5/13 as a Decimal
5/13 = 0.3̅8̅4̅6̅1̅5̅
5/13 as a decimal is 0.3̅8̅4̅6̅1̅5̅ — the digits 384615 repeat forever (≈ 0.384615).
Step by step
- Divide 5 by 13: 0 whole (so the answer starts 0.), remainder 5.
- Bring down a 0: 50 ÷ 13 = 3, remainder 11.
- Bring down a 0: 110 ÷ 13 = 8, remainder 6.
- Bring down a 0: 60 ÷ 13 = 4, remainder 8.
- Bring down a 0: 80 ÷ 13 = 6, remainder 2.
- Bring down a 0: 20 ÷ 13 = 1, remainder 7.
- Bring down a 0: 70 ÷ 13 = 5, remainder 5.
- Result: 5/13 = 0.3̅8̅4̅6̅1̅5̅ (repeating).
Why it repeats: after removing factors of 2 and 5, the denominator 13 still has the factor 13, so the division never ends and the remainders cycle. The repeating block “384615” has 6 digits; round it to the precision you need, for example 0.38 or 0.3846.
Details
- Decimal (rounded)
- 0.384615
- Percent
- 38.4615%
- Type
- Repeating (384615 repeats)
- Equivalent fractions
- 10/26, 15/39, 20/52
How it works
A fraction means division: the numerator (top) divided by the denominator (bottom). Use long division, adding zeros after the decimal point until the remainder is zero or a remainder repeats. If the simplified denominator has only 2 and 5 as prime factors, the decimal terminates; otherwise it repeats forever, and the repeating digits are marked with a bar.
Nearby values
Related conversions
Frequently asked questions
What is 5/13 as a decimal?
5/13 = 0.3̅8̅4̅6̅1̅5̅, which rounds to 0.3846.
How do you convert 5/13 to a decimal?
Divide 5 by 13. 5 ÷ 13 = 0.384615….
What is 5/13 as a percent?
38.4615%.
Is 5/13 a terminating or repeating decimal?
Repeating — the block “384615” repeats forever.