What is 3/13 as a Decimal?

Fraction to Decimal Converter

What is 3/13 as a decimal?

Answer

Fraction 3/13 as a decimal is

0.230769

≈ 0.23 to hundredths

Repeating decimal: denominator 13 has the factor 13, not 2 or 5 · the bar marks the period 230769 — 6 digits repeat forever

remainder	×10	= digit × 13 + new remainder	digit
3	30	2 × 13 + 4	2
4	40	3 × 13 + 1	3
1	10	0 × 13 + 10	0
10	100	7 × 13 + 9	7
9	90	6 × 13 + 12	6
12	120	9 × 13 + 3	9

Remainder 3 is back after the 6th division → the 6 digits 230769 repeat: 0.230769.

Fraction 3/13 as a decimal is 0.(230769)

To convert 3/13 to a decimal, divide the numerator by the denominator: 3 ÷ 13 = 0.(230769).

In lowest terms its denominator 13 has the prime factor 13, so the division never ends: a remainder comes back and the same digits repeat forever.

Multiply by 100: 3/13 ≈ 23.08%.