Fraction to Decimal Conversion

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...