| Need to convert a repeating decimal to a fraction? Follow these examples: Note the following pattern for repeating decimals: 0.22222222... = 2/9 0.54545454... = 54/99 0.298298298... = 298/999 Division by 9's causes the repeating pattern. Note the pattern if zeros preceed the repeating decimal: 0.022222222... = 2/90 0.00054545454... = 54/99000 0.00298298298... = 298/99900 Adding zero's to the denominator adds zero's before the repeating decimal. To convert a decimal that begins with a non-repeating part, such as 0.21456456456456456..., to a fraction, write it as the sum of the non-repeating part and the repeating part. 0.21 + 0.00456456456456456... Next, convert each of these decimals to fractions. The first decimal has a divisor of power ten. The second decimal (which repeats) is convirted according to the pattern given above. 21/100 + 456/99900 Now add these fraction by expressing both with a common divisor 20979/99900 + 456/99900 and add. 21435/99900 Finally simplify it to lowest terms 1429/6660 and check on your calculator or with long division. = 0.2145645645... |
| Converting a Repeating Decimal to a Fraction. |