Results update as you type. For a repeating decimal, put the repeating digits in brackets: 0.(3) is 1/3 and 0.1(6) is 1/6.
Fraction to decimal chart (1/64 to 1 inch)
Every 64th of an inch from 1/64 to 1 as a decimal and in millimeters. Fractions are shown in lowest terms; the bold rows are the 1/16-inch marks found on most tape measures. Read it the other way round as a decimal to fraction chart: find the closest decimal and read the fraction on the left.
Decimals and millimeters are rounded half up to 4 decimal places. Millimeters use 1 in = 25.4 mm exactly.
| Fraction (in) | Decimal (in) | mm |
|---|---|---|
| 1/64 | 0.0156 | 0.3969 |
| 1/32 | 0.0313 | 0.7938 |
| 3/64 | 0.0469 | 1.1906 |
| 1/16 | 0.0625 | 1.5875 |
| 5/64 | 0.0781 | 1.9844 |
| 3/32 | 0.0938 | 2.3813 |
| 7/64 | 0.1094 | 2.7781 |
| 1/8 | 0.1250 | 3.1750 |
| 9/64 | 0.1406 | 3.5719 |
| 5/32 | 0.1563 | 3.9688 |
| 11/64 | 0.1719 | 4.3656 |
| 3/16 | 0.1875 | 4.7625 |
| 13/64 | 0.2031 | 5.1594 |
| 7/32 | 0.2188 | 5.5563 |
| 15/64 | 0.2344 | 5.9531 |
| 1/4 | 0.2500 | 6.3500 |
| 17/64 | 0.2656 | 6.7469 |
| 9/32 | 0.2813 | 7.1438 |
| 19/64 | 0.2969 | 7.5406 |
| 5/16 | 0.3125 | 7.9375 |
| 21/64 | 0.3281 | 8.3344 |
| 11/32 | 0.3438 | 8.7313 |
| 23/64 | 0.3594 | 9.1281 |
| 3/8 | 0.3750 | 9.5250 |
| 25/64 | 0.3906 | 9.9219 |
| 13/32 | 0.4063 | 10.3188 |
| 27/64 | 0.4219 | 10.7156 |
| 7/16 | 0.4375 | 11.1125 |
| 29/64 | 0.4531 | 11.5094 |
| 15/32 | 0.4688 | 11.9063 |
| 31/64 | 0.4844 | 12.3031 |
| 1/2 | 0.5000 | 12.7000 |
| Fraction (in) | Decimal (in) | mm |
|---|---|---|
| 33/64 | 0.5156 | 13.0969 |
| 17/32 | 0.5313 | 13.4938 |
| 35/64 | 0.5469 | 13.8906 |
| 9/16 | 0.5625 | 14.2875 |
| 37/64 | 0.5781 | 14.6844 |
| 19/32 | 0.5938 | 15.0813 |
| 39/64 | 0.6094 | 15.4781 |
| 5/8 | 0.6250 | 15.8750 |
| 41/64 | 0.6406 | 16.2719 |
| 21/32 | 0.6563 | 16.6688 |
| 43/64 | 0.6719 | 17.0656 |
| 11/16 | 0.6875 | 17.4625 |
| 45/64 | 0.7031 | 17.8594 |
| 23/32 | 0.7188 | 18.2563 |
| 47/64 | 0.7344 | 18.6531 |
| 3/4 | 0.7500 | 19.0500 |
| 49/64 | 0.7656 | 19.4469 |
| 25/32 | 0.7813 | 19.8438 |
| 51/64 | 0.7969 | 20.2406 |
| 13/16 | 0.8125 | 20.6375 |
| 53/64 | 0.8281 | 21.0344 |
| 27/32 | 0.8438 | 21.4313 |
| 55/64 | 0.8594 | 21.8281 |
| 7/8 | 0.8750 | 22.2250 |
| 57/64 | 0.8906 | 22.6219 |
| 29/32 | 0.9063 | 23.0188 |
| 59/64 | 0.9219 | 23.4156 |
| 15/16 | 0.9375 | 23.8125 |
| 61/64 | 0.9531 | 24.2094 |
| 31/32 | 0.9688 | 24.6063 |
| 63/64 | 0.9844 | 25.0031 |
| 1 | 1.0000 | 25.4000 |
Common fractions to decimals
| Fraction | Exact decimal | 4 places | Percent | Type |
|---|---|---|---|---|
| 1/2 | 0.5 | 0.5000 | 50.00% | terminates |
| 1/3 | 0.3 | 0.3333 | 33.33% | repeats (1-digit cycle) |
| 2/3 | 0.6 | 0.6667 | 66.67% | repeats (1-digit cycle) |
| 1/4 | 0.25 | 0.2500 | 25.00% | terminates |
| 3/4 | 0.75 | 0.7500 | 75.00% | terminates |
| 1/5 | 0.2 | 0.2000 | 20.00% | terminates |
| 2/5 | 0.4 | 0.4000 | 40.00% | terminates |
| 3/5 | 0.6 | 0.6000 | 60.00% | terminates |
| 4/5 | 0.8 | 0.8000 | 80.00% | terminates |
| 1/6 | 0.16 | 0.1667 | 16.67% | repeats (1-digit cycle) |
| 5/6 | 0.83 | 0.8333 | 83.33% | repeats (1-digit cycle) |
| 1/7 | 0.142857 | 0.1429 | 14.29% | repeats (6-digit cycle) |
| 1/8 | 0.125 | 0.1250 | 12.50% | terminates |
| 3/8 | 0.375 | 0.3750 | 37.50% | terminates |
| 5/8 | 0.625 | 0.6250 | 62.50% | terminates |
| 7/8 | 0.875 | 0.8750 | 87.50% | terminates |
| 1/9 | 0.1 | 0.1111 | 11.11% | repeats (1-digit cycle) |
| 1/10 | 0.1 | 0.1000 | 10.00% | terminates |
| 3/10 | 0.3 | 0.3000 | 30.00% | terminates |
| 1/12 | 0.083 | 0.0833 | 8.33% | repeats (1-digit cycle) |
| 5/12 | 0.416 | 0.4167 | 41.67% | repeats (1-digit cycle) |
| 7/12 | 0.583 | 0.5833 | 58.33% | repeats (1-digit cycle) |
| 11/12 | 0.916 | 0.9167 | 91.67% | repeats (1-digit cycle) |
| 1/16 | 0.0625 | 0.0625 | 6.25% | terminates |
Source: thealltools.com/tools/fraction-to-decimal-chart
About this tool
This page has two parts: a converter and a printable fraction to decimal chart. The converter works with exact whole-number arithmetic rather than floating point, so 1/3 comes out as the repeating decimal 0.(3) instead of 0.3333333333333333, and a terminating decimal such as 0.4375 turns back into exactly 7/16. The chart above lists every 64th of an inch with its decimal and millimeter value, which covers the fractions on US tape measures, rulers and drill bit sets. Everything runs in your browser.
How to use the converter
- Fraction to decimal: type a fraction such as
7/16, a mixed number such as3 5/8(whole number, space, fraction), or a negative value such as-1 1/2. The tool shows the exact decimal with any repeating part marked, the value rounded to 4 places, the fraction in lowest terms, the percent, and the millimeter value if the number is in inches. - Decimal to fraction: type a decimal such as
0.3or2.375. You get the simplest exact fraction, and the nearest 1/16, 1/32 and 1/64 inch with how far each is from your number. - Repeating decimals can be typed with the repeating digits in brackets, for example
0.(6)for 2/3. - Click Print chart to print only the chart, without the rest of the page.
How to convert a fraction to a decimal by long division
A fraction is a division: the numerator divided by the denominator. To convert 5/6 by hand, divide 5 by 6. Six goes into 5 zero times, so write 0. and bring down a zero to make 50. Six goes into 50 eight times (48), remainder 2. Bring down a zero: 20. Six goes into 20 three times (18), remainder 2 again. Because the remainder 2 has come back, every following step is the same, and the digit 3 repeats forever: 5/6 = 0.8(3), also written with a bar over the 3.
For a mixed number, convert the fraction part and add the whole number. For the converter's default 2 5/6, that gives 2 + 0.8(3) = 2.8(3). As an improper fraction it is 17/6, rounded to 4 places it is 2.8333, and as a length in inches it is 71.9667 mm.
Why some fractions repeat
Write the fraction in lowest terms and look at the prime factors of the denominator. If the only prime factors are 2 and 5, the decimal terminates, because 10 = 2 × 5 and the fraction can be rewritten over a power of 10. That is why every fraction on a 64ths chart terminates: 64 = 26, so 1/64 = 15,625/1,000,000 = 0.015625. If the denominator has any other prime factor, such as 3, 7 or 11, the decimal repeats forever. 1/3, 1/6, 1/7, 1/9 and 1/12 all repeat, while 1/8 and 3/20 do not. The repeating cycle can never be longer than the denominator minus 1 digits, since long division can only produce that many different non-zero remainders. 1/7 hits that limit, with a six-digit cycle: 0.(142857).
How to convert a decimal to a fraction
Terminating decimals: write the digits over the matching power of 10 and reduce. The converter's default 0.3 is 3/10, which is already in lowest terms. 0.4375 is 4375/10000; dividing both by their greatest common divisor, 625, gives 7/16.
Repeating decimals: for 0.1(6), take the digits up to the end of the first cycle (16), subtract the digits before the cycle (1), and divide by a number made of one 9 for each repeating digit followed by one 0 for each non-repeating decimal digit (90). So 0.1(6) = (16 − 1) ÷ 90 = 15/90 = 1/6.
Nearest tape-measure fraction: multiply the decimal by 16, 32 or 64, round to a whole number, and put it over that denominator. For 0.3: 0.3 × 16 = 4.8, which rounds to 5, giving 5/16 inch (0.0125 in, or 0.3175 mm, too long). 0.3 × 32 = 9.6 rounds to 10, and 10/32 also reduces to 5/16. 0.3 × 64 = 19.2 rounds to 19, giving 19/64 inch, which is 0.0031 in (0.0794 mm) short. Values exactly halfway are rounded up.
Common mistakes
- Treating a rounded decimal as exact. 0.333 is 333/1000, not 1/3. Type
0.(3)if you mean one third. - Reading the mixed number wrong.
3 5/8means 3 + 5/8 = 3.625, not 35/8. Keep a space between the whole number and the fraction. - Forgetting to reduce. 8/16, 16/32 and 32/64 are all 1/2. The chart shows each fraction in lowest terms, which is how rulers label them.
- Mixing up a fraction of an inch with millimeters. 1/16 inch is 1.5875 mm, not 1.6 mm, and the small difference adds up over many parts. For metric sizes, the MM to Inches converter has its own fraction chart.
Common use cases
- Converting a tape-measure reading such as 7/16 inch to a decimal for a CAD drawing or a spreadsheet
- Turning a caliper reading in decimal inches into the nearest 1/32 or 1/64 inch
- Checking math homework that asks for a fraction as a repeating decimal
- Turning a fraction into a percent; for other percent sums, use the Percentage Calculator
The millimeter values use the exact definition 1 inch = 0.0254 meter, listed as an exact factor in the NIST Guide to the SI, Appendix B.
Frequently asked questions
5/8 is 0.625 exactly. Divide 5 by 8: the denominator 8 is a power of 2, so the decimal stops after three places. In millimeters, 5/8 inch is 15.875 mm, because one inch is defined as exactly 25.4 mm. The chart lists it as the 40/64 row in lowest terms.
0.375 is 3/8. Write it as 375/1000, then divide the top and bottom by their greatest common divisor, 125, to get 3/8. On a tape measure, 3/8 inch is the same mark as 6/16 inch, and the chart shows it as 0.3750 inch or 9.5250 mm.
The usual notation is a bar, called a vinculum, over the digits that repeat, so one sixth is 0.16 with a bar over the 6. When a bar is hard to type, people use brackets, 0.1(6), or a dot above the digit. Writing three dots, as in 0.1666..., is common but does not show which digits repeat.
Multiply the decimal part by 16 and round to the nearest whole number; that is the number of sixteenths. For 0.69 inch, 0.69 × 16 = 11.04, which rounds to 11, so the nearest mark is 11/16 inch. Reduce the fraction if the result is even, for example 8/16 becomes 1/2.
Every terminating or repeating decimal can be written exactly as a fraction of two whole numbers. Decimals that never end and never repeat, such as pi or the square root of 2, are irrational, so no fraction is exactly equal to them. You can still find a close fraction, such as 22/7 for pi.
One third of an inch is 25.4 ÷ 3 = 8.4(6) mm, about 8.47 mm. It is not on a standard tape measure, because inch rulers are divided by halves down to 1/16 or smaller. The closest 1/16 mark is 5/16 inch and the closest 1/64 mark is 21/64 inch.