                          1. 4050678<\/li>\n\n\n\n
                                                          2. 48121620<\/li>\n\n\n\n
                                                          3. 20022002<\/li>\n<\/ol>\n\n\n\n

                                                            Solution:<\/p>\n\n\n\n

                                                              \n
                                                            1. 40,50,67840,50,678
                                                              Forty lakh fifty thousand six hundred and seventy-eight.
                                                              Four million fifty thousand six hundred and seventy-eight.<\/li>\n\n\n\n
                                                            2. 48121620
                                                              Four crore eighty-one lakh twenty-one thousand six hundred twenty.
                                                              Forty-eight million one hundred twenty-one thousand six hundred twenty.<\/li>\n\n\n\n
                                                            3. 20022002
                                                              Two crore twenty-two thousand and two.
                                                              Twenty million twenty-two thousand and two.<\/li>\n<\/ol>\n\n\n\n
                                                              \n\n\n\n

                                                              Q.50: Read the following numbers in Indian place value notation and write their number names in both the Indian and American systems:<\/p>\n\n\n\n

                                                                \n
                                                              1. 246813579<\/li>\n\n\n\n
                                                              2. 345000543<\/li>\n\n\n\n
                                                              3. 1020304050<\/li>\n<\/ol>\n\n\n\n

                                                                Solution:<\/p>\n\n\n\n

                                                                  \n
                                                                1. 246813579
                                                                  Twenty four crore sixty eight lakh thirteen thousand five hundred and seventy nine.
                                                                  Two hundred forty-six million eight hundred thirteen thousand five hundred seventy nine.<\/li>\n\n\n\n
                                                                2. 345000543
                                                                  Thirty-four crore fifty lakh five hundred and forty-three.
                                                                  Three hundred forty-five million five hundred forty-three.<\/li>\n\n\n\n
                                                                3. 1020304050
                                                                  One arab two crore three lakh four thousand and fifty.
                                                                  One billion, twenty million three hundred four thousand and fifty.<\/li>\n<\/ol>\n\n\n\n
                                                                  \n\n\n\n

                                                                  Q.51: Write the following numbers in Indian place value notation:<\/p>\n\n\n\n

                                                                    \n
                                                                  1. One crore one lakh one thousand ten<\/li>\n\n\n\n
                                                                  2. One billion one million one thousand one<\/li>\n\n\n\n
                                                                  3. Ten crore twenty lakh thirty thousand forty<\/li>\n\n\n\n
                                                                  4. Nine billion eighty million seven hundred thousand six hundred<\/li>\n<\/ol>\n\n\n\n

                                                                    Solution:<\/p>\n\n\n\n

                                                                      \n
                                                                    1. 1,01,01,010.<\/li>\n\n\n\n
                                                                    2. 1,001,001,001.<\/li>\n\n\n\n
                                                                    3. 10,20,30,040.<\/li>\n\n\n\n
                                                                    4. 9,080,700,600.<\/li>\n<\/ol>\n\n\n\n
                                                                      \n\n\n\n

                                                                      Q.52: Compare and write ‘<<‘, ‘>>’ or ‘==’:<\/p>\n\n\n\n

                                                                        \n
                                                                      1. 30 thousand ________ 3 lakhs<\/li>\n\n\n\n
                                                                      2. 500 lakhs ________ 5 million<\/li>\n<\/ol>\n\n\n\n

                                                                        Solution:<\/p>\n\n\n\n

                                                                          \n
                                                                        1. 30,000<3,00,00030,000<3,00,000
                                                                          \u223430\u223430 thousand <3<3 lakhs.<\/li>\n\n\n\n
                                                                        2. 5,00,00,000>5,000,0005,00,00,000>5,000,000
                                                                          \u2234500\u2234500 lakhs >5>5 million.<\/li>\n<\/ol>\n\n\n\n
                                                                          \n\n\n\n

                                                                          Q.53: Compare and write ‘<<‘, ‘>>’ or ‘==’:<\/p>\n\n\n\n

                                                                            \n
                                                                          1. 800 thousand ________ 8 million<\/li>\n\n\n\n
                                                                          2. 640 crore ________ 60 billion<\/li>\n<\/ol>\n\n\n\n

                                                                            Solution:<\/p>\n\n\n\n

                                                                              \n
                                                                            1. 8,00,000<5,000,0008,00,000<5,000,000
                                                                              \u2234800\u2234800 thousand <8<8 million.<\/li>\n\n\n\n
                                                                            2. 6,40,00,00,000<60,000,000,0006,40,00,00,000<60,000,000,000
                                                                              \u2234640\u2234640 crore <60<60 billion.<\/li>\n<\/ol>\n\n\n\n
                                                                              \n\n\n\n

                                                                              Q.54: Find quick ways to calculate these products:<\/p>\n\n\n\n

                                                                                \n
                                                                              1. 2\u00d71768\u00d7502\u00d71768\u00d750<\/li>\n\n\n\n
                                                                              2. 72\u00d7125[ Hint: 125=10008]72\u00d7125[ Hint: 125=10008]<\/li>\n\n\n\n
                                                                              3. 125\u00d740\u00d78\u00d725125\u00d740\u00d78\u00d725<\/li>\n<\/ol>\n\n\n\n

                                                                                Solution:<\/p>\n\n\n\n

                                                                                  \n
                                                                                1. 2\u00d71768\u00d750=2\u00d750\u00d717682\u00d71768\u00d750=2\u00d750\u00d71768
                                                                                  =100\u00d71768=100\u00d71768
                                                                                  =17680=17680<\/li>\n\n\n\n
                                                                                2. 72\u00d7125=72\u00d71000872\u00d7125=72\u00d710008
                                                                                  =9\u00d71000=9\u00d71000
                                                                                  =9000.=9000.<\/li>\n\n\n\n
                                                                                3. 125\u00d740\u00d78\u00d725=125\u00d78\u00d740\u00d725125\u00d740\u00d78\u00d725=125\u00d78\u00d740\u00d725
                                                                                  =1000\u00d71000=1000\u00d71000
                                                                                  =10,00,000.=10,00,000.<\/li>\n<\/ol>\n\n\n\n
                                                                                  \n\n\n\n

                                                                                  Q.55: Calculate these products quickly.<\/p>\n\n\n\n

                                                                                    \n
                                                                                  1. 25 \u00d7\u00d7 12 = ________<\/li>\n\n\n\n
                                                                                  2. 25 \u00d7\u00d7 240 = ________<\/li>\n\n\n\n
                                                                                  3. 250 \u00d7\u00d7 120 = ________<\/li>\n\n\n\n
                                                                                  4. 2500 \u00d7\u00d7 12 = ________<\/li>\n\n\n\n
                                                                                  5. ________ \u00d7\u00d7 ________ = 120000000<\/li>\n<\/ol>\n\n\n\n

                                                                                    Solution:<\/p>\n\n\n\n

                                                                                      \n
                                                                                    1. 25\u00d712=1004\u00d71225\u00d712=1004\u00d712
                                                                                      =100\u00d73=100\u00d73
                                                                                      =300=300<\/li>\n\n\n\n
                                                                                    2. 25\u00d7240=1004\u00d724025\u00d7240=1004\u00d7240
                                                                                      =100\u00d760=100\u00d760
                                                                                      =6000.=6000.<\/li>\n\n\n\n
                                                                                    3. 250\u00d7120=1,0004\u00d7120250\u00d7120=1,0004\u00d7120
                                                                                      =1000\u00d730=1000\u00d730
                                                                                      =30000=30000<\/li>\n\n\n\n
                                                                                    4. 2500\u00d712=10,0004\u00d7122500\u00d712=10,0004\u00d712
                                                                                      =10,000\u00d73=10,000\u00d73
                                                                                      =30,000.=30,000.<\/li>\n\n\n\n
                                                                                    5. 4800\u00d725000=12,00,00,0004800\u00d725000=12,00,00,000
                                                                                      4800\u00d71,00,0004=12,00,00,0004800\u00d71,00,0004=12,00,00,000
                                                                                      1200\u00d71,00,000=12,00,00,000.1200\u00d71,00,000=12,00,00,000.<\/li>\n<\/ol>\n\n\n\n
                                                                                      \n\n\n\n

                                                                                      Q.56: Using all digits from 0 – 9 exactly once (the first digit cannot be 0) to create a 10-digit number, write the –<\/p>\n\n\n\n

                                                                                        \n
                                                                                      1. Largest multiple of 5<\/li>\n\n\n\n
                                                                                      2. Smallest even number<\/li>\n<\/ol>\n\n\n\n

                                                                                        Solution:<\/p>\n\n\n\n

                                                                                          \n
                                                                                        1. Arranging digits in decreasing order = 9, 8, 7, 6, 5, 4, 3, 2, 1, 0
                                                                                          All multiples of 5 can end only in 5 or 0.
                                                                                          \u2234\u2234 Largest multiple of 5 = 9876543210.<\/li>\n\n\n\n
                                                                                        2. Arranging digits in ascending order = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
                                                                                          Since, number can\u2019t start with zero. So, the smallest number = 1023456789
                                                                                          Swapping the last two digits to make the above number even.
                                                                                          \u2234\u2234 Smallest even number = 1023456798.<\/li>\n<\/ol>\n\n\n\n
                                                                                          \n\n\n\n

                                                                                          Q.57: The number 10,30,285 in words is Ten lakhs thirty thousand two hundred eighty five, which has 43 letters. Give a 7-digit number name which has the maximum number of letters.<\/p>\n\n\n\n

                                                                                          Solution:<\/p>\n\n\n\n

                                                                                          Using 7 and 8 to make such a number since both numbers contain 5 letters when written in words.
                                                                                          77,77,777=77,77,777= Seventy-seven lakh seventy-seven thousand seven hundred seventy-seven.
                                                                                          Letters in 77,77,777=6077,77,777=60.
                                                                                          88,88,88888,88,888 = Eighty – eight lakh eighty-eight thousand eight hundred eighty-eight.
                                                                                          Letters in 88,88,888=5788,88,888=57.
                                                                                          Therefore, 77,77,777 has the maximum number of letters in its number name.<\/p>\n\n\n\n

                                                                                          \n\n\n\n

                                                                                          Q.58: Write a 9-digit number where exchanging any two digits results in a bigger number. How many such numbers exist?<\/p>\n\n\n\n

                                                                                          Solution:<\/p>\n\n\n\n

                                                                                          A 9-digit number where exchanging any two digits results in a bigger number = 987654321. Only one such number exists.<\/p>\n\n\n\n

                                                                                          \n\n\n\n

                                                                                          Q.59: Strike out 10 digits from the number 12345123451234512345 so that the remaining number is as large as possible.<\/p>\n\n\n\n

                                                                                          Solution:<\/p>\n\n\n\n

                                                                                          Striking out smaller numbers 1,2,3,4 from the given number, we get 5534512345.<\/p>\n\n\n\n

                                                                                          \n\n\n\n

                                                                                          Q.60: The words \u2018zero\u2019 and \u2018one\u2019 share letters \u2018e\u2019 and \u2018o\u2019. The words \u2018one\u2019 and \u2018two\u2019 share a letter \u2018o\u2019, and the words \u2018two\u2019 and \u2018three\u2019 also share a letter \u2018t\u2019. How far do you have to count to find two consecutive numbers which do not share an English letter in common?<\/p>\n\n\n\n

                                                                                          Solution:<\/p>\n\n\n\n

                                                                                          Let’s check:
                                                                                          one & two share o
                                                                                          two & three share t, e
                                                                                          three & four share rr
                                                                                          four & five share f
                                                                                          five & six share i
                                                                                          six & seven share s
                                                                                          seven & eight share e
                                                                                          eight & nine share e, i, n
                                                                                          nine & ten share n, e
                                                                                          It shows that all consecutive numbers have at least one common letter.
                                                                                          So, there is no such pair of consecutive numbers that do not share an English letter in common.<\/p>\n\n\n\n

                                                                                          \n\n\n\n

                                                                                          Q.61: Suppose you write down all the numbers 1, 2, 3, 4, …, 9, 10, 11, … The tenth digit you write is \u20181\u2019 and the eleventh digit is \u20180\u2019, as part of the number 10.<\/p>\n\n\n\n

                                                                                            \n
                                                                                          1. What would the 1000th digit be? At which number would it occur?<\/li>\n\n\n\n
                                                                                          2. What number would contain the millionth digit?<\/li>\n\n\n\n
                                                                                          3. When would you have written the digit \u20185\u2019 for the 5000th time?<\/li>\n<\/ol>\n\n\n\n

                                                                                            Solution:<\/p>\n\n\n\n

                                                                                              \n
                                                                                            1. Digits from 1 to 9 = 9 digits
                                                                                              Digits from 10 to 99=9099=90 numbers \u00d72=180\u00d72=180 digits
                                                                                              Total digits from 1 to 99=18999=189 digits
                                                                                              Remaining digits to reach 1000th digit =1000\u2212189=811=1000\u2212189=811
                                                                                              Numbers with 33 -digit numbers =811\/3=270=811\/3=270 full numbers +1 digit left over.
                                                                                              The first 3 -digit number is 100
                                                                                              270th 3 digit number is 100+270\u22121=369100+270\u22121=369
                                                                                              The next number is 370 .
                                                                                              The first digit of 370, which is 3, is the 1000th digit.<\/li>\n<\/ol>\n\n\n\n
                                                                                              \n\n\n\n

                                                                                              Q.62: A calculator has only \u2018+10,000\u2019 and \u2018+100\u2019 buttons. Write an expression describing the number of button clicks to be made for the following numbers:<\/p>\n\n\n\n

                                                                                                \n
                                                                                              1. 20,800<\/li>\n\n\n\n
                                                                                              2. 92,100<\/li>\n\n\n\n
                                                                                              3. 1,20,500<\/li>\n\n\n\n
                                                                                              4. 65,30,000<\/li>\n\n\n\n
                                                                                              5. 70,25,700<\/li>\n<\/ol>\n\n\n\n

                                                                                                Solution:<\/p>\n\n\n\n

                                                                                                  \n
                                                                                                1. 20,800=(2\u00d710,000)+(8\u00d7100)20,800=(2\u00d710,000)+(8\u00d7100)
                                                                                                  Total clicks =2+8=10=2+8=10 clicks.<\/li>\n\n\n\n
                                                                                                2. 92,100=(9\u00d710,000)+(21\u00d7100)92,100=(9\u00d710,000)+(21\u00d7100)
                                                                                                  Total clicks =9+21=30=9+21=30 clicks.<\/li>\n\n\n\n
                                                                                                3. 1,20,000=(12\u00d710,000)1,20,000=(12\u00d710,000)
                                                                                                  Total clicks =12=12 clicks.<\/li>\n\n\n\n
                                                                                                4. 65,30,000=(653\u00d710,000)65,30,000=(653\u00d710,000)
                                                                                                  Total clicks =653=653 clicks.<\/li>\n\n\n\n
                                                                                                5. 70,25,700=(702\u00d710,000)+(57\u00d7100)70,25,700=(702\u00d710,000)+(57\u00d7100)
                                                                                                  Total clicks = 759 clicks.<\/li>\n<\/ol>\n\n\n\n
                                                                                                  \n\n\n\n

                                                                                                  Q.63: How many lakhs make a billion?<\/p>\n\n\n\n

                                                                                                  Solution:<\/p>\n\n\n\n

                                                                                                  1 lakh =1,00,0001 lakh =1,00,000
                                                                                                  1 billion =1,000,000,0001 billion =1,000,000,000
                                                                                                  Number of lakhs making a billion =1,000,000,0001,00,000=10,000.=1,000,000,0001,00,000=10,000.<\/p>\n\n\n\n

                                                                                                  \n\n\n\n

                                                                                                  Q.64: You are given two sets of number cards numbered from 1 – 9. Place a number card in each box below to get the<\/p>\n\n\n\n

                                                                                                    \n
                                                                                                  1. largest possible sum<\/li>\n\n\n\n
                                                                                                  2. smallest possible difference of the two resulting numbers.<\/li>\n<\/ol>\n\n\n\n
                                                                                                    \"\"\/<\/figure>\n\n\n\n

                                                                                                    Solution:<\/p>\n\n\n\n

                                                                                                      \n

                                                                                                    1. To get the largest possible sum, both the 7-digit and 5-digit numbers need to be the largest.
                                                                                                      7-digit number = 98,76,543
                                                                                                      5-digit number = 98,765
                                                                                                      Sum = 98,76,543 + 98,765 = 99,75,308.<\/li>\n\n\n\n

                                                                                                    2. To get the smallest possible difference, the 7-digit number needs to be the smallest and the 5-digit number needs to be the largest.
                                                                                                      7-digit number = 12,34,567 5-digit number = 98,765
                                                                                                      Difference = 12,34,567 – 98,765 = 11,35,802<\/li>\n<\/ol>\n\n\n\n
                                                                                                      \n\n\n\n

                                                                                                      Q.65: You are given some number cards; 4000, 13000, 300, 70000, 150000, 20, 5. Using the cards get as close as you can to the numbers below using any operation you want. Each card can be used only once for making a particular number.<\/p>\n\n\n\n

                                                                                                        \n
                                                                                                      1. 1,10,000: Closest I could make is 4000 \u00d7\u00d7 (20 + 5) + 13000 = 1,13,000<\/li>\n\n\n\n
                                                                                                      2. 2,00,000:<\/li>\n\n\n\n
                                                                                                      3. 5,80,000:<\/li>\n\n\n\n
                                                                                                      4. 12,45,000:<\/li>\n\n\n\n
                                                                                                      5. 20,90,800:<\/li>\n<\/ol>\n\n\n\n

                                                                                                        Solution:<\/p>\n\n\n\n

                                                                                                          \n
                                                                                                        1. 1,10,0001,10,000:
                                                                                                          Closest estimate =70,000+(4,000\u00d75)+13,000=1,03,000=70,000+(4,000\u00d75)+13,000=1,03,000.<\/li>\n\n\n\n
                                                                                                        2. 2,00,000:
                                                                                                          Closest estimate =1,50,000+70,000\u2212(4,000\u00d75)=2,00,000=1,50,000+70,000\u2212(4,000\u00d75)=2,00,000.<\/li>\n\n\n\n
                                                                                                        3. 5,80,000:
                                                                                                          Closest estimate =(1,50,000\u00d74)\u2212(4000\u00d75)=5,80,000=(1,50,000\u00d74)\u2212(4000\u00d75)=5,80,000.<\/li>\n\n\n\n
                                                                                                        4. 12,45,00012,45,000:
                                                                                                          Closest estimate =(1,50,000\u00d78)+(13,000\u00d74)=(1,50,000\u00d78)+(13,000\u00d74)\u22124,000=12,48,000\u22124,000=12,48,000<\/li>\n\n\n\n
                                                                                                        5. 20,90,800:
                                                                                                          Closest estimate =(1,50,000\u00d714)+4000=(1,50,000\u00d714)+4000\u221213000=20,91,000\u221213000=20,91,000.<\/li>\n<\/ol>\n\n\n\n
                                                                                                          \n\n\n\n

                                                                                                          Q.66: Find out how many coins should be stacked to match the height of the Statue of Unity. Assume each coin is 1 mm thick.<\/p>\n\n\n\n

                                                                                                          Solution:<\/p>\n\n\n\n

                                                                                                           Height of each coin = 1 mm Height of each coin = 1 mm
                                                                                                           Height of Statue of Unity =  Height of Statue of Unity = 180 m=180\u00d7100\u00d710 mm180 m=180\u00d7100\u00d710 mm
                                                                                                          =1,80,000 mm.=1,80,000 mm.
                                                                                                           Number of coins to be stacked  Number of coins to be stacked  =1,80,000 mm1 mm=1,80,000 mm1 mm
                                                                                                          =1,80,000 coins. =1,80,000 coins. <\/p>\n\n\n\n

                                                                                                          \n\n\n\n

                                                                                                          Q.67: Grey-headed albatrosses have a roughly 7-feet wide wingspan. They are known to migrate across several oceans. Albatrosses can cover about 900 – 1000 km in a day. One of the longest single trips recorded is about 12,000 km. How many days would such a trip take to cross the Pacific Ocean approximately?<\/p>\n\n\n\n

                                                                                                          Solution:<\/p>\n\n\n\n

                                                                                                          Total trip = 12,000 km
                                                                                                          Distance covered in a day =900\u22121000 km=900\u22121000 km
                                                                                                          Estimated Number of days if it flies 900 km\/900 km\/ day =12,000900=13.3=12,000900=13.3 days
                                                                                                          Estimated Number of days if it flies 1000 km\/1000 km\/ day =12,0001,000=12=12,0001,000=12 days
                                                                                                          \u2234\u2234 It would take approximately 12 to 14 days for a grey-headed albatross to complete a 12,000 km12,000 km trip across the Pacific Ocean.<\/p>\n\n\n\n

                                                                                                          \n\n\n\n

                                                                                                          Q.68: A bar-tailed godwit holds the record for the longest recorded non-stop flight. It travelled 13,560 km from Alaska to Australia without stopping. Its journey started on 13 October 2022 and continued for about 11 days. Find out the approximate distance it covered every day. Find out the approximate distance it covered every hour.<\/p>\n\n\n\n

                                                                                                          Solution:<\/p>\n\n\n\n

                                                                                                          Total distance =13,560 km=13,560 km
                                                                                                          Duration = 11 days
                                                                                                          Each day =24=24 hours
                                                                                                          Duration in hours =11\u00d724=264=11\u00d724=264 hours
                                                                                                          Distance covered per day =13,560 km11 days =1232.73 km=13,560 km11 days =1232.73 km or 1233 km.
                                                                                                          Distance covered per hour =13,560 km264 hours =51.36 km=13,560 km264 hours =51.36 km or 51 km.<\/p>\n\n\n\n

                                                                                                          \n\n\n\n

                                                                                                          Q.69: Bald eagles are known to fly as high as 4500 – 6000 m above the ground level. Mount Everest is about 8850 m high. Aeroplanes can fly as high as 10,000 – 12,800 m. How many times bigger are these heights compared to Somu\u2019s building?<\/p>\n\n\n\n

                                                                                                          Solution:<\/p>\n\n\n\n

                                                                                                          Height of Somu\u2019s building = 40 m<\/p>\n\n\n\n

                                                                                                            \n
                                                                                                          1. Bald eagles\u2019 flight height = 4500 – 6000 m\n