# RD Sharma Solutions Class 7 Decimals Exercise 3.1

## RD Sharma Solutions Class 7 Chapter 3 Exercise 3.1

#### Exercise 3.1

Q1. Write each of the following as decimals:

(i) $\frac{8}{100}$

Mark the decimal point two places from right to left

=$\frac{8}{100}=0.08$

(ii) 20+$\frac{9}{10}$+$\frac{4}{100}$

Convert $\frac{9}{10}$ and $\frac{4}{100}$ into decimals

$\frac{9}{10}$

Mark the decimal point one place from right to left

$\frac{9}{10}$=0.9

$\frac{4}{100}$

Mark the decimal point two places from right to left

$\frac{4}{100}$

=0.04

=20+$\frac{9}{10}$+$\frac{4}{100}$

= 20+0.9+0.04

=20.94

(iii) 23+$\frac{2}{10}$+$\frac{6}{1000}$

Convert $\frac{2}{10}$ and $\frac{6}{1000}$ into decimals

$\frac{2}{10}$

Mark the decimal point one place from right to left

$\frac{2}{10}$

=0.2

$\frac{6}{1000}$

Mark the decimal point three places from right to left

$\frac{6}{1000}$

=0.006

23, 0.2, 0.006 are unlike decimals. So we convert them into like decimals.

=23+$\frac{2}{10}$+$\frac{6}{1000}$

=23+0.2+0.006

=23.206

Q2. Convert each of the following into fractions in the lowest form:

(i) 0.04

$=\frac{0.04}{1}\\ =\frac{0.04\times100}{1\times100}\\ =\frac{4}{100}\\ =\frac{1}{25}$

(ii) 2.34

$=\frac{2.34}{1}\\ =\frac{2.34\times100}{1\times100}\\ =\frac{234}{100}\\ =\frac{117}{50}$

(iii) 0.342

$=\frac{0.342}{1}\\ =\frac{0.342\times1000}{1\times1000}\\ =\frac{342}{1000}\\ =\frac{171}{500}$

(iv) 17.38

$=\frac{17.38}{1}\\ =\frac{17.38\times100}{1\times100}\\ =\frac{1738}{100}\\ =\frac{869}{50}$

Q3. Express the following fractions as decimals:

(ii) $\frac{23}{10}$

$=\frac{23}{10}\\ =2.3$

(i) $25\frac{1}{8}$

$=25+\frac{1}{8}\\ =25+\frac{1\times125}{8\times125}\\ =25+\frac{125}{1000}\\ =25+0.125\\ =25.125$

(iii) $39\frac{7}{35}$

$=\frac{1372}{35}\\ =39.2$

(iv) $15tfrac{1}{25}$

$=15+\frac{1}{25}\\ =15+\frac{1\times4}{25\times4}\\ =15+\frac{4}{100}\\ =15+0.04\\ =15.04$

(i) 41.8, 39.24, 5.01 and 62.6

(ii) 18.03, 146.3, 0.829 and 5.324

Q5. Find the value of:

(i) 9.756-6.28

(ii) 48.1-0.37

(iii) 108.032-86.8

(iv) 100 -26.32

Q6. Take out 3.547 from 7.2

Q7. What is to be added to 36.85 to get 59.41?

x+36.85=59.41

x=59.41-36.85

x=22.56

Therefore 22.56 is added to 36.85 to get 59.41

Q8. What is to be subtracted from 17.1 to get 2.051?

17.1-x=2.051

17.1=x+2.051

x=17.1-2.051

x=15.049

Therefore 15.049 is subtracted from 17.1 to get 15.049

Q9. By how much should 34.79 be increased to get 70.15?

34.79+x=70.15

x=70.15-34.79

x=35.36

Therefore 35.36 is increased to 70.15

Q10. By how much should 59.71 be decreased to get 34.58?

59.71-x=34.58

59.71-34.58=x

x=25.13

Therefore 25.13 is decreased to get 34.58