Converting decimals into fractions

Converting decimals into fractions

Remember that place values of decimals decrease by tenth towards the right of the decimal point. Thus, if the decimal has one decimal place, its fraction will have a denominator of 10. If the decimal has two decimal places, its fraction will have a denominator of 100, and if the decimal has three decimal places, its fraction will have a denominator of 1,000. The numerator will be a whole number after converting the decimal into fraction with a denominator of 10, 100 or 1,000.

Example

Convert each of the following decimals into fractions:

(a) 0.2 (b) 0.32

Solution

(a) 0.2

Write the decimal as a fraction. That is, $\frac{0.2}{1}$.

Multiply both the numerator and the denominator by 10 to remove the decimal place:

$\frac{0.2 \times 10}{1 \times 10} = \frac{2}{10} = \frac{1}{5}$

Therefore, 0.2 in fraction is $\frac{1}{5}$.

(b) 0.32

Write the decimal as a fraction. That is, $\frac{0.32}{1}$.

Multiply both the numerator and the denominator by 100 to remove the decimal places:

$\frac{0.32 \times 100}{1 \times 100} = \frac{32}{100}$

Simplify $\frac{32}{100}$ to get $\frac{8}{25}$.

Therefore, 0.32 in fraction is $\frac{8}{25}$.