# Converting recurring decimals to fractions

There are five kinds of recurring decimals

# With 0 as the whole number

1. $0.\overline{X}$ This is the simplest recurring decimal, where there is only one number after the decimal and it is recurring. To convert, see one recurring digit after the decimal

2. $0.\overline{X...Y}$ A slightly more complex recurring decimal, where there are two or more numbers after the decimal and all of them are recurring. To convert, see N recurring digits after the decimal

3. $0.W...X\overline{Y...Z}$ Any number of non-recurring numbers after the decimal, along with any number of recurring decimals. To convert, see N non-recurring and N recurring digits after the decimal

# With any number as the whole number

If any number apart from 0 is the whole number, separate the expression into whole + 0.decimal.

For ex.

$1.\overline{3} = 1+0.\overline{3}$

Then solve using the 0 as a whole number method and convert the resulting mixed fraction to improper form.

$=1+\frac{3}{9} = 1+\frac{1}{3} = 1\frac{1}{3} = \frac{4}{3}$