Decimal to Fraction Calculator

Count the digits after the decimal point

A terminating decimal already names its own denominator. The digit farthest to the right carries a place value, and that place value is the fraction's bottom number before any reducing. One digit means tenths, two digits mean hundredths, three digits mean thousandths, and so on. George Mason University's basic math refresher states the same rule: place the digits over 10, 100 or 1000 and reduce.

Trailing zeros belong in the raw fraction and then cancel. The decimal 0.50 has two digits, so the raw fraction is 50/100, and dividing both parts by 50 leaves 1/2. Writing 0.5 instead skips a step but gives the same answer, which is worth checking once by hand so the place value logic feels concrete.

Whole digits sit to the left of the point and stay whole. The decimal 12.5 has one digit after the point, so the fractional part is 5/10, and the raw improper fraction is 125/10 before reducing to 25/2.

Reduce with the greatest common factor

The raw fraction is correct but oversized. Reducing divides the top and bottom by their greatest common factor, the largest number that divides both with no remainder. The fast way to find it is the Euclidean algorithm: divide, keep the remainder, repeat until the remainder hits zero.

The last nonzero remainder, 25, is the greatest common factor of 275 and 1000. Divide both by 25 and 275/1000 becomes 11/40, which is the shortest fraction equal to 0.275. The calculator runs the same algorithm on whatever you type and prints the dividing step in its output.

Powers of ten reduce more often than people expect, because 10 has only the prime factors 2 and 5. A denominator of 1000 is 2 to the third times 5 to the third, so any numerator made of 2s and 5s cancels cleanly. That is why 0.625 = 625/1000 reduces by 125 to 5/8, and why eighths, sixteenths and thirty-seconds all show up as terminating decimals with short, tidy forms.

Mixed numbers and negative decimals

A decimal with a whole part converts to an improper fraction first and can be read as a mixed number afterward. The improper form is what arithmetic wants; the mixed form is what a tape measure, a recipe card or a saw cut wants.

Take 2.375: three digits after the point give 2375/1000, the greatest common factor is 125, and dividing leaves 19/8. Eight fits into 19 twice with 3 left over, so the mixed number is 2 3/8. The calculator prints both forms on the same result line, plus the divide-back check described below.

Negative decimals keep the sign on the numerator and leave the denominator positive, which is the convention used in the calculator's output: -0.6 becomes -3/5, not 3 over negative 5. Both describe the same number, but the first form matches how the rest of arithmetic expects fractions to look.

Repeating decimals need one subtraction

A decimal that repeats forever, like 0.333333..., cannot be written over a power of ten, because no finite denominator captures it. The fix is to multiply by the right powers of ten and subtract, which cancels the repeating tail exactly.

If the digits before the repeating block number k and the block has r digits, then the fraction is (all digits minus the digits before the block) over (10 to the k+r minus 10 to the k). The subtraction is the whole trick: the repeating tails line up and cancel.

Check the third row by hand: 0.363636... times 100 is 36.363636..., and the original times 1 is 0.363636..., so subtracting leaves exactly 36 over 99, which reduces by 9 to 4/11. Divide 4 by 11 and the calculator display shows 0.36363636, the repeating pattern back again.

The block has to be typed for the exact answer. A truncated decimal such as 0.333333 is an ordinary terminating decimal equal to 333333/1000000, which is close to 1/3 but not equal to it. If you know the digits repeat, enter the block and the calculator uses the subtraction method; if you do not, the terminating conversion is the honest reading of what you typed. For truncated approximations of irrational numbers, convergents of a continued fraction give the best rational approximations, a standard result covered in the NIST Digital Library of Mathematical Functions.

Inch fractions on a tape measure

Tape measures, drill bits and wrenches use fractions with denominators that double: halves, quarters, eighths, sixteenths, thirty-seconds. Those denominators are why so many practical decimals terminate so quickly. The table lists the sixteenth grid, the spacing between marks on an imperial tape measure.

The millimeter column follows from one exact definition. NIST's Guide to the SI, Appendix B, lists the inch as exactly 2.54 centimeters, so each sixteenth is 25.4 divided by 16, which is 1.5875 mm, and every row above is that value times the numerator. Because 2.54 is exact by definition, none of those conversions rounds.

Real measurements rarely land on a mark, so the last step is rounding. A caliper reading of 0.62 inch sits closest to the 5/8 mark, since 0.62 times 16 is 9.92 and the nearest sixteenth is 10/16, which reduces to 5/8. A reading of 1.44 inches rounds to 14 thirty-seconds, or 1 7/16. The calculator's rounding menu covers 1/2 through 1/64 and prints the reduced result with its decimal value.

Common conversions worth knowing

A short list of conversions covers most everyday decimals. The first block is tenths, the middle block is the eighth family, and the last two rows are the repeating thirds.

Every row can be reproduced with the two methods above: count the digits, reduce by the greatest common factor, or spot the repeating block. The three-dot rows are shorthand for an infinite repeat and need the subtraction method, since 0.666 as typed is 666/1000, or 333/500, which is a different number from 2/3.

Percentages ride along for free, because a percent is a decimal times 100. The decimal 0.85 is 85 percent, and the same digits over 100 reduce to 17/20.

Check the answer by dividing back

Every conversion can be verified in one step: divide the numerator by the denominator and compare against the original decimal. The calculator prints that division to eight places so the check is visible on the result panel.

The first three rows are exact because terminating decimals always divide back cleanly. The last row never terminates: 1/3 produces 3 in every decimal place forever, and any finite display truncates it. That is the signature of a repeating decimal, and it is the practical test for whether the subtraction method applies.

When a check comes back close but not equal, the input was probably a rounded measurement rather than an exact decimal. 0.333333 differs from 1/3 by about 0.00000033, which is invisible on most displays and irrelevant for a wood cut, but it is a real difference if the number feeds into further arithmetic.

Where the method needs care

Three habits produce wrong fractions from right-looking inputs. The first is rounding before converting. A value displayed as 0.6667 is not 2/3, it is 6667/10000, and converting it gives a fraction with a four digit denominator that pretends to be more precise than the source. If the number came from a repeating decimal, recover the block and convert that instead.

The second is forgetting the whole part. The decimal 12.5 is not 5/10 with a 12 floating nearby; the raw improper fraction is 125/10. The calculator handles the split, but on paper the common error is reducing only the fractional part and gluing the whole number back on top of a different fraction.

The third is carrying more precision than the measurement supports. A dimension quoted as 0.3750 inch has four decimal places, but a tape measure resolves to a sixteenth, and the honest fraction is 3/8. Convert the number you measured, at the precision your tool supports, and let the reducing step tidy the rest.

For anything that feeds engineering work, state the precision next to the fraction. 19/8 and 2.375 are the same number, but 2.3750 and 19/8 make different claims about how the value was obtained.