0.3777… as a Fraction

0.3777… (0.37 repeating) as a fraction is 17/45.

How to convert 0.3777… to a fraction

  1. Let x = 0.3777... (the underlined part, 7, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 37.777...
  3. Move the decimal point past the non-repeating digits too: 10x = 3.7777...
  4. Subtract to cancel the repeating tail: 100x − 10x = 37 − 3, so 90x = 34.
  5. Solve: x = 34/90. The greatest common divisor is 2, so x = 17/45.

Check

Divide 17 by 45 on a calculator: 17 ÷ 45 = 0.3777777778… which matches 0.3777….

Similar repeating decimals

DecimalFraction
0.3555…16/45
0.363636…4/11
0.3666…11/30
0.373737…37/99
0.383838…38/99
0.384384384…128/333
0.3888…7/18
0.393939…13/33

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