Let us see the relationship between fractions and decimals. 1. Conversion of Fractions to Decimals 2. Conversion of Decimals to Fractions

**Fractions and Decimals**

Let us see the relationship between fractions
and decimals.

** **

__1. Conversion of Fractions to Decimals__

We are familiar with fraction as a part
of a whole. The place value of the decimal digits of a number are tenths (1/10),
hundredths (1/100) , thousandths (1/1000) and so on.

If the denominator of a fraction is any
of 10,10^{2} ,10^{3}, ... we can express them as decimals. Consider
the example of distributing a box of 10 pencils to ten students. The portion of
pencils given to 6 students will be 6/10 which can be expressed as 0.6.

If the denominator of a fraction is any
number that can be made as powers of 10 using the concept of equivalent fractions,
then it can also be expressed as decimals. Consider the example of sharing 5 peanut
cakes among five friends. The share of one person is 1/5. To represent this
fraction as a decinal number. We first convert the denominator into 10. This can
be done by writing the equivalent fraction of 1/5, namely 2/10 . Now the decimal representation
of 2/10 is 0.2

**Think**

Can you express the denominators
of all fractions as powers of 10?

** **

__2. Conversion of Decimals to Fractions__

As we convert
fractions into a decimal number, the decimal numbers can also be expressed as fractions.

For example,
let the price of brand ‘*x*’ slippers be ₹ 399.95

Expanding the
above price, we get,

399.95 = 3 ×100 + 9 ×10 + 9 ×1 + 9 × 1/10 + 5×1/100

= 399 + 95/100 = 39995/100 = 7999/20

Similarly, if the price of brand ‘y’
slipper is ₹ 159.95, then it can be expressed in terms of fractions as below.

159.95 = 159 + 95/100 = 15995/100 = 3199/20

**Try these**

**1. Convert the following fractions into the decimal numbers. **

**(i) 16/1000**

**(ii) 638/10**

**(iii) 1/20**

**(iv) 3/50 **

**(i)** 16/1000 = 0.016

**(ii)** 638 / 10 = 638

**(iii) **1/20 × 5/5 = 5/100 = 0.05

**(iv) **3/50 × 2/2 = 6/100 = 0.06

**2. Write the fraction for each of the following:**

**(i) 6 hundreds + 3 tens + 3 ones + 6 hundredths + 3 thousandths.**

**(ii) 3 thousands + 3 hundreds + 4 tens + 9 ones + 6 tenths.**

**(i) 6 hudreds + 3 tens
+ 3 ones + 6 hundredths + 3 thousandths. . .**

6 × 100 – 3 × 10 + 3 × 1+ 6 × 1/100 + 3 × 1/ 1000

600+ 30 + 3 + 6/100 + 3/1000

633063

**(ii) 3 thousands +
3 hundreds + 4 tens + 9 ones + 6 tenths.**

3 × 1000 + 3 × 100 + 4 × 10
+ 9 × 1+ 6 × 1/10

3000– 300 + 40 + 9 + 6/10

33496

**3. Convert the following decimals into fractions.**

**(i) 0.0005 **

**(ii) 6.24**

**(i) **0.0005 = 5 / 10000 = 1 / 2000

**(ii) **6.24 = 624 / 100 = 156 / 25

** **

__Example 1.6__

Write the shaded portion
of the figures given below as a fraction and as a** **decimal number.

*Solution*

** **

__Example 1.7 __

Express the following fractions
as decimal numbers.

*Solution*

** **

__Example 1.8____ __

Write the following fractions as decimals.

*Solution*

(i) We have to find a fraction equivalent
to 2/5 whose denominator is 10.

(ii) We have to find a fraction equivalent
to 3/4 with denominator 100. Since there is no whole number that gives 10 when multiplied
by 4, let us make the denominator as 100.

(iii) In 9/1000 , tenth and hundredth
place is zero.

Therefore, = 9/1000 = 0.009

(iv) We have to find a fraction equivalent
to 1/50 whose denominator is 100.

(v) In 3 1/5, keep the whole number 3
as such, we can find a fraction equivalent to 1/5 with denominator 10.

** **

__Example 1.9__

Convert the following into simplest fractions.

(i) 0.04

(ii) 3.46

(iii) 0.862

**Solution**

** **

__Example 1.10 __

Find the decimal form of
the following fractions.

**Solution**

= 23.608 (since hundredths place is not there, it is taken as '0')

** **

__Example 1.11__

Write each of the following as decimals.

(i) Four hundred four and five hundredths

(ii) Two and twenty five thousandths.

**Solution**

(i) Four hundred four and five hundredths.

= 404 + 5/100

= 404 + [ 0 × 1/10 + 5 × 1/100 ] = 404.05

(ii) Two and twenty five thousandths

= 2.025 [as there is no tenth we take it as
0 tenth]

**Note**

For any decimal number,
number of zeroes in the denominator and number
of decimal digits are equal.

** **

__Example 1.12__

Express the following as fractions (i)
A capsule contains 0.85 mg of medicine. (ii) A juice container has 4.5 litres of
mango juice.

**Solution**

A decimal is a fraction
written in a special form. Decimal comes from the Latin word 'decimus' which means
tenth. It comes from the root word 'decem'

Tags : Number System | Term 2 Chapter 1 | 7th Maths , 7th Maths : Term 2 Unit 1 : Number System

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7th Maths : Term 2 Unit 1 : Number System : Fractions and Decimals | Number System | Term 2 Chapter 1 | 7th Maths

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