# Converting Fractions to Decimals

In converting fractions to decimals, we know that decimals are fractions with denominators 10, 100, 1000 etc. In order to convert other fractions into decimals, we follow the following steps:

Step I: Convert the fraction into an equivalent fraction with denominator 10 or 100 or 1000 if it is not so.

Step II: Take the given fraction’s numerator. Then mark the decimal point after one place or two places or three places from right towards left if the given fraction’s denominator is 10 or 100 or 1000 respectively.

Note that; insert zeroes at the left of the numerator if the numerator has fewer digits.

● To convert a fraction having 10 in the denominator, we put the decimal point one place left of the first digit in the numerator.

For example:

(i) $$\frac{6}{10}$$ = .6 or 0.6

(ii) $$\frac{16}{10}$$ = 1.6

(iii) $$\frac{116}{10}$$ = 11.6

(iv) $$\frac{1116}{10}$$ = 111.6

● To convert a fraction having 100 in the denominator, we put the decimal point two places left of the first digit in the numerator.

For example:

(i) $$\frac{7}{100}$$ = 0.07

(ii) $$\frac{77}{100}$$ = 0.77

(iii) $$\frac{777}{100}$$ = 7.77

(iv) $$\frac{7777}{100}$$ = 77.77

● To convert a fraction having 1000 in the denominator, we put the decimal point three places left of the first digit in the numerator.

For example:

(i) $$\frac{9}{1000}$$ = 0.009

(ii) $$\frac{99}{1000}$$ = 0.099

(iii) $$\frac{999}{1000}$$ = 0.999

(iv) $$\frac{9999}{1000}$$ = 9.999

The problem will help us to understand how to convert fraction into decimal.

In $$\frac{351}{100}$$ we will change the fraction to decimal.

First write the numerator and then divide the numerator by denominator and complete the division.

Put the decimal point such that the number of digits in the decimal part is the same as the number of zeros in the denominator. Let us check the division of decimal by showing a complete step by step decimal divide. We know that when the number obtained by dividing by the denominator is the decimal form of the fraction.

There can be two situations in converting fractions to decimals:

When division stops after a certain number of steps as the remainder becomes zero.

When division continues as there is a remainder after every step.

Here, we will discuss when the division is complete.

Explanation on the method using a step-by-step example:

Divide the numerator by denominator and complete the division.

If a non-zero remainder is left, then put the decimal point in the dividend and the quotient.

Now, put zero to the right of dividend and to the right of remainder.

Divide as in case of whole number by repeating the above process until the remainder becomes zero.

1. Convert $$\frac{233}{100}$$ into decimal.

Solution: 2. Express each of the following as decimals.

(i) $$\frac{15}{2}$$

Solution:

$$\frac{15}{2}$$

= $$\frac{15 × 5}{2 × 5}$$

= $$\frac{75}{10}$$

= 7.5

(Making the denominator 10 or higher power of 10)

(ii) $$\frac{19}{25}$$

Solution:

$$\frac{19}{25}$$

= $$\frac{19 × 4}{25 × 4}$$

= $$\frac{76}{100}$$

= 0.76

(iii) $$\frac{7}{50}$$

Solution:

$$\frac{7}{50}$$ = $$\frac{7 × 2}{50 × 2}$$ = $$\frac{14}{100}$$ = 0.14

Note:

Conversion of fractions into decimals when denominator cannot be converted to 10 or higher power of 10 will be done in division of decimals.

Examples on Conversion of Fractions into Decimal Numbers:

Express the following fractions as decimals:

1. $$\frac{3}{10}$$

Solution:

Using the above method, we have

$$\frac{3}{10}$$

= 0.3

2. $$\frac{1479}{1000}$$

Solution:

$$\frac{1479}{1000}$$

= 1.479

3. 7$$\frac{1}{2}$$

Solution:

7$$\frac{1}{2}$$

= 7 + $$\frac{1}{2}$$

= 7 + $$\frac{5 × 1}{5 × 2}$$

= 7 + $$\frac{5}{10}$$

= 7 + 0.5

= 7.5

4. 9$$\frac{1}{4}$$

Solution:

9$$\frac{1}{4}$$

= 9 + $$\frac{1}{4}$$

= 9 + $$\frac{25 × 1}{25 × 4}$$

= 9 + $$\frac{25}{100}$$

= 9 + 0.25

= 9.25

5. 12$$\frac{1}{8}$$

Solution:

12$$\frac{1}{8}$$

= 12 + $$\frac{1}{8}$$

= 12 + $$\frac{125 × 1}{125 × 8}$$

= 12 + $$\frac{125}{1000}$$

= 12 + 0.125

= 12.125

Practice Problems on Converting Fractions to Decimals:

1. Convert the following fractional numbers to decimal numbers:

(i) $$\frac{7}{10}$$

(ii) $$\frac{23}{100}$$

(iii) $$\frac{172}{100}$$

(iv) $$\frac{4905}{100}$$

(v) $$\frac{9}{1000}$$

(vi) $$\frac{84}{1000}$$

(i) $$\frac{672}{1000}$$

(i) $$\frac{4747}{1000}$$

(i) 0.7

(ii) 0.23

(iii) 1.72

(iv) 49.05

(v) 0.009

(vi) 0.084

(i) 0.672

(i) 4.747

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