0.789789789… as a Fraction

0.789789789… (0.789 repeating) as a fraction is 263/333.

How to convert 0.789789789… to a fraction

  1. Let x = 0.789789789... (the underlined part, 789, repeats forever).
  2. Move the decimal point past one full repeating block: 1000x = 789.789789789...
  3. Subtract to cancel the repeating tail: 1000x − x = 789 − 0, so 999x = 789.
  4. Solve: x = 789/999. The greatest common divisor is 3, so x = 263/333.

Check

Divide 263 by 333 on a calculator: 263 ÷ 333 = 0.7897897898… which matches 0.789789789….

Similar repeating decimals

DecimalFraction
0.767676…76/99
0.769769769…769/999
0.777…7/9
0.787878…26/33
0.7888…71/90
0.797979…79/99
0.808080…80/99
0.8111…73/90

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