0.1555… as a Fraction

0.1555… (0.15 repeating) as a fraction is 7/45.

How to convert 0.1555… to a fraction

  1. Let x = 0.1555... (the underlined part, 5, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 15.555...
  3. Move the decimal point past the non-repeating digits too: 10x = 1.5555...
  4. Subtract to cancel the repeating tail: 100x − 10x = 15 − 1, so 90x = 14.
  5. Solve: x = 14/90. The greatest common divisor is 2, so x = 7/45.

Check

Divide 7 by 45 on a calculator: 7 ÷ 45 = 0.1555555556… which matches 0.1555….

Similar repeating decimals

DecimalFraction
0.142857142857142857…1/7
0.1444…13/90
0.151515…5/33
0.153153153…17/111
0.161616…16/99
0.16333…49/300
0.1666…1/6
0.16666…1/6

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