Decimal to Fraction Converter

Fractions of an inch with decimal and millimetre equivalents

Decimal inches rounded to the nearest tape mark

Common decimals as fractions

How to convert a decimal to a fraction

1. Count the digits after the decimal point. 0.375 has three, so the denominator is 10 to the power 3, which is 1000. The numerator is the digits without the point: 375.
2. Write the digits over the power of 10. 0.375 = 375/1000. A whole-number part stays: 2.375 = 2375/1000.
3. Divide the top and bottom by their GCD. The greatest common divisor of 375 and 1000 is 125, so 375/1000 = 3/8. 2.375 = 2 3/8, or 19/8 as an improper fraction.
4. For a repeating decimal, subtract a shifted copy. With x = 0.(3), 10x = 3.(3), and subtracting gives 9x = 3, so x = 1/3. Type the repeating digits in parentheses, or end with three dots: 0.666... = 2/3.
5. For a tape measure, round to the nearest mark. Multiply the decimal inches by the number of marks per inch and round to a whole number: 0.7 × 16 = 11.2, which rounds to 11, so 11/16 inch. The rounding error (rounded minus exact) is −0.0125 in, −0.3175 mm.

Frequently asked questions

How do you convert a decimal to a fraction?

Write the digits after the point over 1 followed by as many zeros, then simplify by dividing the top and bottom by their greatest common divisor. 0.375 = 375/1000, and the GCD of 375 and 1000 is 125, so it is 3/8. For 2.375 the answer is 2 3/8, which is 19/8 as an improper fraction.

How do you convert a repeating decimal to a fraction?

Subtract a shifted copy of the number from itself so the repeating part cancels. With x = 0.(3), 10x − x = 3, so x = 3/9 = 1/3. With x = 0.1(6), 100x − 10x = 15, so x = 15/90 = 1/6. Type the repeating digits in parentheses, as in 0.(3) or 0.1(6).

What does 0.333... mean, and does the converter accept it?

Three dots after a decimal mean the last digit repeats forever, so 0.333... is 0.(3) = 1/3 and 0.666... is 2/3. The converter reads three dots (or the … character) that way. For a longer repeating block such as 0.142857142857..., put the block in parentheses: 0.(142857) = 1/7.

How do I convert a decimal inch to a fraction on a tape measure?

Choose tape measure mode and the finest mark your tape or project needs. A tape shows halves, quarters, eighths, sixteenths and sometimes thirty-seconds, so 0.7 inch is 11/16" to the nearest 1/16 inch, 11/16" to the nearest 1/32 inch and 45/64" to the nearest 1/64 inch. The rounding error is shown in inches and millimetres, so you can decide whether it matters for the cut.

How much error does rounding to 1/16 inch cause?

At most half a mark: 1/32 inch, or about 0.79 mm, for a 1/16 inch tape. The converter shows the actual error for your number, for example 0.7 inch is 11/16" (−0.0125 in, −0.3175 mm). Rounding to 1/32 inch halves the worst case to 1/64 inch, about 0.4 mm.

Why does 0.99 inch round to 1 inch?

Because 0.99 is closer to 1 than to 15/16, which is 0.9375. At 1/16 inch the nearest mark is 1", only 0.01 inch away. A decimal that lands on a whole number of marks needs no fraction at all, and a result of 12 inches or more is also shown in feet and inches.

Can I enter feet instead of inches?

Yes. In tape measure mode choose “Feet” for the unit and the number is multiplied by 12 first: 5.4 feet is 64.8 inches, which rounds to 64 13/16" at 1/16 inch, or 5' 4 13/16" in feet and inches.

How do I convert a fraction to a decimal?

Type the fraction and the converter divides the top by the bottom. 5/16 = 5 ÷ 16 = 0.3125, and in millimetres a 5/16 inch mark is 7.9375 mm. Fractions such as 1/3 do not end, and the repeating digits are shown in parentheses: 0.(3).

Does it handle negative numbers and mixed numbers?

Yes. A minus sign is carried through: −0.75 = −3/4. A mixed number such as 2 3/8 is read exactly and shown as the decimal 2.375.

Is the conversion exact, or does it use floating point?

It is exact. Digits are kept as whole numbers of any size (up to 30 digits), never as floating-point values, so a decimal such as 0.30000000000000004 gives its true fraction instead of 3/10. Rounding happens only in tape measure mode, once, and the error is shown.