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Math and Arithmetic
Percentages, Fractions, and Decimal Values

# How do you do recurring decimals to a percentage?

###### October 10, 2010 9:29PM

Multiplying decimals by 100 will convert them to percentages.

If you wish to remove the recurring decimal, convert it to a fraction by putting the recurring digit(s) as the numerator over a denominator of the same number of 9s and reducing the fraction to its lowest terms.

Examples

• 0.333333333...
To a percentage: 0.333333333... x 100 = 33.3333333...%

0.3333333... as a fraction: repeating digit is 3 so put as the numerator over a denominator of one 9 to give the fraction 3/9 = 1/3

So 0.333333333... = 33 1/3 %

• 0.1428571428...
To a percentage: 0.1428571428... x 100 = 14.28571428...%

0.28571428... as a fraction: repeating digits are 285714 of which there are six, so put as numerator over a denominator of six 9s to give the fraction 285714/999999 = 2/7

So 0.1428571428... = 14 2/7 %