2/3 as a decimal
2/3 = 0.(6) (0.666667…) inches = 16.9333 mm.
0.(6)
2/3 of an inch — the bracketed digits repeat forever, so this form is exact where 0.666667… is not
Millimetres
16.9333 mm
Centimetres
1.69333 cm
Percent
66.6667%
Decimal
repeats
3 goes into 2 0 times with 2 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 | 20 ÷ 3 | 6 | 20 − 18 | 2 |
Remainder 2 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): 2/3 = 0.(6).
Where 2/3 falls at each precision, and whether the mark is the value exactly
| Rule | Nearest mark | Exact? |
|---|---|---|
| 1/16 | 11/16 | nearest |
| 1/32 | 21/32 | nearest |
| 1/64 | 43/64 | nearest |
Mixed numbers with 2/3
A whole number of inches plus 2/3: the whole number goes in front of the decimal point and 2/3 supplies the digits after it
| Mixed | Inches | mm |
|---|---|---|
| 1 2/3 | 1.(6) | 42.3333 |
| 2 2/3 | 2.(6) | 67.7333 |
| 3 2/3 | 3.(6) | 93.1333 |
| 4 2/3 | 4.(6) | 118.5333 |
| 5 2/3 | 5.(6) | 143.9333 |
| 6 2/3 | 6.(6) | 169.3333 |
| 7 2/3 | 7.(6) | 194.7333 |
| 8 2/3 | 8.(6) | 220.1333 |
| 9 2/3 | 9.(6) | 245.5333 |
| 10 2/3 | 10.(6) | 270.9333 |
| 11 2/3 | 11.(6) | 296.3333 |
| 12 2/3 | 12.(6) | 321.7333 |
Converting 2/3 to a decimal
A fraction is a division. 2/3 = 2 ÷ 3 = 0.(6) (0.666667…). The decimal repeats forever, written 0.(6) 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 16.9333 millimetres (1.69333 cm), since one inch is exactly 25.4 mm. As a percentage of an inch it is 66.6667%.
2/3 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 11/16 on a 1/16 rule, 21/32 on a 1/32 rule, 43/64 on a 1/64 rule, none of them exact.
Going the other way
To turn 0.666667 back into a fraction, pick the precision you are working to and multiply. At 1/16: 0.666667 × 16 = 10.6667, giving 11/16 after rounding to the nearest mark. At 1/32: 0.666667 × 32 = 21.3333, giving 21/32 after rounding to the nearest mark. At 1/64: 0.666667 × 64 = 42.6667, giving 43/64 after rounding to the nearest mark.
What is 2/3 as a decimal?
2/3 as a decimal is 0.(6) (0.666667…). Divide the numerator by the denominator: 2 ÷ 3 = 0.(6) (0.666667…). The division never comes out exactly, so the digits repeat.
What is 2 2/3 as a decimal?
2 2/3 as a decimal is 2.(6). The whole number stays in front of the decimal point and 2/3 supplies the digits after it, so 2 2/3 = 2 + 0.(6). In millimetres that is 67.7333 mm. This page's mixed-numbers table runs from 1 2/3 to 12 2/3.
What is 2/3 as a percent?
2/3 as a percent is about 66.6667%. Its decimal repeats, so the percentage does too; it is rounded here to four decimal places.
What is 0.(6) (0.666667…) as a fraction?
0.666667… as a fraction is 2/3, in lowest terms.
How many millimetres is 2/3 of an inch?
2/3 of an inch is 16.9333 mm, or 1.69333 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 2/3 on a tape measure?
2/3 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 11/16 on a 1/16 rule, 21/32 on a 1/32 rule, 43/64 on a 1/64 rule, none of them exact.