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**NCERT solutions for Class 9 Maths Number Systems Download as PDF**

## NCERT Solutions for Class 9 Maths Number Systems

**1. Write the following in decimal form and say what kind of decimal expansion each has: **

**(i) **

**(ii) **

**(iii) **

**(iv) **

**(v) **

**(vi) **

**Ans. (i)**

###### On dividing 36 by 100, we get

Therefore, we conclude that, which is a terminating decimal.

**(ii)**

###### On dividing 1 by 11, we get

We can observe that while dividing 1 by 11, we got the remainder as 1, which will continue to be 1.

Therefore, we conclude that, which is a non-terminating decimal and recurring decimal.

**(iii)**

###### On dividing 33 by 8, we get

We can observe that while dividing 33 by 8, we got the remainder as 0.

Therefore, we conclude that, which is a terminating decimal.

**(iv)**

###### On dividing 3 by 13, we get

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.

Therefore, we conclude that, which is a non-terminating decimal and recurring decimal.

**(v)**

On dividing 2 by 11, we get

###### 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.

Therefore, we conclude that, which is a non-terminating decimal and recurring decimal.

**(vi)**

On dividing 329 by 400, we get

We can observe that while dividing 329 by 400, we got the remainder as 0.

Therefore, we conclude that, which is a terminating decimal.

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?**

**[Hint: Study the remainders while finding the value of carefully.]**

**Ans. **We are given that.

We need to find the values of, without performing long division.

We know that, can be rewritten as.

###### On substituting value of as, we get

Therefore, we conclude that, we can predict the values of, without performing long division, to get

NCERT Solutions for Class 9 Maths Exercise 1.3

**3. Express the following in the form, where ***p *and *q *are integers and *q*0.

*p*and

*q*are integers and

*q*0.

**(i) **

**(ii) **

**(iii) **

**Ans. **Solution:

**(i)**

We need to multiply both sides by 10 to get

We need to subtract (*a*)from (*b*), to get

###### We can also writeas or.

Therefore, on converting in theform, we get the answer as.

**(ii)**

We need to multiply both sides by 10 to get

We need to subtract (*a*)from (*b*), to get

###### We can also writeas or.

Therefore, on converting in theform, we get the answer as.

**(iii)**

We need to multiply both sides by 1000 to get

We need to subtract (*a*)from (*b*), to get

We can also write as.

Therefore, on converting in theform, we get the answer as.

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.**

**Ans. **

We need to multiply both sides by 10 to get

We need to subtract (*a*)from (*b*), to get

We can also write as.

Therefore, on converting in theform, we get the answer as.

Yes, at a glance we are surprised at our answer.

But the answer makes sense when we observe that 0.9999……… goes on forever. SO there is not gap between 1 and 0.9999……. and hence they are equal.

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.**

**Ans. **We need to find the number of digits in the recurring block of.

Let us perform the long division to get the recurring block of.

We need to divide 1 by 17, to get

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.

Therefore, we conclude that, which is a non-terminating decimal and recurring decimal.

NCERT Solutions for Class 9 Maths Exercise 1.3

**6. Look at several examples of rational numbers in the form (***q *0), 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?

*q*0), 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?

**Ans. **Solution:

Let us consider the examples of the form that are terminating decimals.

We can observe that the denominators of the above rational numbers have powers of 2, 5 or both.

Therefore, we can conclude that the property, which *q *must satisfy in, so that the rational numberis a terminating decimal is that *q* must have powers of 2, 5 or both.

NCERT Solutions for Class 9 Maths Exercise 1.3

**7. Write three numbers whose decimal expansions are non-terminating non-recurring.**

**Ans. **The three numbers that have their expansions as non-terminating on recurring decimal are given below.

0.04004000400004….

0.07007000700007….

0.013001300013000013….

NCERT Solutions for Class 9 Maths Exercise 1.3

**8. Find three different irrational numbers between the rational numbersand.**

**Ans. **Let us convertinto decimal form, to get

and

Three irrational numbers that lie betweenare:

0.73073007300073….

0.74074007400074….

0.76076007600076….

NCERT Solutions for Class 9 Maths Exercise 1.3

**9. Classify the following numbers as rational or irrational:**

**(i) 23**

**(ii) 225**

**(iii) 0.3796 **

**(iv) 7.478478…**

**(v) 1.101001000100001…**

**Ans. (i)**

We know that on finding the square root of 23, we will not get an integer.

Therefore, we conclude thatis an irrational number.

**(ii)**

We know that on finding the square root of 225, we get 15, which is an integer.

Therefore, we conclude thatis a rational number.

**(iii)** 0.3796

We know that 0.3796 can be converted into.

While, converting 0.3796 intoform, we get

.

The rational numbercan be converted into lowest fractions, to get.

We can observe that 0.3796 can be converted into a rational number.

Therefore, we conclude that 0.3796 is a rational number.

**(iv)** 7.478478….

We know that 7.478478…. is a non-terminating recurring decimal, which can be converted intoform.

While, converting 7.478478…. intoform, we get

While, subtracting (a) from (b), we get

###### We know thatcan also be written as.

Therefore, we conclude that 7.478478…. is a rational number.

**(v)** 1.101001000100001….

We can observe that the number 1.101001000100001…. is a non-terminating on recurring decimal.

We know that non-terminating and non-recurring decimals cannot be converted intoform.

Therefore, we conclude that 1.101001000100001…. is an irrational number.

## NCERT Solutions for Class 9 Maths Exercise 1.3

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.

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