0.787878… as a Fraction

0.787878… (0.78 repeating) as a fraction is 26/33.

How to convert 0.787878… to a fraction

  1. Let x = 0.787878... (the underlined part, 78, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 78.787878...
  3. Subtract to cancel the repeating tail: 100x − x = 78 − 0, so 99x = 78.
  4. Solve: x = 78/99. The greatest common divisor is 3, so x = 26/33.

Check

Divide 26 by 33 on a calculator: 26 ÷ 33 = 0.7878787879… which matches 0.787878….

Similar repeating decimals

DecimalFraction
0.7666…23/30
0.767676…76/99
0.769769769…769/999
0.777…7/9
0.7888…71/90
0.789789789…263/333
0.797979…79/99
0.808080…80/99

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