0.5333… as a Fraction

0.5333… (0.53 repeating) as a fraction is 8/15.

How to convert 0.5333… to a fraction

  1. Let x = 0.5333... (the underlined part, 3, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 53.333...
  3. Move the decimal point past the non-repeating digits too: 10x = 5.3333...
  4. Subtract to cancel the repeating tail: 100x − 10x = 53 − 5, so 90x = 48.
  5. Solve: x = 48/90. The greatest common divisor is 6, so x = 8/15.

Check

Divide 8 by 15 on a calculator: 8 ÷ 15 = 0.5333333333… which matches 0.5333….

Similar repeating decimals

DecimalFraction
0.5111…23/45
0.515151…17/33
0.5222…47/90
0.525252…52/99
0.535353…53/99
0.538538538…538/999
0.5444…49/90
0.545454…6/11

See also: 8/15 as a decimal.

Another decimal? Browse the repeating decimal to fraction chart, the terminating decimal chart, or use the decimal to fraction converter.