{"id":4981,"date":"2016-05-19T11:49:00","date_gmt":"2016-05-19T06:19:00","guid":{"rendered":"http:\/\/mycbseguide.com\/blog\/ncert-solutions-class-9-maths-exercise-1-3\/"},"modified":"2018-06-16T17:16:56","modified_gmt":"2018-06-16T11:46:56","slug":"ncert-solutions-for-class-9-maths-exercise-1-3","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-1-3\/","title":{"rendered":"NCERT Solutions for Class 9 Maths Exercise 1.3"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_76 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-toggle-hide-by-default' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-1-3\/#NCERT_Solutions_for_Class_9_Maths_Number_Systems\" >NCERT Solutions for Class 9 Maths Number Systems<\/a><ul class='ez-toc-list-level-6' ><li class='ez-toc-heading-level-6'><ul class='ez-toc-list-level-6' ><li class='ez-toc-heading-level-6'><ul class='ez-toc-list-level-6' ><li class='ez-toc-heading-level-6'><ul class='ez-toc-list-level-6' ><li class='ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-1-3\/#1_Write_the_following_in_decimal_form_and_say_what_kind_of_decimal_expansion_each_has\" >1. Write the following in decimal form and say what kind of decimal expansion each has:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-1-3\/#On_dividing_36_by_100_we_get\" >On dividing 36 by 100, we get<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-1-3\/#On_dividing_1_by_11_we_get\" >On dividing 1 by 11, we get<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-1-3\/#On_dividing_33_by_8_we_get\" >On dividing 33 by 8, we get<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-1-3\/#On_dividing_3_by_13_we_get\" >On dividing 3 by 13, we get<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-1-3\/#We_can_observe_that_while_dividing_2_by_11_first_we_got_the_remainder_as_2_and_then_9_which_will_continue_to_be_2_and_9_alternately\" >We can observe that while dividing 2 by 11, first we got the remainder as 2 and then 9, which will continue to be 2 and 9 alternately.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-1-3\/#2_You_know_that_Can_you_predict_what_the_decimal_expansions_ofare_without_actually_doing_the_long_division_If_so_how\" >2. You know that. Can you predict what the decimal expansions ofare, without actually doing the long division? If so, how?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-1-3\/#On_substituting_value_of_as_we_get\" >On substituting value of as, we get<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-1-3\/#3_Express_the_following_in_the_form_where_p_and_q_are_integers_and_q0\" >3. Express the following in the form, where p and q are integers and q0.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-1-3\/#We_can_also_writeas_or\" >We can also writeas or.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-1-3\/#We_can_also_writeas_or-2\" >We can also writeas or.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-1-3\/#4_Express_in_the_form_Are_you_surprised_by_your_answer_Discuss_why_the_answer_makes_sense_with_your_teacher_and_classmates\" >4. Express in the form. Are you surprised by your answer? Discuss why the answer makes sense with your teacher and classmates.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-1-3\/#5_What_can_the_maximum_number_of_digits_be_in_the_recurring_block_of_digits_in_the_decimal_expansion_of_Perform_the_division_to_check_your_answer\" >5. What can the maximum number of digits be in the recurring block of digits in the decimal expansion of? Perform the division to check your answer.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-1-3\/#6_Look_at_several_examples_of_rational_numbers_in_the_form_q_%EF%82%B9%EF%80%A00_where_p_and_q_are_integers_with_no_common_factors_other_than_1_and_having_terminating_decimal_representations_expansions_Can_you_guess_what_property_q_must_satisfy\" >6. Look at several examples of rational numbers in the form (q \uf0b9\uf0200), where p and q are integers with no common factors other than 1 and having terminating decimal representations (expansions). Can you guess what property q must satisfy?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-1-3\/#7_Write_three_numbers_whose_decimal_expansions_are_non-terminating_non-recurring\" >7. Write three numbers whose decimal expansions are non-terminating non-recurring.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-1-3\/#8_Find_three_different_irrational_numbers_between_the_rational_numbersand\" >8. Find three different irrational numbers between the rational numbersand.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-18\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-1-3\/#9_Classify_the_following_numbers_as_rational_or_irrational\" >9. Classify the following numbers as rational or irrational:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-19\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-1-3\/#iv_7478478%E2%80%A6\" >(iv) 7.478478\u2026.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-20\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-1-3\/#We_know_thatcan_also_be_written_as\" >We know thatcan also be written as.<\/a><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-21\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-1-3\/#NCERT_Solutions_for_Class_9_Maths_Exercise_13\" >NCERT Solutions for Class 9 Maths Exercise 1.3<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-22\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-1-3\/#CBSE_app_for_Class_9\" >CBSE app for Class 9<\/a><\/li><\/ul><\/nav><\/div>\n<p>NCERT Solutions for Class 9 Maths Exercise 1.3 book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 9 Maths chapter wise NCERT solution for Maths Book for all the chapters can be downloaded from our website and myCBSEguide mobile app for free.<\/p>\n<p style=\"text-align: center;\"><strong>NCERT solutions for Class 9 Maths\u00a0Number Systems\u00a0<a class=\"button\" href=\"https:\/\/mycbseguide.com\/downloads\/cbse-class-09-mathematics-number-systems\/1235\/ncert-solutions\/5\/\">Download as PDF<\/a><\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/media-mycbseguide.s3.ap-south-1.amazonaws.com\/images\/blog\/09_Class_Maths_Book.jpg\" alt=\"NCERT Solutions for Class 9 Maths Exercise 1.3\" width=\"200\" height=\"258\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_for_Class_9_Maths_Number_Systems\"><\/span>NCERT Solutions for Class 9 Maths Number Systems<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"1_Write_the_following_in_decimal_form_and_say_what_kind_of_decimal_expansion_each_has\"><\/span><strong>1. Write the following in decimal form and say what kind of decimal expansion each has: <img decoding=\"async\" style=\"height: 28px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image001.png\" \/> <\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>(i) <img decoding=\"async\" style=\"height: 41px; width: 29px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image002.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) <img decoding=\"async\" style=\"height: 41px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image003.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iii) <img decoding=\"async\" style=\"height: 41px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image004.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iv) <img decoding=\"async\" style=\"height: 41px; width: 21px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image005.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(v) <img decoding=\"async\" style=\"height: 41px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image006.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(vi) <img decoding=\"async\" style=\"height: 41px; width: 32px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image007.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. (i)<\/strong> <img decoding=\"async\" style=\"height: 41px; width: 29px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image002.png\" \/><\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"On_dividing_36_by_100_we_get\"><\/span>On dividing 36 by 100, we get<span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 184px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image008.png\" \/><\/p>\n<p style=\"text-align: justify;\">Therefore, we conclude that<img decoding=\"async\" style=\"height: 41px; width: 73px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image009.png\" \/>, which is a terminating decimal.<\/p>\n<p style=\"text-align: justify;\"><strong>(ii)<\/strong> <img decoding=\"async\" style=\"height: 41px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image003.png\" \/><\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"On_dividing_1_by_11_we_get\"><\/span>On dividing 1 by 11, we get<span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 280px; width: 117px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image010.png\" \/><\/p>\n<p style=\"text-align: justify;\">We can observe that while dividing 1 by 11, we got the remainder as 1, which will continue to be 1.<\/p>\n<p style=\"text-align: justify;\">Therefore, we conclude that<img decoding=\"async\" style=\"height: 41px; width: 183px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image011.png\" \/>, which is a non-terminating decimal and recurring decimal.<\/p>\n<p style=\"text-align: justify;\"><strong>(iii)<\/strong> <img decoding=\"async\" style=\"height: 41px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image004.png\" \/><img decoding=\"async\" style=\"height: 41px; width: 35px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image012.png\" \/><\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"On_dividing_33_by_8_we_get\"><\/span>On dividing 33 by 8, we get<span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 243px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image013.png\" \/><\/p>\n<p style=\"text-align: justify;\">We can observe that while dividing 33 by 8, we got the remainder as 0.<\/p>\n<p style=\"text-align: justify;\">Therefore, we conclude that<img decoding=\"async\" style=\"height: 41px; width: 111px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image014.png\" \/>, which is a terminating decimal.<\/p>\n<p style=\"text-align: justify;\"><strong>(iv)<\/strong> <img decoding=\"async\" style=\"height: 41px; width: 21px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image005.png\" \/><\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"On_dividing_3_by_13_we_get\"><\/span>On dividing 3 by 13, we get<span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 376px; width: 129px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image015.png\" \/><\/p>\n<p style=\"text-align: justify;\">We can observe that while dividing 3 by 13 we got the remainder as 3, which will continue to be 3 after carrying out 6 continuous divisions.<\/p>\n<p style=\"text-align: justify;\">Therefore, we conclude that<img decoding=\"async\" style=\"height: 41px; width: 232px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image016.png\" \/>, which is a non-terminating decimal and recurring decimal.<\/p>\n<p style=\"text-align: justify;\"><strong>(v)<\/strong> <img decoding=\"async\" style=\"height: 41px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image006.png\" \/><\/p>\n<p style=\"text-align: justify;\">On dividing 2 by 11, we get<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 280px; width: 116px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image017.png\" \/><\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"We_can_observe_that_while_dividing_2_by_11_first_we_got_the_remainder_as_2_and_then_9_which_will_continue_to_be_2_and_9_alternately\"><\/span>We can observe that while dividing 2 by 11, first we got the remainder as 2 and then 9, which will continue to be 2 and 9 alternately.<span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\">Therefore, we conclude that<img decoding=\"async\" style=\"height: 41px; width: 181px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image018.png\" \/>, which is a non-terminating decimal and recurring decimal.<\/p>\n<p style=\"text-align: justify;\"><strong>(vi)<\/strong> <img decoding=\"async\" style=\"height: 41px; width: 32px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image007.png\" \/><\/p>\n<p style=\"text-align: justify;\">On dividing 329 by 400, we get<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 285px; width: 87px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image019.png\" \/><\/p>\n<p style=\"text-align: justify;\">We can observe that while dividing 329 by 400, we got the remainder as 0.<\/p>\n<p style=\"text-align: justify;\">Therefore, we conclude that<img decoding=\"async\" style=\"height: 41px; width: 91px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image020.png\" \/>, which is a terminating decimal.<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 1.3<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"2_You_know_that_Can_you_predict_what_the_decimal_expansions_ofare_without_actually_doing_the_long_division_If_so_how\"><\/span><strong>2. You know that<img decoding=\"async\" style=\"height: 41px; width: 111px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image021.png\" \/>. Can you predict what the decimal expansions of<img decoding=\"async\" style=\"height: 41px; width: 88px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image022.png\" \/>are, without actually doing the long division? If so, how?<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>[Hint: Study the remainders while finding the value of <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image023.png\" \/>carefully.]<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>We are given that<img decoding=\"async\" style=\"height: 41px; width: 220px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image024.png\" \/>.<\/p>\n<p style=\"text-align: justify;\">We need to find the values of<img decoding=\"async\" style=\"height: 41px; width: 117px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image025.png\" \/>, without performing long division.<\/p>\n<p style=\"text-align: justify;\">We know that, <img decoding=\"async\" style=\"height: 41px; width: 117px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image025.png\" \/>can be rewritten as<img decoding=\"async\" style=\"height: 41px; width: 215px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image026.png\" \/>.<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"On_substituting_value_of_as_we_get\"><\/span>On substituting value of <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image023.png\" \/>as<img decoding=\"async\" style=\"height: 19px; width: 84px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image027.png\" \/>, we get<span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 41px; width: 152px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image028.png\" \/><strong><img decoding=\"async\" style=\"height: 19px; width: 112px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image029.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" style=\"height: 41px; width: 145px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image030.png\" \/><img decoding=\"async\" style=\"height: 19px; width: 76px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image031.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" style=\"height: 41px; width: 144px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image032.png\" \/><img decoding=\"async\" style=\"height: 19px; width: 77px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image033.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" style=\"height: 41px; width: 145px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image034.png\" \/><img decoding=\"async\" style=\"height: 19px; width: 83px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image035.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" style=\"height: 41px; width: 151px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image036.png\" \/><img decoding=\"async\" style=\"height: 19px; width: 77px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image037.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\">Therefore, we conclude that, we can predict the values of<img decoding=\"async\" style=\"height: 41px; width: 117px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image025.png\" \/>, without performing long division, to get<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 41px; width: 107px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image038.png\" \/><img decoding=\"async\" style=\"height: 41px; width: 183px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image039.png\" \/><img decoding=\"async\" style=\"height: 41px; width: 197px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image040.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 1.3<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"3_Express_the_following_in_the_form_where_p_and_q_are_integers_and_q0\"><\/span><strong>3. Express the following in the form<img decoding=\"async\" style=\"height: 44px; width: 19px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image041.png\" \/>, where <em>p <\/em>and <em>q <\/em>are integers and <em>q<img decoding=\"async\" style=\"height: 15px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image042.png\" \/><\/em>0.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>(i) <img decoding=\"async\" style=\"height: 23px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image043.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) <img decoding=\"async\" style=\"height: 23px; width: 33px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image044.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iii) <img decoding=\"async\" style=\"height: 23px; width: 39px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image045.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Solution:<\/p>\n<p style=\"text-align: justify;\"><strong>(i)<\/strong> <img decoding=\"async\" style=\"height: 23px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image046.png\" \/><img decoding=\"async\" style=\"height: 21px; width: 149px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image047.png\" \/><\/p>\n<p style=\"text-align: justify;\">We need to multiply both sides by 10 to get<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 21px; width: 328px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image048.png\" \/><\/p>\n<p style=\"text-align: justify;\">We need to subtract (<em>a<\/em>)from (<em>b<\/em>), to get<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 73px; width: 107px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image049.png\" \/><\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"We_can_also_writeas_or\"><\/span>We can also write<img decoding=\"async\" style=\"height: 19px; width: 45px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image050.png\" \/>as<img decoding=\"async\" style=\"height: 41px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image051.png\" \/> or<img decoding=\"async\" style=\"height: 41px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image052.png\" \/>.<span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\">Therefore, on converting<img decoding=\"async\" style=\"height: 23px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image043.png\" \/> in the<img decoding=\"async\" style=\"height: 44px; width: 19px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image041.png\" \/>form, we get the answer as<img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image053.png\" \/>.<\/p>\n<p style=\"text-align: justify;\"><strong>(ii)<\/strong> <img decoding=\"async\" style=\"height: 23px; width: 81px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image054.png\" \/><img decoding=\"async\" style=\"height: 21px; width: 151px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image055.png\" \/><\/p>\n<p style=\"text-align: justify;\">We need to multiply both sides by 10 to get<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 21px; width: 125px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image056.png\" \/><\/p>\n<p style=\"text-align: justify;\">We need to subtract (<em>a<\/em>)from (<em>b<\/em>), to get<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 73px; width: 105px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image057.png\" \/><\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"We_can_also_writeas_or-2\"><\/span>We can also write<img decoding=\"async\" style=\"height: 19px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image058.png\" \/>as<img decoding=\"async\" style=\"height: 41px; width: 52px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image059.png\" \/> or<img decoding=\"async\" style=\"height: 41px; width: 48px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image060.png\" \/>.<span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\">Therefore, on converting<img decoding=\"async\" style=\"height: 23px; width: 33px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image044.png\" \/> in the<img decoding=\"async\" style=\"height: 44px; width: 19px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image041.png\" \/>form, we get the answer as<img decoding=\"async\" style=\"height: 41px; width: 23px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image061.png\" \/>.<\/p>\n<p style=\"text-align: justify;\"><strong>(iii)<\/strong> <img decoding=\"async\" style=\"height: 23px; width: 87px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image062.png\" \/><img decoding=\"async\" style=\"height: 21px; width: 160px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image063.png\" \/><\/p>\n<p style=\"text-align: justify;\">We need to multiply both sides by 1000 to get<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 21px; width: 328px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image064.png\" \/><\/p>\n<p style=\"text-align: justify;\">We need to subtract (<em>a<\/em>)from (<em>b<\/em>), to get<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 73px; width: 136px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image065.png\" \/><\/p>\n<p style=\"text-align: justify;\">We can also write <img decoding=\"async\" style=\"height: 19px; width: 57px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image066.png\" \/>as<img decoding=\"async\" style=\"height: 41px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image067.png\" \/>.<\/p>\n<p style=\"text-align: justify;\">Therefore, on converting<img decoding=\"async\" style=\"height: 23px; width: 39px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image045.png\" \/> in the<img decoding=\"async\" style=\"height: 44px; width: 19px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image041.png\" \/>form, we get the answer as<img decoding=\"async\" style=\"height: 41px; width: 31px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image068.png\" \/>.<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 1.3<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"4_Express_in_the_form_Are_you_surprised_by_your_answer_Discuss_why_the_answer_makes_sense_with_your_teacher_and_classmates\"><\/span><strong>4. Express<img decoding=\"async\" style=\"height: 19px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image069.png\" \/> in the form<img decoding=\"async\" style=\"height: 44px; width: 19px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image041.png\" \/>. Are you surprised by your answer? Discuss why the answer makes sense with your teacher and classmates.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong><img decoding=\"async\" style=\"height: 21px; width: 149px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image070.png\" \/><\/p>\n<p style=\"text-align: justify;\">We need to multiply both sides by 10 to get<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 21px; width: 129px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image071.png\" \/><\/p>\n<p style=\"text-align: justify;\">We need to subtract (<em>a<\/em>)from (<em>b<\/em>), to get<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 73px; width: 113px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image072.png\" \/><\/p>\n<p style=\"text-align: justify;\">We can also write <img decoding=\"async\" style=\"height: 19px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image073.png\" \/>as<img decoding=\"async\" style=\"height: 41px; width: 92px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image074.png\" \/>.<\/p>\n<p style=\"text-align: justify;\">Therefore, on converting<img decoding=\"async\" style=\"height: 19px; width: 73px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image075.png\" \/> in the<img decoding=\"async\" style=\"height: 44px; width: 19px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image041.png\" \/>form, we get the answer as<img decoding=\"async\" style=\"height: 17px; width: 9px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image076.png\" \/>.<\/p>\n<p style=\"text-align: justify;\">Yes, at a glance we are surprised at our answer.<\/p>\n<p style=\"text-align: justify;\">But the answer makes sense when we observe that 0.9999\u2026\u2026\u2026 goes on forever. SO there is not gap between 1 and 0.9999\u2026\u2026. and hence they are equal.<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 1.3<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"5_What_can_the_maximum_number_of_digits_be_in_the_recurring_block_of_digits_in_the_decimal_expansion_of_Perform_the_division_to_check_your_answer\"><\/span><strong>5. What can the maximum number of digits be in the recurring block of digits in the decimal expansion of<img decoding=\"async\" style=\"height: 41px; width: 23px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image077.png\" \/>? Perform the division to check your answer.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>We need to find the number of digits in the recurring block of<img decoding=\"async\" style=\"height: 41px; width: 23px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image077.png\" \/>.<\/p>\n<p style=\"text-align: justify;\">Let us perform the long division to get the recurring block of<img decoding=\"async\" style=\"height: 41px; width: 23px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image077.png\" \/>.<\/p>\n<p style=\"text-align: justify;\">We need to divide 1 by 17, to get<\/p>\n<p style=\"text-align: justify;\">We can observe that while dividing 1 by 17 we got the remainder as 1, which will continue to be 1 after carrying out 16 continuous divisions.<\/p>\n<p style=\"text-align: justify;\">Therefore, we conclude that<img decoding=\"async\" style=\"height: 41px; width: 393px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image078.png\" \/>, which is a non-terminating decimal and recurring decimal.<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 1.3<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"6_Look_at_several_examples_of_rational_numbers_in_the_form_q_%EF%82%B9%EF%80%A00_where_p_and_q_are_integers_with_no_common_factors_other_than_1_and_having_terminating_decimal_representations_expansions_Can_you_guess_what_property_q_must_satisfy\"><\/span><strong>6. Look at several examples of rational numbers in the form <img decoding=\"async\" style=\"height: 44px; width: 19px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image041.png\" \/>(<em>q <\/em>\uf0b9\uf0200), where <em>p <\/em>and <em>q <\/em>are integers with no common factors other than 1 and having terminating decimal representations (expansions). Can you guess what property <em>q <\/em>must satisfy?<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Solution:<\/p>\n<p style=\"text-align: justify;\">Let us consider the examples of the form<img decoding=\"async\" style=\"height: 44px; width: 19px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image041.png\" \/> that are terminating decimals.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 41px; width: 52px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image079.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 41px; width: 57px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image080.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 41px; width: 52px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image081.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 41px; width: 57px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image082.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 41px; width: 81px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image083.png\" \/><\/p>\n<p style=\"text-align: justify;\">We can observe that the denominators of the above rational numbers have powers of 2, 5 or both.<\/p>\n<p style=\"text-align: justify;\">Therefore, we can conclude that the property, which <em>q <\/em>must satisfy in<img decoding=\"async\" style=\"height: 44px; width: 19px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image041.png\" \/>, so that the rational number<img decoding=\"async\" style=\"height: 44px; width: 19px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image041.png\" \/>is a terminating decimal is that <em>q<\/em> must have powers of 2, 5 or both.<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 1.3<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"7_Write_three_numbers_whose_decimal_expansions_are_non-terminating_non-recurring\"><\/span><strong>7. Write three numbers whose decimal expansions are non-terminating non-recurring.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>The three numbers that have their expansions as non-terminating on recurring decimal are given below.<\/p>\n<p style=\"text-align: justify;\">0.04004000400004\u2026.<\/p>\n<p style=\"text-align: justify;\">0.07007000700007\u2026.<\/p>\n<p style=\"text-align: justify;\">0.013001300013000013\u2026.<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 1.3<\/p>\n<h6><span class=\"ez-toc-section\" id=\"8_Find_three_different_irrational_numbers_between_the_rational_numbersand\"><\/span><strong>8. Find three different irrational numbers between the rational numbers<img decoding=\"async\" style=\"height: 41px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image084.png\" \/>and<img decoding=\"async\" style=\"height: 41px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image085.png\" \/>.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Let us convert<img decoding=\"async\" style=\"height: 41px; width: 67px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image086.png\" \/>into decimal form, to get<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 41px; width: 108px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image087.png\" \/>and <img decoding=\"async\" style=\"height: 41px; width: 112px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image088.png\" \/><\/p>\n<p style=\"text-align: justify;\">Three irrational numbers that lie between<img decoding=\"async\" style=\"height: 19px; width: 188px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image089.png\" \/>are:<\/p>\n<p style=\"text-align: justify;\">0.73073007300073\u2026.<\/p>\n<p style=\"text-align: justify;\">0.74074007400074\u2026.<\/p>\n<p style=\"text-align: justify;\">0.76076007600076\u2026.<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 1.3<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"9_Classify_the_following_numbers_as_rational_or_irrational\"><\/span><strong>9. Classify the following numbers as rational or irrational:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>(i) 23<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) 225<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iii) 0.3796 <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iv) 7.478478&#8230;<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(v) 1.101001000100001&#8230;<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. (i)<\/strong> <img decoding=\"async\" style=\"height: 24px; width: 32px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image090.png\" \/><\/p>\n<p style=\"text-align: justify;\">We know that on finding the square root of 23, we will not get an integer.<\/p>\n<p style=\"text-align: justify;\">Therefore, we conclude that<img decoding=\"async\" style=\"height: 24px; width: 32px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image090.png\" \/>is an irrational number.<\/p>\n<p style=\"text-align: justify;\"><strong>(ii)<\/strong> <img decoding=\"async\" style=\"height: 24px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image091.png\" \/><\/p>\n<p style=\"text-align: justify;\">We know that on finding the square root of 225, we get 15, which is an integer.<\/p>\n<p style=\"text-align: justify;\">Therefore, we conclude that<img decoding=\"async\" style=\"height: 24px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image091.png\" \/>is a rational number.<\/p>\n<p style=\"text-align: justify;\"><strong>(iii)<\/strong> 0.3796<\/p>\n<p style=\"text-align: justify;\">We know that 0.3796 can be converted into<img decoding=\"async\" style=\"height: 44px; width: 19px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image041.png\" \/>.<\/p>\n<p style=\"text-align: justify;\">While, converting 0.3796 into<img decoding=\"async\" style=\"height: 44px; width: 19px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image041.png\" \/>form, we get<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 41px; width: 105px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image092.png\" \/>.<\/p>\n<p style=\"text-align: justify;\">The rational number<img decoding=\"async\" style=\"height: 41px; width: 45px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image093.png\" \/>can be converted into lowest fractions, to get<img decoding=\"async\" style=\"height: 41px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image094.png\" \/>.<\/p>\n<p style=\"text-align: justify;\">We can observe that 0.3796 can be converted into a rational number.<\/p>\n<p style=\"text-align: justify;\">Therefore, we conclude that 0.3796 is a rational number.<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"iv_7478478%E2%80%A6\"><\/span><strong>(iv)<\/strong> 7.478478\u2026.<span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\">We know that 7.478478\u2026. is a non-terminating recurring decimal, which can be converted into<img decoding=\"async\" style=\"height: 44px; width: 19px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image041.png\" \/>form.<\/p>\n<p style=\"text-align: justify;\">While, converting 7.478478\u2026. into<img decoding=\"async\" style=\"height: 44px; width: 19px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image041.png\" \/>form, we get<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 27px; width: 174px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image095.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 27px; width: 193px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image096.png\" \/><\/p>\n<p style=\"text-align: justify;\">While, subtracting (a) from (b), we get<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 73px; width: 159px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image097.png\" \/><\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"We_know_thatcan_also_be_written_as\"><\/span>We know that<img decoding=\"async\" style=\"height: 19px; width: 84px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image098.png\" \/>can also be written as<img decoding=\"async\" style=\"height: 41px; width: 63px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image099.png\" \/>.<span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\">Therefore, we conclude that 7.478478\u2026. is a rational number.<\/p>\n<p style=\"text-align: justify;\"><strong>(v)<\/strong> 1.101001000100001&#8230;.<\/p>\n<p style=\"text-align: justify;\">We can observe that the number 1.101001000100001&#8230;. is a non-terminating on recurring decimal.<\/p>\n<p style=\"text-align: justify;\">We know that non-terminating and non-recurring decimals cannot be converted into<img decoding=\"async\" style=\"height: 44px; width: 19px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.3\/image041.png\" \/>form.<\/p>\n<p style=\"text-align: justify;\">Therefore, we conclude that 1.101001000100001&#8230;. is an irrational number.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_for_Class_9_Maths_Exercise_13\"><\/span>NCERT Solutions for Class 9 Maths Exercise 1.3<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>NCERT Solutions Class 9 Maths PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 9 Maths includes text book solutions from Mathematics Book. NCERT Solutions for CBSE Class 9 Maths have total 15 chapters. 9 Maths NCERT Solutions in PDF for free Download on our website. Ncert Maths class 9 solutions PDF and Maths ncert class 9 PDF solutions with latest modifications and as per the latest CBSE syllabus are only available in myCBSEguide.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"CBSE_app_for_Class_9\"><\/span>CBSE app for Class 9<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>To download NCERT Solutions for Class 9 Maths, Computer Science, Home Science,Hindi ,English, Social Science do check myCBSEguide app or website. myCBSEguide provides sample papers with solution, test papers for chapter-wise practice, NCERT solutions, NCERT Exemplar solutions, quick revision notes for ready reference, CBSE guess papers and CBSE important question papers. Sample Paper all are made available through\u00a0<a href=\"https:\/\/play.google.com\/store\/apps\/details?id=in.techchefs.MyCBSEGuide&amp;referrer=utm_source%3Dmycbse_bottom%26utm_medium%3Dtext%26utm_campaign%3Dmycbseads\"><strong>the best app for CBSE students<\/strong><\/a>\u00a0and myCBSEguide website.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions for Class 9 Maths Exercise 1.3 book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 9 Maths chapter &#8230; <a title=\"NCERT Solutions for Class 9 Maths Exercise 1.3\" class=\"read-more\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-1-3\/\" aria-label=\"More on NCERT Solutions for Class 9 Maths Exercise 1.3\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":-1,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1376,281],"tags":[283,1344,321,1485,216],"class_list":["post-4981","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematics-cbse-class-09","category-ncert-solutions","tag-cbse-study-material","tag-class-9","tag-mathematics","tag-maths","tag-ncert-solutions"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>NCERT Solutions for Class 9 Maths Exercise 1.3 | myCBSEguide<\/title>\n<meta name=\"description\" content=\"NCERT Solutions for Class 9 Maths Exercise 1.3 in PDF format for free download. NCERT Solutions Class 9 Mathematics.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-1-3\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Solutions for Class 9 Maths Exercise 1.3 | myCBSEguide\" \/>\n<meta property=\"og:description\" content=\"NCERT Solutions for Class 9 Maths Exercise 1.3 in PDF format for free download. NCERT Solutions Class 9 Mathematics.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-1-3\/\" \/>\n<meta property=\"og:site_name\" content=\"myCBSEguide\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/mycbseguide\/\" \/>\n<meta property=\"article:published_time\" content=\"2016-05-19T06:19:00+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2018-06-16T11:46:56+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mycbseguide.com\/blog\/wp-content\/uploads\/2016\/09\/mycbseguide_n.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"599\" \/>\n\t<meta property=\"og:image:height\" content=\"242\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"author\" content=\"myCBSEguide\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@mycbseguide\" \/>\n<meta name=\"twitter:site\" content=\"@mycbseguide\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"myCBSEguide\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"6 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-1-3\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-1-3\/\"},\"author\":{\"name\":\"myCBSEguide\",\"@id\":\"https:\/\/mycbseguide.com\/blog\/#\/schema\/person\/10b8c7820ff29025ab8524da7c025f65\"},\"headline\":\"NCERT Solutions for Class 9 Maths Exercise 1.3\",\"datePublished\":\"2016-05-19T06:19:00+00:00\",\"dateModified\":\"2018-06-16T11:46:56+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-1-3\/\"},\"wordCount\":1197,\"commentCount\":11,\"publisher\":{\"@id\":\"https:\/\/mycbseguide.com\/blog\/#organization\"},\"image\":{\"@id\":\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-1-3\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/media-mycbseguide.s3.ap-south-1.amazonaws.com\/images\/blog\/09_Class_Maths_Book.jpg\",\"keywords\":[\"CBSE Study Material\",\"Class 9\",\"Mathematics\",\"maths\",\"NCERT Solutions\"],\"articleSection\":[\"Mathematics\",\"NCERT Solutions\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-1-3\/\",\"url\":\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-1-3\/\",\"name\":\"NCERT Solutions for Class 9 Maths Exercise 1.3 | myCBSEguide\",\"isPartOf\":{\"@id\":\"https:\/\/mycbseguide.com\/blog\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-1-3\/#primaryimage\"},\"image\":{\"@id\":\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-1-3\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/media-mycbseguide.s3.ap-south-1.amazonaws.com\/images\/blog\/09_Class_Maths_Book.jpg\",\"datePublished\":\"2016-05-19T06:19:00+00:00\",\"dateModified\":\"2018-06-16T11:46:56+00:00\",\"description\":\"NCERT Solutions for Class 9 Maths Exercise 1.3 in PDF format for free download. NCERT Solutions Class 9 Mathematics.\",\"breadcrumb\":{\"@id\":\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-1-3\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-1-3\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-1-3\/#primaryimage\",\"url\":\"https:\/\/media-mycbseguide.s3.ap-south-1.amazonaws.com\/images\/blog\/09_Class_Maths_Book.jpg\",\"contentUrl\":\"https:\/\/media-mycbseguide.s3.ap-south-1.amazonaws.com\/images\/blog\/09_Class_Maths_Book.jpg\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-1-3\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mycbseguide.com\/blog\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"NCERT Solutions\",\"item\":\"https:\/\/mycbseguide.com\/blog\/category\/ncert-solutions\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"NCERT Solutions for Class 9 Maths Exercise 1.3\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mycbseguide.com\/blog\/#website\",\"url\":\"https:\/\/mycbseguide.com\/blog\/\",\"name\":\"myCBSEguide\",\"description\":\"\",\"publisher\":{\"@id\":\"https:\/\/mycbseguide.com\/blog\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mycbseguide.com\/blog\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/mycbseguide.com\/blog\/#organization\",\"name\":\"myCBSEguide\",\"url\":\"https:\/\/mycbseguide.com\/blog\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/mycbseguide.com\/blog\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/mycbseguide.com\/blog\/wp-content\/uploads\/2016\/04\/books_square.png\",\"contentUrl\":\"https:\/\/mycbseguide.com\/blog\/wp-content\/uploads\/2016\/04\/books_square.png\",\"width\":180,\"height\":180,\"caption\":\"myCBSEguide\"},\"image\":{\"@id\":\"https:\/\/mycbseguide.com\/blog\/#\/schema\/logo\/image\/\"},\"sameAs\":[\"https:\/\/www.facebook.com\/mycbseguide\/\",\"https:\/\/x.com\/mycbseguide\",\"https:\/\/www.linkedin.com\/company\/mycbseguide\/\",\"http:\/\/in.pinterest.com\/mycbseguide\/\",\"https:\/\/www.youtube.com\/channel\/UCxuqSnnygFzwJG0pwogCNEQ\"]},{\"@type\":\"Person\",\"@id\":\"https:\/\/mycbseguide.com\/blog\/#\/schema\/person\/10b8c7820ff29025ab8524da7c025f65\",\"name\":\"myCBSEguide\",\"sameAs\":[\"http:\/\/mycbseguide.com\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"NCERT Solutions for Class 9 Maths Exercise 1.3 | myCBSEguide","description":"NCERT Solutions for Class 9 Maths Exercise 1.3 in PDF format for free download. NCERT Solutions Class 9 Mathematics.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-1-3\/","og_locale":"en_US","og_type":"article","og_title":"NCERT Solutions for Class 9 Maths Exercise 1.3 | myCBSEguide","og_description":"NCERT Solutions for Class 9 Maths Exercise 1.3 in PDF format for free download. NCERT Solutions Class 9 Mathematics.","og_url":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-1-3\/","og_site_name":"myCBSEguide","article_publisher":"https:\/\/www.facebook.com\/mycbseguide\/","article_published_time":"2016-05-19T06:19:00+00:00","article_modified_time":"2018-06-16T11:46:56+00:00","og_image":[{"width":599,"height":242,"url":"https:\/\/mycbseguide.com\/blog\/wp-content\/uploads\/2016\/09\/mycbseguide_n.jpg","type":"image\/jpeg"}],"author":"myCBSEguide","twitter_card":"summary_large_image","twitter_creator":"@mycbseguide","twitter_site":"@mycbseguide","twitter_misc":{"Written by":"myCBSEguide","Est. reading time":"6 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-1-3\/#article","isPartOf":{"@id":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-1-3\/"},"author":{"name":"myCBSEguide","@id":"https:\/\/mycbseguide.com\/blog\/#\/schema\/person\/10b8c7820ff29025ab8524da7c025f65"},"headline":"NCERT Solutions for Class 9 Maths Exercise 1.3","datePublished":"2016-05-19T06:19:00+00:00","dateModified":"2018-06-16T11:46:56+00:00","mainEntityOfPage":{"@id":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-1-3\/"},"wordCount":1197,"commentCount":11,"publisher":{"@id":"https:\/\/mycbseguide.com\/blog\/#organization"},"image":{"@id":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-1-3\/#primaryimage"},"thumbnailUrl":"https:\/\/media-mycbseguide.s3.ap-south-1.amazonaws.com\/images\/blog\/09_Class_Maths_Book.jpg","keywords":["CBSE Study Material","Class 9","Mathematics","maths","NCERT Solutions"],"articleSection":["Mathematics","NCERT Solutions"],"inLanguage":"en-US"},{"@type":"WebPage","@id":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-1-3\/","url":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-1-3\/","name":"NCERT Solutions for Class 9 Maths Exercise 1.3 | myCBSEguide","isPartOf":{"@id":"https:\/\/mycbseguide.com\/blog\/#website"},"primaryImageOfPage":{"@id":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-1-3\/#primaryimage"},"image":{"@id":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-1-3\/#primaryimage"},"thumbnailUrl":"https:\/\/media-mycbseguide.s3.ap-south-1.amazonaws.com\/images\/blog\/09_Class_Maths_Book.jpg","datePublished":"2016-05-19T06:19:00+00:00","dateModified":"2018-06-16T11:46:56+00:00","description":"NCERT Solutions for Class 9 Maths Exercise 1.3 in PDF format for free download. NCERT Solutions Class 9 Mathematics.","breadcrumb":{"@id":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-1-3\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-1-3\/"]}]},{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-1-3\/#primaryimage","url":"https:\/\/media-mycbseguide.s3.ap-south-1.amazonaws.com\/images\/blog\/09_Class_Maths_Book.jpg","contentUrl":"https:\/\/media-mycbseguide.s3.ap-south-1.amazonaws.com\/images\/blog\/09_Class_Maths_Book.jpg"},{"@type":"BreadcrumbList","@id":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-1-3\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mycbseguide.com\/blog\/"},{"@type":"ListItem","position":2,"name":"NCERT Solutions","item":"https:\/\/mycbseguide.com\/blog\/category\/ncert-solutions\/"},{"@type":"ListItem","position":3,"name":"NCERT Solutions for Class 9 Maths Exercise 1.3"}]},{"@type":"WebSite","@id":"https:\/\/mycbseguide.com\/blog\/#website","url":"https:\/\/mycbseguide.com\/blog\/","name":"myCBSEguide","description":"","publisher":{"@id":"https:\/\/mycbseguide.com\/blog\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mycbseguide.com\/blog\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/mycbseguide.com\/blog\/#organization","name":"myCBSEguide","url":"https:\/\/mycbseguide.com\/blog\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/mycbseguide.com\/blog\/#\/schema\/logo\/image\/","url":"https:\/\/mycbseguide.com\/blog\/wp-content\/uploads\/2016\/04\/books_square.png","contentUrl":"https:\/\/mycbseguide.com\/blog\/wp-content\/uploads\/2016\/04\/books_square.png","width":180,"height":180,"caption":"myCBSEguide"},"image":{"@id":"https:\/\/mycbseguide.com\/blog\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.facebook.com\/mycbseguide\/","https:\/\/x.com\/mycbseguide","https:\/\/www.linkedin.com\/company\/mycbseguide\/","http:\/\/in.pinterest.com\/mycbseguide\/","https:\/\/www.youtube.com\/channel\/UCxuqSnnygFzwJG0pwogCNEQ"]},{"@type":"Person","@id":"https:\/\/mycbseguide.com\/blog\/#\/schema\/person\/10b8c7820ff29025ab8524da7c025f65","name":"myCBSEguide","sameAs":["http:\/\/mycbseguide.com"]}]}},"_links":{"self":[{"href":"https:\/\/mycbseguide.com\/blog\/wp-json\/wp\/v2\/posts\/4981","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mycbseguide.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mycbseguide.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mycbseguide.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mycbseguide.com\/blog\/wp-json\/wp\/v2\/comments?post=4981"}],"version-history":[{"count":4,"href":"https:\/\/mycbseguide.com\/blog\/wp-json\/wp\/v2\/posts\/4981\/revisions"}],"predecessor-version":[{"id":16831,"href":"https:\/\/mycbseguide.com\/blog\/wp-json\/wp\/v2\/posts\/4981\/revisions\/16831"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/mycbseguide.com\/blog\/wp-json\/"}],"wp:attachment":[{"href":"https:\/\/mycbseguide.com\/blog\/wp-json\/wp\/v2\/media?parent=4981"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mycbseguide.com\/blog\/wp-json\/wp\/v2\/categories?post=4981"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mycbseguide.com\/blog\/wp-json\/wp\/v2\/tags?post=4981"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}