0.0777… as a Fraction

0.0777… (0.07 repeating) as a fraction is 7/90.

How to convert 0.0777… to a fraction

  1. Let x = 0.0777... (the underlined part, 7, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 7.777...
  3. Move the decimal point past the non-repeating digits too: 10x = 0.7777...
  4. Subtract to cancel the repeating tail: 100x − 10x = 7 − 0, so 90x = 7.
  5. Solve: x = 7/90. The greatest common divisor is 1, so x = 7/90 (already in lowest terms).

Check

Divide 7 by 90 on a calculator: 7 ÷ 90 = 0.0777777778… which matches 0.0777….

Similar repeating decimals

DecimalFraction
0.070707…7/99
0.074074074…2/27
0.076076076…76/999
0.076923076923076923…1/13
0.080808…8/99
0.081081081…3/37
0.08333…1/12
0.08666…13/150

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