What is 5 and 1/13 as a Decimal?

Fraction to Decimal Converter

What is 5 1/13 as a decimal?

Answer

Fraction 5 1/13 as a decimal is

5.076923

≈ 5.08 to hundredths

Repeating decimal: denominator 13 has the factor 13, not 2 or 5 · the bar marks the period 076923 — 6 digits repeat forever

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

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

Remainder 1 is back after the 6th division → the 6 digits 076923 repeat: 0.076923.

5 + 0.076923 = 5.076923

Fraction 5 1/13 as a decimal is 5.(076923)

To convert 5 1/13 to a decimal, divide the numerator by the denominator, 1 ÷ 13 = 0.(076923), then add the whole part: 5 + 0.(076923) = 5.(076923).

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 1/13 ≈ 507.69%.