To convert a fraction to a decimal, divide the numerator by the denominator. The line in a fraction is a division sign, so 3/4 means 3 ÷ 4, which is 0.75. That one rule covers every fraction there is, and the shortcuts below simply save you the long division when the denominator happens to be a convenient one.
Key points to remember
- The numerator is the number above the line, and it counts how many parts you have.
- The denominator is the number below the line, and it says how many equal parts the whole was split into.
- The line between them is a divide symbol.
- To convert a fraction to a decimal, divide the numerator by the denominator.
Take 1/2 as the simplest case. 1 is the numerator, 2 is the denominator, and 1 ÷ 2 = 0.5. A decimal writes the same value in a different way, using place value after the point: tenths, then hundredths, then thousandths.
Fractions are not limited to values below one whole. 1/2 is 0.5, but 7/4 is 1.75 and 12/4 is 3, so a converted fraction can easily be larger than one.
Fractions and decimals appear constantly in numerical reasoning tests, where converting to decimals is usually the quickest way to compare options or spot the largest share in a table.
How to convert a fraction to a decimal
Step 1: Read the fraction as a division
The dividing line means divide, so every fraction is a division waiting to be carried out. The numerator goes first and the denominator second: 5/8 is 5 ÷ 8, not 8 ÷ 5.
Reversing the two is the most common error in this topic, and it is easy to spot once you know the sizes. 5 ÷ 8 = 0.625, while 8 ÷ 5 = 1.6. A proper fraction can never convert to more than 1.
Step 2: Scale the denominator to 10, 100 or 1,000 where you can
If the denominator divides into 10, 100 or 1,000, multiply the top and the bottom by whatever takes you there and read the decimal straight off.
For 1/2, 2 x 5 = 10, so 1/2 = 5/10 = 0.5. For 3/4, 4 x 25 = 100, so 3/4 = 75/100 = 0.75. Tenths give one decimal place, hundredths two and thousandths three.
This shortcut only works when the denominator is built from 2s and 5s, so it handles 2, 4, 5, 8, 10, 16, 20, 25 and 50, but it will never work for 3, 6, 7, 9 or 11.
Step 3: Otherwise divide it out, adding a decimal point and zeros
Set the numerator up as a long division, put a decimal point after it and add zeros as you need them.
Take 5/8. 8 does not go into 5, so start with 0 and carry the 5 to make 50. 8 goes into 50 six times with 2 left over, giving 0.6. Bring down a zero to make 20, and 8 goes in twice with 4 left over, giving 0.62. Bring down another zero to make 40, and 8 goes in five times exactly, giving 0.625.
If the remainder starts repeating instead of reaching zero, the decimal recurs. 2 ÷ 3 keeps returning a remainder of 2, so it runs 0.666… without ending, and you either mark the recurring digit or round to the number of decimal places the question asks for.
Fraction to decimal chart
These come up often enough that learning them saves real time in a timed test.
| Fraction | Decimal |
|---|---|
| 1/2 | 0.5 |
| 1/3 | 0.333… |
| 2/3 | 0.666… |
| 1/4 | 0.25 |
| 3/4 | 0.75 |
| 1/5 | 0.2 |
| 2/5 | 0.4 |
| 3/5 | 0.6 |
| 4/5 | 0.8 |
| 1/6 | 0.1666… |
| 5/6 | 0.8333… |
| 1/8 | 0.125 |
| 3/8 | 0.375 |
| 5/8 | 0.625 |
| 7/8 | 0.875 |
| 1/9 | 0.111… |
| 1/10 | 0.1 |
| 1/16 | 0.0625 |
| 1/20 | 0.05 |
| 1/25 | 0.04 |
Example questions
Below are five worked examples. The first two use the scaling shortcut, the next two use division, and the last one deals with a fraction worth more than one whole.
Example question 1
What is four-fifths as a decimal?
- Find a number that multiplies 5 up to 10, 100 or 1,000. The easiest target is 10, since 5 x 2 = 10, so 2 is our number.
- Multiply both parts by 2: 4 x 2 = 8 and 5 x 2 = 10. That gives a new fraction of 8/10, or eight tenths.
- Eight tenths is one decimal place, so the 8 sits immediately after the point.
Answer: 4/5 = 0.8
Example question 2
What is three-quarters as a decimal?
- No whole number multiplies 4 up to 10, so aim for 100 instead.
- 4 x 25 = 100, so 25 is our number.
- Multiply both parts by 25: 3 x 25 = 75 and 4 x 25 = 100, giving 75/100.
- Hundredths need two decimal places, so 75/100 is written as 0.75.
Answer: 3/4 = 0.75
Example question 3
What is 5/8 as a decimal?
8 does not divide into 10 or 100, but it does divide into 1,000, so either method works. Taking the division route, 5 ÷ 8 gives 0.6 after the first step, 0.62 after the second and 0.625 after the third, when the remainder finally reaches zero.
The scaling route agrees: 8 x 125 = 1,000 and 5 x 125 = 625, so 5/8 = 625/1000 = 0.625.
Answer: 5/8 = 0.625
Example question 4
What is 4/11 as a decimal?
11 is not built from 2s and 5s, so there is no shortcut here and division is the only route.
4 ÷ 11 starts with 40, and 11 goes into 40 three times with 7 left over, giving 0.3. Bring down a zero to make 70, and 11 goes in six times with 4 left over, giving 0.36. The remainder of 4 is where we began, so the pattern repeats without ending.
Answer: 4/11 = 0.3636…, usually written as 0.36 with the 3 and the 6 marked as recurring, or rounded to 0.36 for two decimal places.
Example question 5
What is 9/4 as a decimal?
The numerator is larger than the denominator, so the answer will be more than one whole. 4 goes into 9 twice with 1 left over, which gives 2 before the point. Carry the 1 to make 10, and 4 goes in twice with 2 left over, giving 2.2. Bring down a zero to make 20, and 4 goes in five times exactly.
Answer: 9/4 = 2.25. The same logic converts a mixed number: 2 3/8 is 2 plus 0.375, which is 2.375.
Recurring decimals and rounding
A decimal recurs when the division never produces a remainder of zero. Denominators of 3, 6, 7, 9, 11 and 12 all produce recurring decimals, and 1/7 is the classic case, running 0.142857 over and over.
In an exam you almost always round rather than write the recurrence out. 1/3 = 0.333…, which is 0.33 to two decimal places. 2/3 = 0.666…, which rounds up to 0.67 to two decimal places, because the next digit is a 6.
Round at the end of a calculation, never at the start. Rounding 2/3 to 0.7 before multiplying it by a large figure introduces an error big enough to change which multiple choice option looks right.
Dividing decimals by whole numbers
Converting a fraction often leaves you dividing a decimal by a whole number, and it works exactly like ordinary long division. Keep the decimal point in the answer directly above the decimal point in the number you are dividing, then divide digit by digit.
Take 9.36 ÷ 4. 4 goes into 9 twice with 1 left over, so the answer starts with 2. Carry the 1 to make 13, and 4 goes into 13 three times with 1 left over, giving 2.3. Carry the 1 to make 16, and 4 goes into 16 exactly four times, giving 2.34.
Two more to check yourself against: 7.2 ÷ 6 = 1.2, and 0.6 ÷ 5 = 0.12, where you have to add a zero after the 6 to finish the division. Multiplying back is the fastest check, since 6 x 1.2 = 7.2 and 5 x 0.12 = 0.6.
Turning the decimal into a percentage
Test questions often want a percentage rather than a decimal, and the decimal is the halfway house. Multiply by 100 and add the sign, so 7/20 = 0.35 = 35 per cent, and 5/8 = 0.625 = 62.5 per cent.
Mistakes that cost marks
- Dividing the denominator by the numerator. The top number goes into the calculator first.
- Forcing the scaling shortcut on a denominator that will not cooperate. If it has a factor of 3, 7 or 11 in it, divide instead.
- Miscounting decimal places when scaling. 3/4 is 75/100, which is 0.75, not 0.075.
- Truncating a recurring decimal instead of rounding it. 2/3 to two decimal places is 0.67, not 0.66.
- Rounding too early in a multi step question.
Practice fraction and decimal questions
Converting fractions is worth drilling until it is automatic, because in a real test it is never the question itself. It is the step you take before comparing figures, calculating a percentage change or reading a share off a table.
Work through numerical reasoning tests for the table based questions, basic numeracy tests to sharpen the arithmetic itself, and the free aptitude tests if you want to time yourself first.
