RD Sharma solution class 7 chapter 3 Decimals Exercise 3.1

Exercise 3.1

Page-3.4

Question 1:

Write each of the following as decimals:
(i) 8100
(ii) 20+910+4100
(iii) 23+210+61000

Answer 1:

(i)  We have 8 hundredths.
∴ 8100 = 0.08

(ii) We have 2 tens, 9 tenths and 4 hundredths.
∴ 20 + 910 + 4100 = 20 + 0.9 + 0.04
= 20.94

(iii) We have 2 tens, 3 ones , 2 tenths and 6 thousandths.
23+ 210+ 61000= 23 +0.2 + 0.006
= 23.2006

Question 2:

Convert each of the following into fractions in the lowest form:
(i) 0.04
(ii) 2.34
(iii) 0.342
(iv) 17.38

Answer 2:

i) Multiplying and Dividing 0.04 by 100, we get:
 
0.04×100100=4100=125 
Thus, fraction in the lowest form is 125.

ii) Multiplying and Dividing 2.34 by 100, we get:
 
2.34×100100=234100=11750
Thus, fraction in the lowest form is 11750.

iii) Multiplying and Dividing 0.342 by 1000, we get: 

0.342×10001000=3421000=171500
Therefore, fraction in the lowest form is 171500.

iv) Multiplying and Dividing 17.38 by 100, we get:
 
17.38×100100=1738100=86950
Thus, fraction in the lowest form is 86950.

Question 3:

Express the following fractions as decimals:
(i) 2310
(ii) 2518
(iii) 39735
(iv) 15125

Answer 3:

i)  In the given fraction, we have 2 tenths and 3 ones.

 2310= 2.3
ii) Let us first convert the given fraction to a proper fraction. We get:
 
25182018
To convert 2018 into decimals, let us multiply the numerator and denominator separately by 125. We get:

201×1258×125=251251000=25.125

iii)By simplifying 39735 we get

39 735=3915
Now let us first convert the fraction to a proper fraction. We get: 
3915 = 1965
Now to convert 1965 into decimals, let us multiply the numerator and denominator separately by 2. We get:
196×25×2 = 39210 = 39.2

iv) Let us first convert the given fraction to a proper fraction. We get:

15125 = 37625
To convert 37625 into decimals, let us multiply the numerator and denominator separately by 4. We get:

376×425×4=1504100= 15.04

Question 4:

Add the following:
(i) 41.8, 39.24, 5.01 and 62.6
(ii) 18.03, 146.3, 0.829 and 5.324

Answer 4:

i) Let us first convert the given decimals to like decimals.

We get the decimals as: 41.80, 39.24, 05.01, 62.60

Let us now add them.

   41.80   39.24    05.01+62.60=148.65


ii) Let us first convert the given decimals to like decimals. 

We get the decimals as: 018.030, 146.300, 000.829, 005.324.

Let us now add them.

   018.030
   146.300
   000.829
+ 005.324
= 170.483

Question 5:

Find the value of:
(i) 9.756 − 6.28
(ii) 48.1 − 0.37
(iii) 108.032 − 86.8
(iv) 100 − 26.32

Answer 5:

i) On converting the given decimals to like decimals, we get the new decimals as 9.756 and 6.280.

Let us now subtract them.

        9.756
    - 6.280
    =  3.476
      
ii) On converting the given decimals to like decimals, we get the new decimals as 48.10 and 00.37.

Let us now subtract them.

       48.10
  -  00.37
  =   47.73

iii) On converting the given decimals to like decimals, we get the new decimals as 108.032 and 086.800.  

Let us now subtract them.

      108.032
-   086.800
=      21.232

iv)  On converting the given decimals to like decimals, we get the new decimals as 100.00 and 026.32.

Let us now subtract them.

        100.00
-     026.32
 =      73.68

Question 6:

Take out 3.547 from 7.2

Answer 6:

According to the question, we need to subtract 3.547 from 7.2.

On converting the given decimals to like decimals, we get the new decimals as 3.547 and 7.200.

 Let us now subtract them.

    7.200
- 3.547
=  3.653

Question 7:

What is to be added to 36.85 to get 59.41?

Answer 7:

Let x be added to 36.85 to get 59.41.

36.85 + x = 59.41

or, x = 59.41 - 36.85
        = 22.56

Thus, we need to add 22.56 to 36.85 to get 59.41.

Question 8:

What is to be subtracted from 17.1 to get 2.051?

Answer 8:

Let x be subtracted from 17.1 to get 2.051.

 17.1 - x = 2.051

or, x = 17.1 - 2.051
         =  15.049

Thus, we need to subtract 15.049 from 17.1 to get 2.051.

Question 9:

By how much should 34.79 be increased to get 70.15?

Answer 9:

Let 34.79 be increased by x to get 70.15.

 34.79 + x = 70.15

or, x = 70.15 - 34.79
        = 35.36

Thus, 34.79 should be increased by 35.36 to get 70.15.

Question 10:

By how much should 59.71 be decreased to get 34.58?

Answer 10:

Let 59.71 be decreased by x to get 34.58.
 
 59.71 - x = 34.58

or, x = 59.71 - 34.58
        = 25.13

Thus, 59.71 should be decreased by 25.13 to get 34.58.

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