0.1777… as a Fraction

0.1777… (0.17 repeating) as a fraction is 8/45.

How to convert 0.1777… to a fraction

  1. Let x = 0.1777... (the underlined part, 7, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 17.777...
  3. Move the decimal point past the non-repeating digits too: 10x = 1.7777...
  4. Subtract to cancel the repeating tail: 100x − 10x = 17 − 1, so 90x = 16.
  5. Solve: x = 16/90. The greatest common divisor is 2, so x = 8/45.

Check

Divide 8 by 45 on a calculator: 8 ÷ 45 = 0.1777777778… which matches 0.1777….

Similar repeating decimals

DecimalFraction
0.16333…49/300
0.1666…1/6
0.16666…1/6
0.171717…17/99
0.181818…2/11
0.185185185…5/27
0.1888…17/90
0.191919…19/99

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