What is 3/21 as a Decimal?

Fraction to Decimal Converter

What is 3/21 as a decimal?

Answer

Fraction 3/21 as a decimal is

0.142857

≈ 0.14 to hundredths

Repeating decimal: 3/21 = 1/7 · denominator 7 has the factor 7, not 2 or 5 · the bar marks the period 142857 — 6 digits repeat forever

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

Remainder 3 is back after the 6th division → the 6 digits 142857 repeat: 0.142857.

Fraction 3/21 as a decimal is 0.(142857)

To convert 3/21 to a decimal, divide the numerator by the denominator: 3 ÷ 21 = 0.(142857).

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: 3/21 ≈ 14.29%.