0.0888… as a Fraction

0.0888… (0.08 repeating) as a fraction is 4/45.

How to convert 0.0888… to a fraction

  1. Let x = 0.0888... (the underlined part, 8, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 8.888...
  3. Move the decimal point past the non-repeating digits too: 10x = 0.8888...
  4. Subtract to cancel the repeating tail: 100x − 10x = 8 − 0, so 90x = 8.
  5. Solve: x = 8/90. The greatest common divisor is 2, so x = 4/45.

Check

Divide 4 by 45 on a calculator: 4 ÷ 45 = 0.0888888889… which matches 0.0888….

Similar repeating decimals

DecimalFraction
0.076923076923076923…1/13
0.0777…7/90
0.080808…8/99
0.081081081…3/37
0.08333…1/12
0.08666…13/150
0.090909…1/11
0.101010…10/99

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