What is 5 and 2/13 as a Decimal?

Fraction to Decimal Converter

What is 5 2/13 as a decimal?

Answer

Fraction 5 2/13 as a decimal is

5.153846

≈ 5.15 to hundredths

Repeating decimal: denominator 13 has the factor 13, not 2 or 5 · the bar marks the period 153846 — 6 digits repeat forever

Whole part 5 stays in front; divide the fraction part:

remainder	×10	= digit × 13 + new remainder	digit
2	20	1 × 13 + 7	1
7	70	5 × 13 + 5	5
5	50	3 × 13 + 11	3
11	110	8 × 13 + 6	8
6	60	4 × 13 + 8	4
8	80	6 × 13 + 2	6

Remainder 2 is back after the 6th division → the 6 digits 153846 repeat: 0.153846.

5 + 0.153846 = 5.153846

Fraction 5 2/13 as a decimal is 5.(153846)

To convert 5 2/13 to a decimal, divide the numerator by the denominator, 2 ÷ 13 = 0.(153846), then add the whole part: 5 + 0.(153846) = 5.(153846).

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: 5 2/13 ≈ 515.38%.