1/3 as a decimal
1/3 = 0.(3) (0.333333…) inches = 8.4667 mm.
0.(3)
1/3 of an inch — the bracketed digits repeat forever, so this form is exact where 0.333333… is not
Millimetres
8.4667 mm
Centimetres
0.84667 cm
Percent
33.3333%
Decimal
repeats
3 goes into 1 0 times with 1 left over, so write 0 and a decimal point. Then bring down a zero and divide again, one digit at a time.
| Step | Divide | Digit | Subtract | Remainder |
|---|---|---|---|---|
| 1 | 10 ÷ 3 | 3 | 10 − 9 | 1 |
Remainder 1 has come up before — it is what step 1 started from. From there the division can only produce the same digits again, so every digit repeats forever (shaded): 1/3 = 0.(3).
Where 1/3 falls at each precision, and whether the mark is the value exactly
| Rule | Nearest mark | Exact? |
|---|---|---|
| 1/16 | 5/16 | nearest |
| 1/32 | 11/32 | nearest |
| 1/64 | 21/64 | nearest |
Mixed numbers with 1/3
A whole number of inches plus 1/3: the whole number goes in front of the decimal point and 1/3 supplies the digits after it
| Mixed | Inches | mm |
|---|---|---|
| 1 1/3 | 1.(3) | 33.8667 |
| 2 1/3 | 2.(3) | 59.2667 |
| 3 1/3 | 3.(3) | 84.6667 |
| 4 1/3 | 4.(3) | 110.0667 |
| 5 1/3 | 5.(3) | 135.4667 |
| 6 1/3 | 6.(3) | 160.8667 |
| 7 1/3 | 7.(3) | 186.2667 |
| 8 1/3 | 8.(3) | 211.6667 |
| 9 1/3 | 9.(3) | 237.0667 |
| 10 1/3 | 10.(3) | 262.4667 |
| 11 1/3 | 11.(3) | 287.8667 |
| 12 1/3 | 12.(3) | 313.2667 |
Converting 1/3 to a decimal
A fraction is a division. 1/3 = 1 ÷ 3 = 0.(3) (0.333333…). The decimal repeats forever, written 0.(3) with the repeating digits bracketed. That happens because 3 factors into 3, which includes a prime other than 2 or 5 — so no power of ten is divisible by it and the long division never terminates.
In metric that is 8.4667 millimetres (0.84667 cm), since one inch is exactly 25.4 mm. As a percentage of an inch it is 33.3333%.
1/3 is not a mark on any imperial rule — the denominators on a rule are all powers of two, and 3 is not one. The nearest marks are 5/16 on a 1/16 rule, 11/32 on a 1/32 rule, 21/64 on a 1/64 rule, none of them exact.
Going the other way
To turn 0.333333 back into a fraction, pick the precision you are working to and multiply. At 1/16: 0.333333 × 16 = 5.3333, giving 5/16 after rounding to the nearest mark. At 1/32: 0.333333 × 32 = 10.6667, giving 11/32 after rounding to the nearest mark. At 1/64: 0.333333 × 64 = 21.3333, giving 21/64 after rounding to the nearest mark.
What is 1/3 as a decimal?
1/3 as a decimal is 0.(3) (0.333333…). Divide the numerator by the denominator: 1 ÷ 3 = 0.(3) (0.333333…). The division never comes out exactly, so the digits repeat.
What is 2 1/3 as a decimal?
2 1/3 as a decimal is 2.(3). The whole number stays in front of the decimal point and 1/3 supplies the digits after it, so 2 1/3 = 2 + 0.(3). In millimetres that is 59.2667 mm. This page's mixed-numbers table runs from 1 1/3 to 12 1/3.
What is 1/3 as a percent?
1/3 as a percent is about 33.3333%. Its decimal repeats, so the percentage does too; it is rounded here to four decimal places.
What is 0.(3) (0.333333…) as a fraction?
0.333333… as a fraction is 1/3, in lowest terms.
How many millimetres is 1/3 of an inch?
1/3 of an inch is 8.4667 mm, or 0.84667 cm. An inch has been defined as exactly 25.4 mm since 1959, so this conversion is a definition rather than a measurement.
Where is 1/3 on a tape measure?
1/3 is not a mark on any imperial rule — the denominators on a rule are all powers of two, and 3 is not one. The nearest marks are 5/16 on a 1/16 rule, 11/32 on a 1/32 rule, 21/64 on a 1/64 rule, none of them exact.