Why does 1 divided by 3 equal a bunch of threes repeating?

Answer 1

0.3333

Answer 2

1/3 is equal to the decimal 1.33333 (to infinity) because the remainder after each decimal division is the same (1).

In long division, 1/3 = 0 remainder 1 [decimal point] = 10/3 = 3 remainder 1 = 10/3 remainder 1 and so forth. Decimal quotients that repeat with one or more values are called repeating decimals. When 2 is divided by three, the final digit is usually rounded up (2/3 = 0.67 or 0.667 or 0.6667).