0.142857142857142857… as a Fraction

0.142857142857142857… (0.142857 repeating) as a fraction is 1/7.

How to convert 0.142857142857142857… to a fraction

  1. Let x = 0.142857142857142857... (the underlined part, 142857, repeats forever).
  2. Move the decimal point past one full repeating block: 1000000x = 142857.142857142857142857...
  3. Subtract to cancel the repeating tail: 1000000x − x = 142857 − 0, so 999999x = 142857.
  4. Solve: x = 142857/999999. The greatest common divisor is 142857, so x = 1/7.

Check

Divide 1 by 7 on a calculator: 1 ÷ 7 = 0.1428571429… which matches 0.142857142857142857….

Similar repeating decimals

DecimalFraction
0.131313…13/99
0.1333…2/15
0.135135135…5/37
0.141414…14/99
0.142142142…142/999
0.1444…13/90
0.151515…5/33
0.153153153…17/111

See also: 1/7 as a decimal.

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