0.808080… as a Fraction

0.808080… (0.80 repeating) as a fraction is 80/99.

How to convert 0.808080… to a fraction

  1. Let x = 0.808080... (the underlined part, 80, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 80.808080...
  3. Subtract to cancel the repeating tail: 100x − x = 80 − 0, so 99x = 80.
  4. Solve: x = 80/99. The greatest common divisor is 1, so x = 80/99 (already in lowest terms).

Check

Divide 80 by 99 on a calculator: 80 ÷ 99 = 0.8080808081… which matches 0.808080….

Similar repeating decimals

DecimalFraction
0.787878…26/33
0.7888…71/90
0.789789789…263/333
0.797979…79/99
0.8111…73/90
0.818181…9/11
0.8222…37/45
0.828282…82/99

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