Decimal to Fraction Converter: Exact and Tape Measure

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How to use this tool

Type a decimal and read the fraction. The default answer is the simplest exact fraction, found by continued fractions and then reduced. If you are working to a tape measure, switch the answer type to sixteenths, thirty seconds or sixty fourths and the tool snaps to the nearest real mark and tells you how far off that is.

The two settings underneath control how hard the tool works for a simple answer. Loosening how close is close enough will trade a little accuracy for a much simpler fraction, which is often what you actually want. Capping the largest denominator does the same thing more bluntly. Leave both alone and you get the exact answer.

Why some decimals have no place on a tape measure

A tape measure is divided by repeated halving: a half, then quarters, eighths, sixteenths, sometimes thirty seconds. Every mark on it is a fraction whose denominator is a power of two.

That means a decimal lands exactly on a mark only when its fraction reduces to a power of two underneath. 0.375 is 3/8, so it lands. 0.5 is 1/2, 0.0625 is 1/16, both land. But 0.1 is 1/10, and 10 is 2 times 5, so the 5 will never divide out. No amount of finer graduation will ever produce a mark at exactly 0.1 inches. The tool will happily tell you the nearest sixteenth is 1/8, which is 0.125, and that you are 0.025 of an inch out, about two thirds of a millimetre.

This is the same reason 0.1 cannot be stored exactly in binary floating point, and it is not a coincidence. Both systems are built on powers of two, and any fraction with a factor of five or anything else in the denominator is going to be approximated in both.

A worked check you can repeat on paper

Take 0.375. Write it as 375 over 1000, because there are three digits after the point. Now reduce. Both divide by 25 to give 15 over 40, and both of those divide by 5 to give 3 over 8. That is the answer, and the greatest common divisor you cancelled in total was 125.

Check it the other way: 3 divided by 8 is 0.375 exactly. And 8 is 2 times 2 times 2, a power of two, so this value sits exactly on the third sixteenth mark of the tape.

Now try 0.1 the same way. It is 1 over 10, and 10 factors into 2 and 5. The 5 has nowhere to go, so no power of two denominator will ever equal it. That single factor of five is the whole reason 0.1 is awkward.

Mistakes that catch people out

Rounding a repeating decimal and expecting a clean fraction. If you type 0.333 you asked for exactly three hundred and thirty three thousandths, which is 333/1000, not one third. Type more threes, or loosen the tolerance setting, and one third appears.

Assuming the nearest sixteenth is close enough. A sixteenth of an inch is 1.5875 mm, so snapping can move you by up to 0.79 mm. On a door frame that is invisible and on a machined part it is a reject.

Confusing a decimal foot with a decimal inch. Survey and site drawings often use decimal feet, so 0.5 means six inches, not half an inch. Check the unit before converting anything on a set of grade sheets.

Reducing by hand and stopping early. 375/1000 reduced by 5 gives 75/200, which still reduces. If the numerator and denominator are both even, or both end in 5 or 0, there is more to cancel.

Popular decimal to fraction conversions

The decimals people look up most. Each opens the converter on that value with its own address.

How this was checked

The continued fraction routine was tested against a list of known pairs covering terminating decimals, repeating ones, sixteenths and negatives. Two real bugs turned up in that process and were fixed before publication. The tolerance was initially so tight that 0.142857142857 came back as a twelve digit fraction instead of one seventh, and the formatter dropped the minus sign on values between minus one and zero, so minus 0.75 was displaying as three quarters.

Round tripping was checked on every test value: converting the decimal to a fraction and dividing the fraction back out returns the original number to within a ten thousandth of a billionth, which is floating point noise rather than a real difference.

One result worth explaining, because it looks wrong. Type 3.14159265 and the strict setting gives 3 and 4623/32650 rather than the famous 3 and 16/113. That is correct: 355/113 differs from the digits you typed by about three parts in ten million, which is outside the strict tolerance. Loosen the tolerance one step and the familiar approximation appears. The tool is answering the question you asked rather than the one it guessed you meant.

Related Calculators and Reference

See also the Fraction Calculator for adding, subtracting, multiplying and dividing fractions once you have them. Also see the Long Division Calculator: the other direction, a fraction worked out as a decimal by hand.

See also the Prime Factorisation Calculator for cancelling a fraction properly, which is exactly dividing out the shared prime factors.

See also the Binary, Hex and Decimal Converter for why powers of two matter, which is the same reason only some decimals land on a tape measure mark.

To go straight from a measurement rather than a bare decimal, the Length Converter converts the length and gives you the nearest sixteenth in one step.

• Significant Figures and Rounding Calculator for deciding how many digits a decimal deserves before you convert it.
• Ratio and Proportion Calculator for fractions used as mix ratios and scales rather than measurements.
• Feet and Inches to CM Converter for taking a fractional inch measurement into metric.
• Percentage Calculator for the other common way of expressing a part of a whole.
• Scientific and Engineering Notation Converter for decimals at the very large and very small end.
• GCF Calculator: check that a numerator and denominator share no common factor.