3/13 as a decimal

How to convert this fraction

Divide 3 by 13 using integer long division. The whole-number part is 0; the remaining fraction is 3/13.

1. Bring down a zero: remainder × 10 gives the next decimal digit 2; the new remainder is 4.
2. Bring down a zero: remainder × 10 gives the next decimal digit 3; the new remainder is 1.
3. Bring down a zero: remainder × 10 gives the next decimal digit 0; the new remainder is 10.
4. Bring down a zero: remainder × 10 gives the next decimal digit 7; the new remainder is 9.
5. Bring down a zero: remainder × 10 gives the next decimal digit 6; the new remainder is 12.
6. Bring down a zero: remainder × 10 gives the next decimal digit 9; the new remainder is 3.

The remainder repeats, so the decimal repeats with 230769 as the repeating cycle. The displayed value 0.230769230769 is rounded; the exact value remains 3/13.

Check: 0 × 13 + 3 = 3, so the quotient and remainder reconstruct the original fraction.