Recurring decimals can be converted to fractions by representing the repeating decimal as an equation and multiplying both sides by a power of 10 to eliminate the decimal point, then solving for the variable. For example, to convert 0.1, we write 0.1 = x, multiply both sides by 10 to get 1.1 = 10x, then solve to find x = 1/9, representing 0.1 as the fraction 1/9.

1. Recurring decimals
Grade 9
By Mr Tono

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.

3.  E.g.
are all recurring decimals

4. How to convert recurring decimals to fractions

5. Example 1
 Convert 0. 1 to a fraction

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

7. 1. 1 = 10𝑥 Equation 2
0. 1 = 𝑥 Equation 1
1 = 9𝑥
1 = 9𝑥
1
9
= 𝑥