A mixed number such as 2 3/8 is a whole number plus a fraction. To write it as a decimal you only need to convert the fraction part — the whole number stays in front of the decimal point. This calculator does the division, shows the remainders that reveal any repeating pattern, and rounds the result to the number of places you choose.
How to use the converter
- Enter the whole number in the left box and the fraction in the stacked boxes.
- Choose how many decimal places to round to.
- The tape shows the exact decimal (with a bar over repeating digits), the rounded value, the improper fraction and the percent. A note explains why the decimal terminates or repeats.
- Under the steps, a long-division layout shows the fraction part being divided.
The method
- Divide the numerator by the denominator using long division, adding zeros after the decimal point as needed.
- Stop when the remainder is 0 (the decimal terminates) or when a remainder repeats (the digits repeat from there on).
- Add the whole number.
Equivalently, convert to an improper fraction first — 2 3/8 = 19/8 — and divide: 19 ÷ 8 = 2.375. Both routes give the same answer.
Worked example: 2 3/8
- 3 ÷ 8: 8 goes into 30 three times (24), remainder 6.
- Bring down a 0: 60 ÷ 8 = 7 (56), remainder 4.
- Bring down a 0: 40 ÷ 8 = 5 (40), remainder 0 — the decimal ends. So 3/8 = 0.375.
- Add the whole number: 2 3/8 = 2.375.
Because 8 = 2³ has only the prime factor 2, the decimal was guaranteed to terminate.
Common fraction parts and their decimals
| Fraction part | Decimal | Fraction part | Decimal |
|---|---|---|---|
| 1/2 | 0.5 | 1/3 | 0.333… |
| 1/4 | 0.25 | 2/3 | 0.666… |
| 3/4 | 0.75 | 1/6 | 0.1666… |
| 1/8 | 0.125 | 5/6 | 0.8333… |
| 3/8 | 0.375 | 1/7 | 0.142857… |
| 1/16 | 0.0625 | 1/9 | 0.111… |
So 5 3/4 = 5.75, 1 1/3 = 1.333…, and 3 5/6 = 3.8333…. For a printable chart of every fraction up to 64ths, see the fraction to decimal chart.
Where you need this
- Measurements: a board that is 7 3/16 inches is 7.1875 in, the form most digital calipers and CAD programs use.
- Time: 2 3/4 hours is 2.75 hours on a time sheet.
- Recipes and scaling: 1 2/3 cups is about 1.67 cups when you multiply a recipe.
Rounding repeating decimals
Repeating decimals never end, so you round them to a sensible number of places. Look at the digit after the last place you keep: 5 or more rounds up. 1 2/3 = 1.6666… rounds to 1.67 (two places) or 1.6667 (four places). The exact value is still 5/3, which you can recover with the decimal to fraction calculator. To express the same mixed number as a percentage, use the mixed number to percent calculator.
Frequently asked questions
How do you convert a mixed number to a decimal?
Divide the numerator of the fraction part by its denominator, then add the whole number. For 2 3/8: 3 ÷ 8 = 0.375, and 2 + 0.375 = 2.375.
What if the fraction part gives a repeating decimal?
The digits after the point repeat forever, and the calculator marks the repeating block with a bar. 1 2/3 = 1.666…, written 1.6̅ or 1.(6). The rounded value to four places is 1.6667.
How do I convert a negative mixed number?
Convert the positive mixed number and attach the minus sign: −4 1/7 = −(4 + 0.142857…) = −4.142857…. The whole number and the fraction are both negative.
Which mixed numbers give terminating decimals?
Those whose fraction part, in lowest terms, has a denominator made only of 2s and 5s, such as halves, quarters, eighths, fifths, tenths and sixteenths. Thirds, sixths, sevenths and ninths always repeat.