7/15 as a decimal

How to convert this fraction

Divide 7 by 15 using integer long division. The whole-number part is 0; the remaining fraction is 7/15.

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

The remainder repeats, so the decimal repeats with 6 as the repeating cycle. The displayed value 0.466666666667 is rounded; the exact value remains 7/15.

Check: 0 × 15 + 7 = 7, so the quotient and remainder reconstruct the original fraction.