2/13

2 of 13 equal parts filled — the same share as a bar and as a circle.

Where the decimal comes from

There is no rewrite over 10, 100 or 1000 for 2/13: 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:

1. 20 ÷ 13 = 1remainder 7
2. 70 ÷ 13 = 5remainder 5
3. 50 ÷ 13 = 3remainder 11
4. 110 ÷ 13 = 8remainder 6
5. 60 ÷ 13 = 4remainder 8
6. 80 ÷ 13 = 6remainder 2— this remainder has come around before, so from here the digits repeat

Written exactly: 0.(153846) — the parentheses mark the block that repeats forever.

Every way to write it

Decimal

≈ 0.1538461538

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Percent

≈ 15.384615%

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Ratio

2 : 13 (part to whole)

As inches

2/13″ = 3.907692 mm

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Equivalent fractions

Multiply the top and bottom of 2/13 by the same number and the value does not change:

2/13 = 4/26 = 6/39 = 8/52 = 10/65 = 12/78 · more, or pick a denominator

On the number line

As a measurement

Read as inches, 2/13″ is 3.907692 mm exactly. The nearest marks on the finer rules:

Need a different rule or a tolerance? Nearest fraction · Within tolerance

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