0.080808… as a Fraction

0.080808… (0.08 repeating) as a fraction is 8/99.

How to convert 0.080808… to a fraction

  1. Let x = 0.080808... (the underlined part, 08, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 8.080808...
  3. Subtract to cancel the repeating tail: 100x − x = 8 − 0, so 99x = 8.
  4. Solve: x = 8/99. The greatest common divisor is 1, so x = 8/99 (already in lowest terms).

Check

Divide 8 by 99 on a calculator: 8 ÷ 99 = 0.0808080808… which matches 0.080808….

Similar repeating decimals

DecimalFraction
0.074074074…2/27
0.076076076…76/999
0.076923076923076923…1/13
0.0777…7/90
0.081081081…3/37
0.08333…1/12
0.08666…13/150
0.0888…4/45

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