Fractions to Decimals
A fraction and a decimal are two ways of writing the same number. Once a child sees that, percentages come almost free.
The same number twice
A hundred square makes this one obvious. The grid has 100 small squares, so shading it is a way of counting hundredths.
Shade a quarter of the grid instead and you get 25 squares.
Nothing is being converted in any real sense. The amount never changes. Only the notation does.
Method 1, make it tenths or hundredths
Decimals are built on tenths, hundredths and thousandths. So if you can rewrite a fraction with 10, 100 or 1000 on the bottom, you can read the decimal straight off.
The rule
Use the equivalent fraction rule to get a denominator of 10, 100 or 1000. Then the numerator is your decimal digits.
34: multiply top and bottom by 25 to get 75100, which is 0.75.
This method is fast and it keeps the meaning visible. It only works when the denominator divides into 10, 100 or 1000, which covers 2, 4, 5, 8, 10, 20, 25 and 50.
Method 2, just divide
The fraction line has always meant divide. 34 means 3 divided by 4.
So work out 3 ÷ 4. Set it out as a short division, adding a decimal point and zeros as needed, and you get 0.75.
This method always works, including for denominators like 3, 6 and 7 where the first method cannot help.
Which number goes inside the division?
The top one. 34 is 3 ÷ 4, not 4 ÷ 3. A quick sanity check: 34 is less than 1, so the decimal must start with 0. If you get 1.33 you divided the wrong way round.
Some fractions never finish. 13 gives 0.333 and the threes carry on forever. That is called a recurring decimal, and it is usually rounded or written with a dot above the repeating digit.
Worth learning by heart
These eight come up constantly, in tests and in life. Knowing them saves working out the same thing hundreds of times.
- 12 = 0.5 = 50 percent
- 14 = 0.25 = 25 percent
- 34 = 0.75 = 75 percent
- 15 = 0.2 = 20 percent
- 25 = 0.4 = 40 percent
- 110 = 0.1 = 10 percent
- 18 = 0.125 = 12.5 percent
- 13 = 0.333 and so on, about 33.3 percent
Worked examples
Using equivalent fractions
- Can 5 be turned into 10, 100 or 1000? Yes, 5 × 2 = 10.
- Do the same to the top. 2 × 2 = 4, giving 410.
- Four tenths is written 0.4.
- Check: 2/5 is a bit less than a half, and 0.4 is a bit less than 0.5.
Using division
- 8 does divide into 1000, but the easier route here is division.
- Work out 5 ÷ 8. Since 8 does not go into 5, start with 0 point.
- 8 into 50 goes 6 times with 2 left. 8 into 20 goes 2 times with 4 left. 8 into 40 goes 5 times exactly.
- Reading the digits off gives 0.625.
Simplify first, then convert
- Those numbers look awkward, so simplify before doing anything else.
- Both divide by 15. 15 ÷ 15 = 1 and 60 ÷ 15 = 4, giving 14.
- A quarter is one of the eight worth knowing by heart.
- Simplifying first turned a long division into something you already knew.
Common mistakes
1. Dividing the wrong way round
Working out 4 ÷ 3 for 34 and getting 1.33. The top number goes inside the division. If the fraction is less than 1, the decimal must start with 0, so 1.33 is a signal to try again.
2. Reading the digits straight off the fraction
Writing 14 as 0.14, or 12 as 0.12. The digits of a fraction are not the digits of its decimal. Only a denominator of 10, 100 or 1000 lets you read anything off directly.
3. Losing a place value
Writing 3100 as 0.3 instead of 0.03. Three hundredths needs a zero holding the tenths place. Say the fraction out loud first, then write the decimal to match what you said.
Practice questions
Seven questions. One attempt each, and the explanation appears once the answer is in.
Check yourself
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For parents
The eight conversions in the list above are the highest-value thing your child can memorise in this whole topic. Five minutes of flashcards a few times a week, and they will stop calculating 3/4 as 0.75 and simply know it. That freed-up thinking time is what makes percentage questions feel easy later.
What to learn next
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