1/7 as a decimal

How to convert this fraction

Divide 1 by 7 using integer long division. The whole-number part is 0; the remaining fraction is 1/7.

1. Bring down a zero: remainder × 10 gives the next decimal digit 1; the new remainder is 3.
2. Bring down a zero: remainder × 10 gives the next decimal digit 4; the new remainder is 2.
3. Bring down a zero: remainder × 10 gives the next decimal digit 2; the new remainder is 6.
4. Bring down a zero: remainder × 10 gives the next decimal digit 8; the new remainder is 4.
5. Bring down a zero: remainder × 10 gives the next decimal digit 5; the new remainder is 5.
6. Bring down a zero: remainder × 10 gives the next decimal digit 7; the new remainder is 1.

The remainder repeats, so the decimal repeats with 142857 as the repeating cycle. The displayed value 0.142857142857 is rounded; the exact value remains 1/7.

Check: 0 × 7 + 1 = 1, so the quotient and remainder reconstruct the original fraction.