Fraction to decimal:
divide top by bottom and read the answer

How to convert a fraction to a decimal

The fraction bar means division. Divide the top number by the bottom number and the quotient is the decimal. So 3/4 is 3 ÷ 4 = 0.75.

A calculator does this in one keystroke. By hand, you use long division, adding a decimal point and zeros to the numerator as needed, which is shown in the example below.

1. 1Write the fraction as numerator ÷ denominator.
2. 2If the numerator is smaller, put 0 and a decimal point in the answer and add a zero to the numerator.
3. 3Divide, bring down another zero and repeat.
4. 4Stop when the remainder is zero (terminating) or when a remainder repeats (recurring).

Example: 7/8 by long division

As a percentage that is 87.5%. Read the same fraction as marks: 7 out of 8 is 87.5%, whereas 37 out of 40 is 0.925, or 92.5%.

Fractions with a whole number part work the same way. Convert the fraction and add the whole number, so 2 3/5 is 2 + 0.6 = 2.6.

An improper fraction, one whose numerator is larger than its denominator, always gives a decimal above 1. For 9/4, 9 ÷ 4 = 2 remainder 1, and 1/4 is 0.25, so 9/4 = 2.25. If your answer for an improper fraction comes out below 1, the division was set up upside down.

Long division also shows you a recurring decimal. For 1/6, 10 ÷ 6 = 1 remainder 4, then 40 ÷ 6 = 6 remainder 4. The remainder 4 has appeared twice, so the 6 will repeat for ever: 0.1666…. The moment a remainder repeats, you know the pattern will too, and you can stop.

Will the decimal end or repeat?

Before dividing, you can predict the outcome. Simplify the fraction first, then factorise the denominator. If the only prime factors are 2 and 5, the decimal ends. Any other factor, such as 3 or 7, makes it repeat.

The simplification step matters. 6/15 looks like it has a 3 in the denominator, but it reduces to 2/5, which is 0.4 and ends. Always reduce before you test.

You can also predict how long a terminating decimal is. Write the denominator as 2 raised to a power times 5 raised to a power; the number of decimal places is the larger of the two powers. 3/8 has 2³, so three places (0.375), while 7/20 has 2² and 5¹, so two places (0.35).

Common recurring fractions and how to round them

Round only at the end. Take 2/3 of ₹300. The exact answer is ₹200. If you round 2/3 to 0.67 first, you get ₹201, and the error grows with larger amounts.

Where a recurring decimal is needed in writing, a dot above the repeating digit, or the fraction itself, is exact. A rounded decimal is an approximation, and you should say so.

How many places to keep depends on the job. Money normally needs two places, measurements in millimetres usually need one or two, and a science or engineering result should carry no more digits than the least precise input. When in doubt, keep one more place than you need through the working and round once at the end.

Fractions worth knowing as decimals

A handful of conversions cover most everyday needs. Once you know them, you can build others from them: if 1/8 is 0.125, then 3/8 is three times that, which is 0.375.

• 1/2 = 0.5, 1/4 = 0.25 and 3/4 = 0.75.
• 1/5 = 0.2, 2/5 = 0.4, 3/5 = 0.6 and 4/5 = 0.8.
• 1/8 = 0.125, 3/8 = 0.375, 5/8 = 0.625 and 7/8 = 0.875.
• 1/10 = 0.1 and 1/20 = 0.05, so 3/20 = 0.15.
• 1/16 = 0.0625, a useful one for tool and spanner sizes.

Fractions with a denominator of 2, 4, 5, 8, 10, 20, 25 or 50 always terminate within three places, so those are the ones worth memorising.

Where the decimal is more useful than the fraction

Decimals are easier to compare, enter into a spreadsheet or multiply by an amount. To find 3/8 of ₹2,400, convert 3/8 to 0.375 and multiply: 0.375 × 2,400 = ₹900. The percentage-of-a-number calculator on this page does the same job as 37.5% of 2,400.

Fractions remain better when the numbers are exact and small. Marking a tailor's cut at 5/8 inch is natural, while 0.625 inch is not. Keep the fraction for exactness and convert to decimals for arithmetic and comparison.

The same conversion turns a fraction into a percentage. A test score of 17/20 is 0.85, or 85%, and a reduction of 1/5 off a price is 0.2, or 20% off. In each case you multiply the decimal by 100, so you need only the division.

Mistakes people make when converting

• Dividing the denominator by the numerator. 3/4 is 3 ÷ 4 = 0.75, not 4 ÷ 3 = 1.33.
• Writing 3/4 as 0.34 by placing the digits either side of the point.
• Assuming a decimal ends because a calculator display ends. 1/7 shows 0.142857 on a short display but it repeats forever.
• Rounding a recurring decimal early and using it in further steps.
• Forgetting to simplify first when testing whether the decimal will terminate.
• Dropping the whole number from a mixed number, so 2 3/5 becomes 0.6 instead of 2.6.

To work backwards from a decimal to a fraction, the decimal to fraction guide shows the place-value method. For the arithmetic of fractions themselves, see the fraction guide.