0.707070… as a Fraction

0.707070… (0.70 repeating) as a fraction is 70/99.

How to convert 0.707070… to a fraction

  1. Let x = 0.707070... (the underlined part, 70, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 70.707070...
  3. Subtract to cancel the repeating tail: 100x − x = 70 − 0, so 99x = 70.
  4. Solve: x = 70/99. The greatest common divisor is 1, so x = 70/99 (already in lowest terms).

Check

Divide 70 by 99 on a calculator: 70 ÷ 99 = 0.7070707071… which matches 0.707070….

Similar repeating decimals

DecimalFraction
0.686868…68/99
0.6888…31/45
0.692692692…692/999
0.696969…23/33
0.7111…32/45
0.714714714…238/333
0.717171…71/99
0.7222…13/18

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