What is 12/21 as a Decimal?

Fraction to Decimal Converter

What is 12/21 as a decimal?

Answer

Fraction 12/21 as a decimal is

0.571428

≈ 0.57 to hundredths

Repeating decimal: 12/21 = 4/7 · denominator 7 has the factor 7, not 2 or 5 · the bar marks the period 571428 — 6 digits repeat forever

remainder	×10	= digit × 21 + new remainder	digit
12	120	5 × 21 + 15	5
15	150	7 × 21 + 3	7
3	30	1 × 21 + 9	1
9	90	4 × 21 + 6	4
6	60	2 × 21 + 18	2
18	180	8 × 21 + 12	8

Remainder 12 is back after the 6th division → the 6 digits 571428 repeat: 0.571428.

Fraction 12/21 as a decimal is 0.(571428)

To convert 12/21 to a decimal, divide the numerator by the denominator: 12 ÷ 21 = 0.(571428).

In lowest terms its denominator 7 has the prime factor 7, so the division never ends: a remainder comes back and the same digits repeat forever.

Multiply by 100: 12/21 ≈ 57.14%.