0.282828… as a Fraction

0.282828… (0.28 repeating) as a fraction is 28/99.

How to convert 0.282828… to a fraction

  1. Let x = 0.282828... (the underlined part, 28, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 28.282828...
  3. Subtract to cancel the repeating tail: 100x − x = 28 − 0, so 99x = 28.
  4. Solve: x = 28/99. The greatest common divisor is 1, so x = 28/99 (already in lowest terms).

Check

Divide 28 by 99 on a calculator: 28 ÷ 99 = 0.2828282828… which matches 0.282828….

Similar repeating decimals

DecimalFraction
0.262626…26/99
0.2666…4/15
0.272727…3/11
0.2777…5/18
0.285285285…95/333
0.2888…13/45
0.292929…29/99
0.303030…10/33

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