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RD Sharma Solutions Ex-1.2, Number System, Class 9, Maths Notes | Study RD Sharma Solutions for Class 9 Mathematics - Class 9

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Q1. Express the following rational numbers as decimals:

(i) 42/100

(ii) 327/500

(iii) 15/4

Solution:

(i) By long division method

100) RD Sharma Solutions Ex-1.2, Number System, Class 9, Maths Notes | Study RD Sharma Solutions for Class 9 Mathematics - Class 9 ( 0.42

400

RD Sharma Solutions Ex-1.2, Number System, Class 9, Maths Notes | Study RD Sharma Solutions for Class 9 Mathematics - Class 9

200

RD Sharma Solutions Ex-1.2, Number System, Class 9, Maths Notes | Study RD Sharma Solutions for Class 9 Mathematics - Class 9

Therefore,  42/100 = 0.42

(ii) By long division method

RD Sharma Solutions Ex-1.2, Number System, Class 9, Maths Notes | Study RD Sharma Solutions for Class 9 Mathematics - Class 9

3000

RD Sharma Solutions Ex-1.2, Number System, Class 9, Maths Notes | Study RD Sharma Solutions for Class 9 Mathematics - Class 9

2500

RD Sharma Solutions Ex-1.2, Number System, Class 9, Maths Notes | Study RD Sharma Solutions for Class 9 Mathematics - Class 9

2000

RD Sharma Solutions Ex-1.2, Number System, Class 9, Maths Notes | Study RD Sharma Solutions for Class 9 Mathematics - Class 9

Therefore, 327/500 = 0.654

(iii) By long division method

RD Sharma Solutions Ex-1.2, Number System, Class 9, Maths Notes | Study RD Sharma Solutions for Class 9 Mathematics - Class 9

12

RD Sharma Solutions Ex-1.2, Number System, Class 9, Maths Notes | Study RD Sharma Solutions for Class 9 Mathematics - Class 9

28

RD Sharma Solutions Ex-1.2, Number System, Class 9, Maths Notes | Study RD Sharma Solutions for Class 9 Mathematics - Class 9

20

RD Sharma Solutions Ex-1.2, Number System, Class 9, Maths Notes | Study RD Sharma Solutions for Class 9 Mathematics - Class 9

Therefore, 15/4 = 3.75


Q2. Express the following rational numbers as decimals:

(i) 2/3

(ii)  RD Sharma Solutions Ex-1.2, Number System, Class 9, Maths Notes | Study RD Sharma Solutions for Class 9 Mathematics - Class 9
RD Sharma Solutions Ex-1.2, Number System, Class 9, Maths Notes | Study RD Sharma Solutions for Class 9 Mathematics - Class 9
RD Sharma Solutions Ex-1.2, Number System, Class 9, Maths Notes | Study RD Sharma Solutions for Class 9 Mathematics - Class 9
(v) 437/999

Solution:

(i) By long division method

RD Sharma Solutions Ex-1.2, Number System, Class 9, Maths Notes | Study RD Sharma Solutions for Class 9 Mathematics - Class 9

18

RD Sharma Solutions Ex-1.2, Number System, Class 9, Maths Notes | Study RD Sharma Solutions for Class 9 Mathematics - Class 9

18

RD Sharma Solutions Ex-1.2, Number System, Class 9, Maths Notes | Study RD Sharma Solutions for Class 9 Mathematics - Class 9

Therefore, 2/3 = 0.66

(ii) By long division method

RD Sharma Solutions Ex-1.2, Number System, Class 9, Maths Notes | Study RD Sharma Solutions for Class 9 Mathematics - Class 9

3600

RD Sharma Solutions Ex-1.2, Number System, Class 9, Maths Notes | Study RD Sharma Solutions for Class 9 Mathematics - Class 9

3600

RD Sharma Solutions Ex-1.2, Number System, Class 9, Maths Notes | Study RD Sharma Solutions for Class 9 Mathematics - Class 9

3600

RD Sharma Solutions Ex-1.2, Number System, Class 9, Maths Notes | Study RD Sharma Solutions for Class 9 Mathematics - Class 9

Therefore, RD Sharma Solutions Ex-1.2, Number System, Class 9, Maths Notes | Study RD Sharma Solutions for Class 9 Mathematics - Class 9– 0.444

(iii) By long division method

RD Sharma Solutions Ex-1.2, Number System, Class 9, Maths Notes | Study RD Sharma Solutions for Class 9 Mathematics - Class 9

15

RD Sharma Solutions Ex-1.2, Number System, Class 9, Maths Notes | Study RD Sharma Solutions for Class 9 Mathematics - Class 9

45

RD Sharma Solutions Ex-1.2, Number System, Class 9, Maths Notes | Study RD Sharma Solutions for Class 9 Mathematics - Class 9

45

RD Sharma Solutions Ex-1.2, Number System, Class 9, Maths Notes | Study RD Sharma Solutions for Class 9 Mathematics - Class 9

45

RD Sharma Solutions Ex-1.2, Number System, Class 9, Maths Notes | Study RD Sharma Solutions for Class 9 Mathematics - Class 9

Therefore, 2/15 = -1.333

(iv) By long division method

RD Sharma Solutions Ex-1.2, Number System, Class 9, Maths Notes | Study RD Sharma Solutions for Class 9 Mathematics - Class 9

13

RD Sharma Solutions Ex-1.2, Number System, Class 9, Maths Notes | Study RD Sharma Solutions for Class 9 Mathematics - Class 9

78

RD Sharma Solutions Ex-1.2, Number System, Class 9, Maths Notes | Study RD Sharma Solutions for Class 9 Mathematics - Class 9

117

RD Sharma Solutions Ex-1.2, Number System, Class 9, Maths Notes | Study RD Sharma Solutions for Class 9 Mathematics - Class 9

26

RD Sharma Solutions Ex-1.2, Number System, Class 9, Maths Notes | Study RD Sharma Solutions for Class 9 Mathematics - Class 9

39

RD Sharma Solutions Ex-1.2, Number System, Class 9, Maths Notes | Study RD Sharma Solutions for Class 9 Mathematics - Class 9

91

RD Sharma Solutions Ex-1.2, Number System, Class 9, Maths Notes | Study RD Sharma Solutions for Class 9 Mathematics - Class 9

78

RD Sharma Solutions Ex-1.2, Number System, Class 9, Maths Notes | Study RD Sharma Solutions for Class 9 Mathematics - Class 9

117

RD Sharma Solutions Ex-1.2, Number System, Class 9, Maths Notes | Study RD Sharma Solutions for Class 9 Mathematics - Class 9

Therefore,  RD Sharma Solutions Ex-1.2, Number System, Class 9, Maths Notes | Study RD Sharma Solutions for Class 9 Mathematics - Class 9 = – 1.69230769

(v) By long division method

RD Sharma Solutions Ex-1.2, Number System, Class 9, Maths Notes | Study RD Sharma Solutions for Class 9 Mathematics - Class 9

3996

RD Sharma Solutions Ex-1.2, Number System, Class 9, Maths Notes | Study RD Sharma Solutions for Class 9 Mathematics - Class 9

2997

RD Sharma Solutions Ex-1.2, Number System, Class 9, Maths Notes | Study RD Sharma Solutions for Class 9 Mathematics - Class 9

6993

RD Sharma Solutions Ex-1.2, Number System, Class 9, Maths Notes | Study RD Sharma Solutions for Class 9 Mathematics - Class 9

3996

RD Sharma Solutions Ex-1.2, Number System, Class 9, Maths Notes | Study RD Sharma Solutions for Class 9 Mathematics - Class 9

2997

RD Sharma Solutions Ex-1.2, Number System, Class 9, Maths Notes | Study RD Sharma Solutions for Class 9 Mathematics - Class 9

Therefore, 437/999 = 0.43743


Q3. Look at several examples of rational numbers in the form of p/q (q ≠ 0), where p and q are integers with no common factor other than 1 and having terminating decimal representations. Can you guess what property q must satisfy?

Solution: A rational number p/q is a terminating decimal only, when prime factors of q are q and 5 only. Therefore, p/q  is a terminating decimal only, when prime factorization of q must have only powers of 2 or 5 or both.

The document RD Sharma Solutions Ex-1.2, Number System, Class 9, Maths Notes | Study RD Sharma Solutions for Class 9 Mathematics - Class 9 is a part of the Class 9 Course RD Sharma Solutions for Class 9 Mathematics.
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