# Decimal as Fraction

We will discuss how to express decimal as fraction.

0.5 = $$\frac{5}{10}$$

0.05 = $$\frac{5}{100}$$

0.005 = $$\frac{5}{1000}$$

2.5 = $$\frac{25}{10}$$

2.25 = $$\frac{225}{100}$$

2.275 = $$\frac{2275}{1000}$$

To convert a decimal into a fraction, remember the following steps.

Step I: Write the number as the numerator omitting the decimal point.

Step II: Write 1 in the denominator and add zeroes to it equal to the number of decimal places.

Note: When a decimal is read, each digit of the decimal part is read separately.

Let us consider some of the following examples on expressing a decimal as a fraction.

1. Convert 2.12 into a fraction.

Solution:

 2.12 = 2 + 1 tenth + 2 hundredths        = 2 + $$\frac{1}{10}$$ + $$\frac{2}{100}$$        = 2 + $$\frac{1 × 10}{10 × 10}$$ + $$\frac{2}{100}$$        = 2 + $$\frac{10}{100}$$ + $$\frac{2}{100}$$        = 2 + $$\frac{10 + 2}{100}$$        = 2 + $$\frac{12}{100}$$        = 2 + $$\frac{3}{25}$$        = 2$$\frac{3}{25}$$ We write the place value of digits of decimal and then add as usual.

2. Convert 5.125 into a fraction.

Solution:

 5.125 = 5 + 1 tenth + 2 hundredths + 5 thousandths         = 5 + $$\frac{1}{10}$$ + $$\frac{2}{100}$$ + $$\frac{5}{1000}$$         = 5 + $$\frac{1 × 100}{10 × 100}$$ + $$\frac{2 × 10}{100 × 10}$$ + $$\frac{5}{1000}$$         = 5 + $$\frac{1 × 100}{10 × 100}$$ + $$\frac{2 × 10}{100 × 10}$$ + $$\frac{5}{1000}$$         = 5 + $$\frac{100}{1000}$$ + $$\frac{20}{1000}$$ + $$\frac{5}{1000}$$         = 5 + $$\frac{100 + 20 + 5}{1000}$$         = 5 + $$\frac{125}{1000}$$         = 5 + $$\frac{1}{8}$$         = 5$$\frac{1}{8}$$ We write the place value of digits of decimal and then add as usual.

Express the following decimals in expanded form:

3.62 = 3 × 1 + $$\frac{6}{10}$$ + $$\frac{2}{10}$$

75.86 = 7 × 10 + 5 × 1 + $$\frac{8}{10}$$ + $$\frac{6}{10}$$

216.894 = 2 × 100 + 1 × 10 + 6 × 1 + $$\frac{8}{10}$$ + $$\frac{9}{100}$$ + $$\frac{4}{1000}$$

0.562 = $$\frac{5}{10}$$ + $$\frac{6}{100}$$ + $$\frac{2}{1000}$$

Express the following as decimal numbers:

For examples:

$$\frac{6}{10}$$ + $$\frac{3}{100}$$                                      =             0.63

$$\frac{6}{10}$$ + $$\frac{3}{100}$$ + $$\frac{5}{1000}$$                           =             0.635

4 × 1 + $$\frac{3}{10}$$ + $$\frac{2}{100}$$                         =              4.32

7 × 10 + 2 × 1 + $$\frac{8}{10}$$ + $$\frac{9}{100}$$           =             72.89

Convert the following decimals to fractions in their lowest terms.

For examples:

0.36 = $$\frac{36}{100}$$ = $$\frac{9}{25}$$ [$$\frac{36 ÷ 4}{100 ÷ 4}$$ = $$\frac{9}{25}$$]

5.65 = 5 + 0.65 = 5 + $$\frac{65}{100}$$ = 5$$\frac{65}{100}$$ = 5$$\frac{13}{20}$$]

14.05 = 14 + 0.05 = 14 + $$\frac{5}{100}$$ = 14$$\frac{5}{100}$$ = 14$$\frac{1}{20}$$]

3.004 = 3 + 0.004 = 3 + $$\frac{4}{1000}$$ = 3$$\frac{4}{1000}$$ = 3$$\frac{1}{250}$$]

Note: We always reduce the fraction converted from a decimal to its lowest form.

Questions and Answers on Conversion of a Decimals to a Fractions:

I. Convert the following decimals as fractions or mixed numerals:

(i) 0.6

(ii) 0.09

(iii) 3.65

(iv) 12.132

(v) 16.5

(vi) 5.46

(vii) 12.29

(viii) 0.008

(ix) 8.08

(x) 162.434

II. Express the following in the expanded form.

(i) 46.25

(ii) 115.32

(iii) 14.568

(iv) 19.005

(v) 77.777

III. Write as decimals:

(i) 2 × 1 + $$\frac{7}{10}$$ + $$\frac{4}{100}$$

(ii) 3 × 10 + 5 × 1 + $$\frac{8}{10}$$ + $$\frac{3}{1000}$$

(iii) 7 × 100 + 4 × 10 + 5 × 1 + $$\frac{4}{1000}$$

(iv) 9 × 100 + $$\frac{7}{10}$$

(v) $$\frac{5}{100}$$ + $$\frac{8}{1000}$$

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