0.5222… as a Fraction

0.5222… (0.52 repeating) as a fraction is 47/90.

How to convert 0.5222… to a fraction

  1. Let x = 0.5222... (the underlined part, 2, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 52.222...
  3. Move the decimal point past the non-repeating digits too: 10x = 5.2222...
  4. Subtract to cancel the repeating tail: 100x − 10x = 52 − 5, so 90x = 47.
  5. Solve: x = 47/90. The greatest common divisor is 1, so x = 47/90 (already in lowest terms).

Check

Divide 47 by 90 on a calculator: 47 ÷ 90 = 0.5222222222… which matches 0.5222….

Similar repeating decimals

DecimalFraction
0.505050…50/99
0.5111…23/45
0.515151…17/33
0.525252…52/99
0.5333…8/15
0.535353…53/99
0.538538538…538/999
0.5444…49/90

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