Converting Repeating Decimals to Fractions
This procedure is when all digits after the decimal point repeat. There is one different step if
1
5
you are converting a decimal such as 0.16 , which equals , or 0.83 which equals .
6
6
A. Single digit REPEATING
You have 0.3 and need to change it to a fraction. Follow these steps:
x = 0.3
1. Write your decimal as an equation:
2. How many digits are after the decimal point?
3. Multiply the equation (both sides) by
1
101 = 10
10x = 3.3
(The power you use is the number of digits that repeat.)
4. Subtract the 1st equation from the 2nd equation
10x = 3.3
– x = 0.3
9x = 3.0
5. Divide to get x by itself and simplify!
x=
3
1
=
9
3
B. Multiple digits REPEATING
You have 0.54 and need to change it to a fraction. Follow these steps:
1. Write your decimal as an equation:
x = 0.54
2. How many digits are after the decimal point?
3. Multiply the equation (both sides) by
2
102 = 100
100x = 54.54
(The power you use is the number of digits that repeat.)
4. Subtract the 1st equation from the 2nd equation
100x = 54.54
– x = 0.54
99x = 54.0
5. Divide to get x by itself and simplify!
x=
54
6
=
99
11
Convert 0.5 , 0.18 and 0.003 to fractions, following the steps above.