1/6 as a decimal
1/6 = 0.1(6) (0.166667…) inches = 4.2333 mm.
0.1(6)
1/6 of an inch — the bracketed digits repeat forever, so this form is exact where 0.166667… is not
Millimetres
4.2333 mm
Centimetres
0.42333 cm
Percent
16.6667%
Decimal
repeats
6 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 ÷ 6 | 1 | 10 − 6 | 4 |
| 2 | 40 ÷ 6 | 6 | 40 − 36 | 4 |
Remainder 4 has come up before — it is what step 2 started from. From there the division can only produce the same digits again, so the digits from step 2 on repeat forever (shaded): 1/6 = 0.1(6).
Where 1/6 falls at each precision, and whether the mark is the value exactly
| Rule | Nearest mark | Exact? |
|---|---|---|
| 1/16 | 3/16 | nearest |
| 1/32 | 5/32 | nearest |
| 1/64 | 11/64 | nearest |
Mixed numbers with 1/6
A whole number of inches plus 1/6: the whole number goes in front of the decimal point and 1/6 supplies the digits after it
| Mixed | Inches | mm |
|---|---|---|
| 1 1/6 | 1.1(6) | 29.6333 |
| 2 1/6 | 2.1(6) | 55.0333 |
| 3 1/6 | 3.1(6) | 80.4333 |
| 4 1/6 | 4.1(6) | 105.8333 |
| 5 1/6 | 5.1(6) | 131.2333 |
| 6 1/6 | 6.1(6) | 156.6333 |
| 7 1/6 | 7.1(6) | 182.0333 |
| 8 1/6 | 8.1(6) | 207.4333 |
| 9 1/6 | 9.1(6) | 232.8333 |
| 10 1/6 | 10.1(6) | 258.2333 |
| 11 1/6 | 11.1(6) | 283.6333 |
| 12 1/6 | 12.1(6) | 309.0333 |
Converting 1/6 to a decimal
A fraction is a division. 1/6 = 1 ÷ 6 = 0.1(6) (0.166667…). The decimal repeats forever, written 0.1(6) with the repeating digits bracketed. That happens because 6 factors into 2 × 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 4.2333 millimetres (0.42333 cm), since one inch is exactly 25.4 mm. As a percentage of an inch it is 16.6667%.
1/6 is not a mark on any imperial rule — the denominators on a rule are all powers of two, and 6 is not one. The nearest marks are 3/16 on a 1/16 rule, 5/32 on a 1/32 rule, 11/64 on a 1/64 rule, none of them exact.
Going the other way
To turn 0.166667 back into a fraction, pick the precision you are working to and multiply. At 1/16: 0.166667 × 16 = 2.6667, giving 3/16 after rounding to the nearest mark. At 1/32: 0.166667 × 32 = 5.3333, giving 5/32 after rounding to the nearest mark. At 1/64: 0.166667 × 64 = 10.6667, giving 11/64 after rounding to the nearest mark.
What is 1/6 as a decimal?
1/6 as a decimal is 0.1(6) (0.166667…). Divide the numerator by the denominator: 1 ÷ 6 = 0.1(6) (0.166667…). The division never comes out exactly, so the digits repeat.
What is 2 1/6 as a decimal?
2 1/6 as a decimal is 2.1(6). The whole number stays in front of the decimal point and 1/6 supplies the digits after it, so 2 1/6 = 2 + 0.1(6). In millimetres that is 55.0333 mm. This page's mixed-numbers table runs from 1 1/6 to 12 1/6.
What is 1/6 as a percent?
1/6 as a percent is about 16.6667%. Its decimal repeats, so the percentage does too; it is rounded here to four decimal places.
What is 0.1(6) (0.166667…) as a fraction?
0.166667… as a fraction is 1/6, in lowest terms.
How many millimetres is 1/6 of an inch?
1/6 of an inch is 4.2333 mm, or 0.42333 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 1/6 on a tape measure?
1/6 is not a mark on any imperial rule — the denominators on a rule are all powers of two, and 6 is not one. The nearest marks are 3/16 on a 1/16 rule, 5/32 on a 1/32 rule, 11/64 on a 1/64 rule, none of them exact.