# Converting between decimals and fractions

## Converting decimals to fractions

$$0.38$$ means $$38$$ hundredths, so:

$0.38 = \frac{38}{100} = \frac{19}{50}$

Similarly, $$0.4$$ means $$4$$ tenths, so:

$0.4 = \frac{4}{10} = \frac{2}{5}$

And $$0.125$$ means $$125$$ thousandths, so:

$0.125 = \frac{125}{1,000} = \frac{1}{8}$

Question

Write $$0.7$$ as a fraction in its simplest form.

$\frac{7}{10}$

## Converting fractions to decimals

$$\frac{3}{10}$$ means three tenths, and is written as $$0.3$$.

$$\frac{17}{100}$$ means seventeen hundredths, and is written as $$0.17$$.

Question

Write $$\frac{9}{100}$$ as a decimal.

$\frac{9}{100} = 0.09$

## Using a calculator

When the bottom number isn't a multiple of $$10$$, convert a fraction to a decimal by dividing the top number by the bottom. You can use a calculator to help you.

For example:

$\frac{3}{4} = 3 \div 4 = 0.75$

$\frac{16}{25} = 16 \div 25 = 0.64$