Decimal to mixed number, in lowest terms.

A decimal to mixed number calculator turns a decimal such as 2.375 into 2 3/8. It works for decimals that end and for decimals that repeat, gives the answer in lowest terms and as an improper fraction, and writes out each step. It can also find the nearest eighth, sixteenth or sixty-fourth, which is what you need when a measurement has to match a ruler or a drill set.

How to use the decimal to mixed number calculator

1. Type the decimal in Decimal, such as 2.375.
2. For a repeating decimal, put the repeating digits in brackets. 1.666... is written 1.(6).
3. To match a ruler, pick a size under Also find the nearest. The nearest fraction and how far off it is appear as an extra card.
4. Read the mixed number, then open The steps for the working.

The method for decimals that end

Write the digits after the point over a 1 followed by that many zeros, then simplify. For 2.375, the part after the point is 375 and there are 3 digits, so the fraction is 375/1000. Divide the top and bottom by their greatest common factor, 125, to get 3/8. The whole part is 2, so the answer is 2 3/8. The same steps give 0.75 = 75/100 = 3/4, 3.125 = 3 1/8 and 4.2 = 4 2/10 = 4 1/5.

The method for decimals that repeat

Call the number x. For 0.(3), multiply by 10 to get 10x = 3.(3), then subtract x: 9x = 3, so x = 3/9 = 1/3. The calculator does the same with the right power of ten for the length of the repeating block. 1.(6) gives 1 2/3, and 0.1(6) gives 1/6.

Common decimals and their fractions

Nearest fraction for measuring

Most decimals do not match a ruler mark. To find the nearest sixteenth, multiply the decimal by 16 and round. For 2.43, the fractional part is 0.43 and 0.43 × 16 = 6.88, which rounds to 7, so 2 7/16, or 2.4375. The gap is 0.0075. The exact fraction for 2.43 is 2 43/100, which no ruler shows. A half goes in one step, a quarter in two, so choose the finest size your tool reads.

Negative decimals and whole numbers

A minus sign stays in front of the whole answer: -1.25 is -1 1/4. A decimal with nothing after the point, like 6.0, is the whole number 6. A decimal below 1, like 0.375, has no whole part and is just 3/8.

A ruler reading that comes out exact

0.8125 is 8125/10000, which simplifies by 625 to 13/16. Because the bottom number is 16, the nearest sixteenth card shows 13/16 with nothing off, so you know the reading sits right on a ruler mark. A reading like 0.82 does not, and the card shows how far it is from 13/16.

Common problems

• You typed 0.333... and got a message. Write it as 0.(3) so the calculator knows which digits repeat.
• A long decimal gives a huge fraction. That is exact. 0.3333 is 3333/10000, not 1/3, because the digits stop. Use brackets if you mean forever.
• A comma is read as a thousands separator and removed, so type a point for the decimal mark.

To go back from a mixed number, use mixed number to decimal. For sums with fractions, try the fraction calculator.