0.070707… as a Fraction

0.070707… (0.07 repeating) as a fraction is 7/99.

How to convert 0.070707… to a fraction

  1. Let x = 0.070707... (the underlined part, 07, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 7.070707...
  3. Subtract to cancel the repeating tail: 100x − x = 7 − 0, so 99x = 7.
  4. Solve: x = 7/99. The greatest common divisor is 1, so x = 7/99 (already in lowest terms).

Check

Divide 7 by 99 on a calculator: 7 ÷ 99 = 0.0707070707… which matches 0.070707….

Similar repeating decimals

DecimalFraction
0.060606…2/33
0.0666…1/15
0.074074074…2/27
0.076076076…76/999
0.076923076923076923…1/13
0.0777…7/90
0.080808…8/99
0.081081081…3/37

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