How to Convert Fractions to Decimals

The fraction bar means "divided by". 3/8 is three pizzas shared among eight people, so each person gets 3 ÷ 8 of a pizza:

On any calculator, press 3 ÷ 8 =. The rest of this guide is about doing it by hand, and understanding what you get.

Put the numerator inside the bracket and the denominator outside. 8 doesn't go into 3, so write 0. on top, add a decimal point and zeros after the 3, and keep dividing until the remainder is 0:

30 ÷ 8 = 3 remainder 6, 60 ÷ 8 = 7 remainder 4, 40 ÷ 8 = 5 remainder 0. So 3/8 = 0.375. The long division guide covers the method in detail.

If you can turn the denominator into 10, 100 or 1000 by multiplying, the decimal is easy to read off:

• 3/4 = 75/100 = 0.75 (multiply top and bottom by 25)
• 2/5 = 4/10 = 0.4 (multiply by 2)
• 7/20 = 35/100 = 0.35 (multiply by 5)
• 3/8 = 375/1000 = 0.375 (multiply by 125)

This is often faster than long division in your head. It only works when the denominator can reach a power of 10, which leads to the next question.

Simplify the fraction first, then break the denominator into primes:

• Only 2s and 5s (like 4, 8, 20, 25, 40): the decimal ends, because 10 = 2 × 5.
• Any other prime (3, 7, 11…): the decimal repeats forever.

For 5/6, the denominator 6 = 2 × 3 has a 3, so it repeats. In the long division, the remainder 2 comes back again and again:

We write repeating digits with a bar: 0.83 means 0.8333…. Only the 3 repeats, so the bar goes over the 3 alone. 1/7 = 0.142857 has six repeating digits.

• Mixed numbers: the whole number stays in front of the point. Convert the fraction part and add: 2 3/4 = 2 + 0.75 = 2.75.
• Percents: multiply the decimal by 100, or move the point two places right: 3/8 = 0.375 = 37.5%.

On a basic calculator: 3 ÷ 4 + 2 = gives 2.75, and 3 ÷ 8 × 100 = gives 37.5.

Read the decimal by its last place value, then simplify:

1. 0.375 has three decimal places (thousandths), so it's 375/1000.
2. Find the GCF of 375 and 1000: it's 125. The GCF guide shows three ways.
3. Divide both: 375 ÷ 125 = 3, 1000 ÷ 125 = 8, so 0.375 = 3/8.

For a number above 1, keep the whole part: 2.75 = 2 + 75/100 = 2 3/4, or 11/4 as an improper fraction.

A repeating decimal has no last place, so use a little algebra to make the repeats cancel. For 0.1666…:

1. Let x = 0.1666…
2. Multiply so one full repeat passes the point: 100x = 16.666…
3. Multiply so only the repeating part is after the point: 10x = 1.666…
4. Subtract: the …666 parts cancel, leaving 90x = 15
5. So x = 15/90 = 1/6.

Shortcut: when the repeat starts right after the point, put the repeating digits over the same number of 9s: 0.4 = 4/9, 0.27 = 27/99 = 3/11, and 0.142857 = 142857/999999 = 1/7.

Check your answers with the Fraction to Decimal Calculator.

1. 3/5 as a decimal
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   0.6 (3/5 = 6/10)
2. 7/8 as a decimal
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   0.875
3. 2/9 as a decimal
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   0.222…, written 0.2
4. 5/12 as a decimal
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   0.41666…, written 0.416. 12 = 2² × 3, so it repeats.
5. 1 3/8 as a decimal and a percent
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   1.375 and 137.5%
6. 0.45 as a fraction
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   9/20. 45/100 divided by GCF 5.
7. 0.444… as a fraction
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   4/9
8. 0.8333… as a fraction
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   5/6. 100x = 83.33…, 10x = 8.33…, so 90x = 75 and x = 75/90.