1/3 as a decimal

How to convert this fraction

Divide 1 by 3 using integer long division. The whole-number part is 0; the remaining fraction is 1/3.

1. Bring down a zero: remainder × 10 gives the next decimal digit 3; the new remainder is 1.

The remainder repeats, so the decimal repeats with 3 as the repeating cycle. The displayed value 0.333333333333 is rounded; the exact value remains 1/3.

Check: 0 × 3 + 1 = 1, so the quotient and remainder reconstruct the original fraction.