0.7888… as a Fraction

0.7888… (0.78 repeating) as a fraction is 71/90.

How to convert 0.7888… to a fraction

  1. Let x = 0.7888... (the underlined part, 8, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 78.888...
  3. Move the decimal point past the non-repeating digits too: 10x = 7.8888...
  4. Subtract to cancel the repeating tail: 100x − 10x = 78 − 7, so 90x = 71.
  5. Solve: x = 71/90. The greatest common divisor is 1, so x = 71/90 (already in lowest terms).

Check

Divide 71 by 90 on a calculator: 71 ÷ 90 = 0.7888888889… which matches 0.7888….

Similar repeating decimals

DecimalFraction
0.7666…23/30
0.767676…76/99
0.769769769…769/999
0.777…7/9
0.787878…26/33
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.