0.074074074… as a Fraction

0.074074074… (0.074 repeating) as a fraction is 2/27.

How to convert 0.074074074… to a fraction

  1. Let x = 0.074074074... (the underlined part, 074, repeats forever).
  2. Move the decimal point past one full repeating block: 1000x = 74.074074074...
  3. Subtract to cancel the repeating tail: 1000x − x = 74 − 0, so 999x = 74.
  4. Solve: x = 74/999. The greatest common divisor is 37, so x = 2/27.

Check

Divide 2 by 27 on a calculator: 2 ÷ 27 = 0.0740740741… which matches 0.074074074….

Similar repeating decimals

DecimalFraction
0.0666…1/15
0.070707…7/99
0.076076076…76/999
0.076923076923076923…1/13
0.0777…7/90
0.080808…8/99
0.081081081…3/37
0.08333…1/12

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