Mixed number to decimal, with the long division.

A mixed number to decimal calculator turns a number like 3 5/8 into 3.625. The whole part stays as it is, and the fraction is divided out as a decimal. This calculator gives the exact decimal, marks any digits that repeat forever, can round to a set number of places, and writes out the long division so you can see where each digit comes from.

How to use the mixed number to decimal calculator

1. Type the number in Mixed number, with a space between the whole part and the fraction: 3 5/8.
2. Pick how to show it under Show the decimal: Exactly, or a number of decimal places.
3. Read the big decimal. The cards below give the same value as a mixed number, an improper fraction and a percent.
4. Open The steps for the long division. Press Copy result to copy the answer.

The method

Keep the whole number and divide the top of the fraction by the bottom. For 3 5/8, divide 5 by 8. Add a zero and go on: 50 ÷ 8 = 6 remainder 2, then 20 ÷ 8 = 2 remainder 4, then 40 ÷ 8 = 5 remainder 0. The digits are 0.625, so 3 5/8 = 3.625.

You can also turn the number into an improper fraction first: 3 5/8 = 29/8, and 29 ÷ 8 = 3.625. Both routes agree.

More worked examples

• 1 7/16. 7 ÷ 16 = 0.4375, so the answer is 1.4375. It ends because 16 is 2 × 2 × 2 × 2.
• 5 3/4. 3 ÷ 4 = 0.75, so 5.75.
• 2 1/3. 1 ÷ 3 = 0.333..., and the 3 never stops. The calculator writes 2.3 with the 3 marked as repeating. Rounded to 4 places it is 2.3333.
• 4 5/6. 5 ÷ 6 = 0.8333..., with only the 3 repeating. Rounded to 4 places it is 4.8333.

When does a decimal end, and when does it repeat

Write the fraction in lowest terms. If the bottom number has no prime factors except 2 and 5, the decimal ends. If it has any other factor, such as 3 or 7, the decimal repeats. So 3/8 ends (0.375), 7/20 ends (0.35), 1/3 repeats (0.333...) and 1/7 repeats with the block 142857.

Sixteenths of an inch

On a ruler, each sixteenth is 0.0625. The odd sixteenths are 1/16 = 0.0625, 3/16 = 0.1875, 5/16 = 0.3125, 7/16 = 0.4375, 9/16 = 0.5625, 11/16 = 0.6875, 13/16 = 0.8125 and 15/16 = 0.9375. A board that measures 2 3/16 inches is 2.1875 inches.

Common problems

• You see a decimal that goes on, such as 2.333.... That is correct, not an error. Choose a number of decimal places to cut it.
• You typed 3-5/8 with a dash. That is read as 3 and 5/8. A minus sign only works at the very start.
• Rounding changes the value. 2.3333 is close to 2 1/3 but not equal, so keep the fraction when you need the exact amount.

To go the other way, use decimal to mixed number. For sums with fractions, try the mixed fraction calculator.