2. Converting recurring decimals to
fractions
Converting recurring decimals to fractions is representing a recurring decimal as a
fraction without changing its value.
A recurring decimal is a decimal number that has a digit (or group of digits) that
repeats forever. The part that repeats can also be shown by placing dots over the first
and last digits of the repeating pattern.
6. 0. 1 = 𝑥 Equation 1
Because 0. 1 = 𝑥 has one repeating digit, we will multiply by 10
0. 1 × 10 = 1. 1
Remember because you are multiplying the whole of Equation 1 you also need to
multiply the variable 𝑥 by 10 (see below)
0. 1 = 𝑥 Equation 1
0. 1 × 10 = 𝑥 × 10
1. 1 = 10𝑥 Equation 2