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:

\[\frac{3}{4} = 3 \div 4 = 0.75\]

\[\frac{16}{25} = 16 \div 25 = 0.64\]