RD Sharma Solutions: Decimals (Exercise 7.4)

# Decimals (Exercise 7.4) RD Sharma Solutions | Mathematics (Maths) Class 6 PDF Download

``` Page 1

Exercise 7.4                                                                               page: 7.4
1. Express the following fractions as decimals:
(i) 23/10
(ii) 139/100
(iii) 4375/1000
(iv) 12 1/2
(v) 75 1/4
(vi) 25 1/8
(vii) 18 3/24
(viii) 39 7/35
(ix) 15 1/25
(x) 111/250
Solution:

(i) 23/10
It can be written as
= 20 + 3/10
We get
= 20/10 + 3/10
= 2 + 3/10
So we get
= 2.3

(ii) 139/100
It can be written as
= 100 + 30 + 9/100
We get
= 100/100 + 30/100 + 9/100
= 1 + 3/10 + 9/100
So we get
= 1.39

(iii) 4375/1000
It can be written as
= 4000 + 300 + 70 + 5/1000
We get
= 4000/1000 + 300/1000 + 70/1000 + 5/1000
= 4 + 3/10 + 7/100 + 5/1000
So we get
= 4.375

(iv) 12 1/2
It can be written as
= 12 + 1/2
Multiplying and dividing by 5 to get denominator as 10
Page 2

Exercise 7.4                                                                               page: 7.4
1. Express the following fractions as decimals:
(i) 23/10
(ii) 139/100
(iii) 4375/1000
(iv) 12 1/2
(v) 75 1/4
(vi) 25 1/8
(vii) 18 3/24
(viii) 39 7/35
(ix) 15 1/25
(x) 111/250
Solution:

(i) 23/10
It can be written as
= 20 + 3/10
We get
= 20/10 + 3/10
= 2 + 3/10
So we get
= 2.3

(ii) 139/100
It can be written as
= 100 + 30 + 9/100
We get
= 100/100 + 30/100 + 9/100
= 1 + 3/10 + 9/100
So we get
= 1.39

(iii) 4375/1000
It can be written as
= 4000 + 300 + 70 + 5/1000
We get
= 4000/1000 + 300/1000 + 70/1000 + 5/1000
= 4 + 3/10 + 7/100 + 5/1000
So we get
= 4.375

(iv) 12 1/2
It can be written as
= 12 + 1/2
Multiplying and dividing by 5 to get denominator as 10

= 12 + [(1/2) × (5/5)]
On further calculation
= 12 + 5/10
So we get
= 12.5

(v) 75 1/4
It can be written as
= 75 + 1/4
Multiplying and dividing by 25 to get 100 as denominator
= 75 + [(1/4) × (25/25)]
On further calculation
= 75 + 25/100
= 75.25

(vi) 25 1/8
It can be written as
= 25 + 1/8
Multiplying and dividing by 125 to get 1000 as denominator
= 25 + [(1/8) × (125/125)]
On further calculation
= 25 + 125/1000
= 25.125

(vii) 18 3/24
It can be written as
= 18 + 3/24
We get
= 18 + 1/8
Multiplying and dividing by 125 to get 1000 as denominator
= 18 + [(1/8) × (125/125)]
On further calculation
= 18 + 125/1000
= 18.125

(viii) 39 7/35
It can be written as
= 39 + 7/35
We get
= 39 + 1/5
Multiplying and dividing by 2 to get 10 as denominator
= 39 + [(1/5) × (2/2)]
On further calculation
= 39 + 2/10
= 39.2
Page 3

Exercise 7.4                                                                               page: 7.4
1. Express the following fractions as decimals:
(i) 23/10
(ii) 139/100
(iii) 4375/1000
(iv) 12 1/2
(v) 75 1/4
(vi) 25 1/8
(vii) 18 3/24
(viii) 39 7/35
(ix) 15 1/25
(x) 111/250
Solution:

(i) 23/10
It can be written as
= 20 + 3/10
We get
= 20/10 + 3/10
= 2 + 3/10
So we get
= 2.3

(ii) 139/100
It can be written as
= 100 + 30 + 9/100
We get
= 100/100 + 30/100 + 9/100
= 1 + 3/10 + 9/100
So we get
= 1.39

(iii) 4375/1000
It can be written as
= 4000 + 300 + 70 + 5/1000
We get
= 4000/1000 + 300/1000 + 70/1000 + 5/1000
= 4 + 3/10 + 7/100 + 5/1000
So we get
= 4.375

(iv) 12 1/2
It can be written as
= 12 + 1/2
Multiplying and dividing by 5 to get denominator as 10

= 12 + [(1/2) × (5/5)]
On further calculation
= 12 + 5/10
So we get
= 12.5

(v) 75 1/4
It can be written as
= 75 + 1/4
Multiplying and dividing by 25 to get 100 as denominator
= 75 + [(1/4) × (25/25)]
On further calculation
= 75 + 25/100
= 75.25

(vi) 25 1/8
It can be written as
= 25 + 1/8
Multiplying and dividing by 125 to get 1000 as denominator
= 25 + [(1/8) × (125/125)]
On further calculation
= 25 + 125/1000
= 25.125

(vii) 18 3/24
It can be written as
= 18 + 3/24
We get
= 18 + 1/8
Multiplying and dividing by 125 to get 1000 as denominator
= 18 + [(1/8) × (125/125)]
On further calculation
= 18 + 125/1000
= 18.125

(viii) 39 7/35
It can be written as
= 39 + 7/35
We get
= 39 + 1/5
Multiplying and dividing by 2 to get 10 as denominator
= 39 + [(1/5) × (2/2)]
On further calculation
= 39 + 2/10
= 39.2

(ix) 15 1/25
It can be written as
= 15 + 1/25
Multiplying and dividing by 4 to get 100 as denominator
= 15 + [(1/25) × (4/4)]
On further calculation
= 15 + 4/100
= 15.04

(x) 111/250
It can be written as
= 111 × [(1/250) × (4/4)]
On further calculation
= 444/1000
By division
= 0.444

2. Express the following decimals as fractions in the lowest form:
(i) 0.5
(ii) 2.5
(iii) 0.60
(iv) 0.18
(v) 5.25
(vi) 7.125
(vii) 15.004
(viii) 20.375
(ix) 600.75
(x) 59.48
Solution:

(i) 0.5
It can be written as
= 5/10
By division
= 1/2

(ii) 2.5
It can be written as
= 25/10
By division
= 5/2

(iii) 0.60
It can be written as
= 60/100
By division
= 3/5

(iv) 0.18
Page 4

Exercise 7.4                                                                               page: 7.4
1. Express the following fractions as decimals:
(i) 23/10
(ii) 139/100
(iii) 4375/1000
(iv) 12 1/2
(v) 75 1/4
(vi) 25 1/8
(vii) 18 3/24
(viii) 39 7/35
(ix) 15 1/25
(x) 111/250
Solution:

(i) 23/10
It can be written as
= 20 + 3/10
We get
= 20/10 + 3/10
= 2 + 3/10
So we get
= 2.3

(ii) 139/100
It can be written as
= 100 + 30 + 9/100
We get
= 100/100 + 30/100 + 9/100
= 1 + 3/10 + 9/100
So we get
= 1.39

(iii) 4375/1000
It can be written as
= 4000 + 300 + 70 + 5/1000
We get
= 4000/1000 + 300/1000 + 70/1000 + 5/1000
= 4 + 3/10 + 7/100 + 5/1000
So we get
= 4.375

(iv) 12 1/2
It can be written as
= 12 + 1/2
Multiplying and dividing by 5 to get denominator as 10

= 12 + [(1/2) × (5/5)]
On further calculation
= 12 + 5/10
So we get
= 12.5

(v) 75 1/4
It can be written as
= 75 + 1/4
Multiplying and dividing by 25 to get 100 as denominator
= 75 + [(1/4) × (25/25)]
On further calculation
= 75 + 25/100
= 75.25

(vi) 25 1/8
It can be written as
= 25 + 1/8
Multiplying and dividing by 125 to get 1000 as denominator
= 25 + [(1/8) × (125/125)]
On further calculation
= 25 + 125/1000
= 25.125

(vii) 18 3/24
It can be written as
= 18 + 3/24
We get
= 18 + 1/8
Multiplying and dividing by 125 to get 1000 as denominator
= 18 + [(1/8) × (125/125)]
On further calculation
= 18 + 125/1000
= 18.125

(viii) 39 7/35
It can be written as
= 39 + 7/35
We get
= 39 + 1/5
Multiplying and dividing by 2 to get 10 as denominator
= 39 + [(1/5) × (2/2)]
On further calculation
= 39 + 2/10
= 39.2

(ix) 15 1/25
It can be written as
= 15 + 1/25
Multiplying and dividing by 4 to get 100 as denominator
= 15 + [(1/25) × (4/4)]
On further calculation
= 15 + 4/100
= 15.04

(x) 111/250
It can be written as
= 111 × [(1/250) × (4/4)]
On further calculation
= 444/1000
By division
= 0.444

2. Express the following decimals as fractions in the lowest form:
(i) 0.5
(ii) 2.5
(iii) 0.60
(iv) 0.18
(v) 5.25
(vi) 7.125
(vii) 15.004
(viii) 20.375
(ix) 600.75
(x) 59.48
Solution:

(i) 0.5
It can be written as
= 5/10
By division
= 1/2

(ii) 2.5
It can be written as
= 25/10
By division
= 5/2

(iii) 0.60
It can be written as
= 60/100
By division
= 3/5

(iv) 0.18

It can be written as
= 18/100
By division
= 9/50

(v) 5.25
It can be written as
= 525/100
By division
= 21/4

(vi) 7.125
It can be written as
= 7125/1000
By division
= 57/8

(vii) 15.004
It can be written as
= 15004/1000
By division
= 3751/250

(viii) 20.375
It can be written as
= 20375/1000
By division
= 163/8

(ix) 600.75
It can be written as
= 60075/100
By division
= 2403/4

(x) 59.48
It can be written as
= 5948/100
By division
= 1487/25

```

## Mathematics (Maths) Class 6

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## Mathematics (Maths) Class 6

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