Fraction3/13
Fraction3/13
Decimal≈ 0.2307692308exactly 0.(230769)
Percent≈ 23.076923%exactly 23.(076923)%
Where the decimal comes from
There is no rewrite over 10, 100 or 1000 for 3/13: 13 has a prime factor other than 2 and 5, so no whole-number multiplier reaches a power of ten. Watch the long division to see what happens instead — the remainders start circling, and once a remainder comes back, the digits must too:
- 30 ÷ 13 = 2remainder 4
- 40 ÷ 13 = 3remainder 1
- 10 ÷ 13 = 0remainder 10
- 100 ÷ 13 = 7remainder 9
- 90 ÷ 13 = 6remainder 12
- 120 ÷ 13 = 9remainder 3— this remainder has come around before, so from here the digits repeat
Written exactly: 0.(230769) — the parentheses mark the block that repeats forever.
Every way to write it
- Decimal
- ≈ 0.2307692308
- Percent
- ≈ 23.076923%
- Ratio
- 3 : 13 (part to whole)
- As inches
- 3/13″ = 5.861538 mm
Equivalent fractions
Multiply the top and bottom of 3/13 by the same number and the value does not change:
3/13 = 6/26 = 9/39 = 12/52 = 15/65 = 18/78 · more, or pick a denominator
On the number line
As a measurement
Read as inches, 3/13″ is 5.861538 mm exactly. The nearest marks on the finer rules:
| Rule | Nearest mark | Decimal inches | mm | Difference |
|---|---|---|---|---|
| 16ths | 1/4″ | 0.25 | 6.35 | +0.4885 mm |
| 32ths | 7/32″ | 0.21875 | 5.5563 | −0.3053 mm |
| 64ths | 15/64″ | 0.234375 | 5.9531 | +0.0916 mm |
Need a different rule or a tolerance? Nearest fraction · Within tolerance
Common questions
- What is 3/13 as a decimal?
- 3/13 is 0.2307692308 rounded; exactly, it is the repeating decimal 0.(230769).
- What is 3/13 as a percentage?
- 3/13 is about 23.076923% as a percentage.
- How many millimetres is 3/13 of an inch?
- 3/13 of an inch is 5.861538 mm, computed with the exact definition 1 inch = 25.4 mm.
Related
Fraction–decimal chartThe everyday set, printable.Rule charts16ths, 32nds, 64ths, 128ths.The rulerSee 3/13 in its place.