9/13

9 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 9/13: 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. 90 ÷ 13 = 6remainder 12
2. 120 ÷ 13 = 9remainder 3
3. 30 ÷ 13 = 2remainder 4
4. 40 ÷ 13 = 3remainder 1
5. 10 ÷ 13 = 0remainder 10
6. 100 ÷ 13 = 7remainder 9— this remainder has come around before, so from here the digits repeat

Written exactly: 0.(692307) — the parentheses mark the block that repeats forever.

Every way to write it

Decimal

≈ 0.6923076923

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Percent

≈ 69.230769%

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Ratio

9 : 13 (part to whole)

As inches

9/13″ = 17.584615 mm

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Equivalent fractions

Multiply the top and bottom of 9/13 by the same number and the value does not change:

9/13 = 18/26 = 27/39 = 36/52 = 45/65 = 54/78 · more, or pick a denominator

On the number line

As a measurement

Read as inches, 9/13″ is 17.584615 mm exactly. The nearest marks on the finer rules:

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

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