Fraction1/3
Fraction1/3
Decimal≈ 0.3333333333exactly 0.(3)
Percent≈ 33.333333%exactly 33.(3)%
Where the decimal comes from
There is no rewrite over 10, 100 or 1000 for 1/3: 3 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:
- 10 ÷ 3 = 3remainder 1— this remainder has come around before, so from here the digits repeat
Written exactly: 0.(3) — the parentheses mark the block that repeats forever.
Every way to write it
- Decimal
- ≈ 0.3333333333
- Percent
- ≈ 33.333333%
- Ratio
- 1 : 3 (part to whole)
- As inches
- 1/3″ = 8.466667 mm
Equivalent fractions
Multiply the top and bottom of 1/3 by the same number and the value does not change:
1/3 = 2/6 = 3/9 = 4/12 = 5/15 = 6/18 · more, or pick a denominator
On the number line
As a measurement
Read as inches, 1/3″ is 8.466667 mm exactly. The nearest marks on the finer rules:
| Rule | Nearest mark | Decimal inches | mm | Difference |
|---|---|---|---|---|
| 16ths | 5/16″ | 0.3125 | 7.9375 | −0.5292 mm |
| 32ths | 11/32″ | 0.34375 | 8.7313 | +0.2646 mm |
| 64ths | 21/64″ | 0.328125 | 8.3344 | −0.1323 mm |
Need a different rule or a tolerance? Nearest fraction · Within tolerance
Common questions
- What is 1/3 as a decimal?
- 1/3 is 0.3333333333 rounded; exactly, it is the repeating decimal 0.(3).
- What is 1/3 as a percentage?
- 1/3 is about 33.333333% as a percentage.
- How many millimetres is 1/3 of an inch?
- 1/3 of an inch is 8.466667 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 1/3 in its place.