7/13 as a decimal

How to convert this fraction

Divide 7 by 13 using integer long division. The whole-number part is 0; the remaining fraction is 7/13.

1. Bring down a zero: remainder × 10 gives the next decimal digit 5; the new remainder is 5.
2. Bring down a zero: remainder × 10 gives the next decimal digit 3; the new remainder is 11.
3. Bring down a zero: remainder × 10 gives the next decimal digit 8; the new remainder is 6.
4. Bring down a zero: remainder × 10 gives the next decimal digit 4; the new remainder is 8.
5. Bring down a zero: remainder × 10 gives the next decimal digit 6; the new remainder is 2.
6. Bring down a zero: remainder × 10 gives the next decimal digit 1; the new remainder is 7.

The remainder repeats, so the decimal repeats with 538461 as the repeating cycle. The displayed value 0.538461538462 is rounded; the exact value remains 7/13.

Check: 0 × 13 + 7 = 7, so the quotient and remainder reconstruct the original fraction.