"Fractions to decimals to percentages" is typed by parents in the UK from the autumn of Year 6, when the homework starts asking for the same amount three ways, and by the same parents in the spring, when the SATs papers do it in question 3. It is one idea (a part of a whole, written in three notations), six conversions, and a small chart worth knowing by heart. This page does all six conversions with a worked example each, gives the chart, lists the six mistakes behind most wrong answers, and ends with a free printable chart and a 30-question worksheet with answers.
Download the chart and worksheet (PDF) (A4, the equivalents chart on page 1, 30 questions on page 2, answers on page 3, free).
One amount, three ways of writing it
Three quarters of a pizza, 0.75 of it, 75% of it: the same pizza. A fraction says "3 of 4 equal parts". A decimal says the same thing in tenths, hundredths and thousandths (0.75 = 7 tenths and 5 hundredths). A percentage says it in hundredths only (75 per hundred). Once a child sees that a percentage is just a fraction whose bottom number is always 100, and a decimal is just a fraction whose bottom number is 10, 100 or 1,000 written without the line, most of the converting stops being a set of rules and becomes one idea.
The six conversions, with an example each
| From → to | Method | Example |
|---|---|---|
| Fraction → decimal | Divide the top by the bottom | 3/8 = 3 ÷ 8 = 0.375 |
| Decimal → percentage | Multiply by 100 (digits move two places left) | 0.375 → 37.5% |
| Fraction → percentage | Make the bottom 100 if you can; otherwise go via the decimal | 3/4 = 75/100 = 75%; 3/8 → 0.375 → 37.5% |
| Percentage → decimal | Divide by 100 (digits move two places right) | 45% → 0.45; 5% → 0.05 |
| Percentage → fraction | Write over 100, simplify | 45% = 45/100 = 9/20 |
| Decimal → fraction | Read the place value, then simplify | 0.375 = 375/1000 = 3/8 |
Fraction to decimal in full: 3/8. Write 3 as 3.000 and divide by 8 with the bus-stop (short division) method: 8 into 3 is 0, remainder 3; 8 into 30 is 3, remainder 6 (write 0.3); 8 into 60 is 7, remainder 4 (0.37); 8 into 40 is 5 (0.375). Some fractions never end: 1/3 = 0.3333…, written 0.3 with a dot over the 3 in the UK and a bar over it in the US. Any fraction whose simplified bottom number has only 2s and 5s as factors (2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 100) gives a decimal that ends. Any other bottom number (3, 6, 7, 9, 11, 12) gives a decimal that repeats.
Decimal to percentage: why "times 100". Per cent means "per hundred". 0.375 is 375 thousandths, which is 37.5 hundredths, so 37.5 per hundred, so 37.5%. Multiplying by 100 moves every digit two places to the left, and the decimal point stays where it is; children who "move the point" get the direction wrong about half the time, so teach "the digits move left when the number gets bigger".
Percentage to fraction: simplify properly. 45% = 45/100. Both divide by 5: 9/20. 12.5% is the awkward one: 12.5/100, multiply top and bottom by 10 to clear the decimal (125/1000), then divide both by 125: 1/8. 33⅓% is 1/3 exactly, not 33/100.
The chart to know by heart
| Fraction | Decimal | Percentage | Fraction | Decimal | Percentage |
|---|---|---|---|---|---|
| 1/2 | 0.5 | 50% | 1/8 | 0.125 | 12.5% |
| 1/4 | 0.25 | 25% | 3/8 | 0.375 | 37.5% |
| 3/4 | 0.75 | 75% | 5/8 | 0.625 | 62.5% |
| 1/5 | 0.2 | 20% | 7/8 | 0.875 | 87.5% |
| 2/5 | 0.4 | 40% | 1/3 | 0.333… | 33⅓% |
| 3/5 | 0.6 | 60% | 2/3 | 0.666… | 66⅔% |
| 4/5 | 0.8 | 80% | 1/10 | 0.1 | 10% |
| 1/20 | 0.05 | 5% | 1/100 | 0.01 | 1% |
Two patterns make the chart shorter than it looks. Fifths go up in 0.2s and 20s. Eighths go up in 0.125s and 12.5s, so once 1/8 is known, 3/8, 5/8 and 7/8 are three additions. The thirds are the only recurring ones on the list.
Where it sits in each curriculum
| Curriculum | When | What is expected |
|---|---|---|
| England (National Curriculum) | Year 4 decimals; Year 5 percentages introduced; Year 6 all three | Year 6 SATs: "write 0.35 as a fraction in its simplest form", "which is larger, 3/5 or 55%?", missing-number equivalents; the chart above is assumed |
| USA (Common Core) | Grade 4 (4.NF.6) and 5 decimals; Grade 6 (6.RP.3c) percent | Percent of a quantity, converting between the three, ordering mixed sets |
| Australia | Year 5 and 6 | Connect fractions, decimals and percentages; solve percent-of problems |
| CBSE | Class 5 and 6 decimals; Class 7 Comparing Quantities | Convert in all directions, percentage increase and decrease, simple interest follows |
| Netherlands | Groep 6 to 8 | "Breuken, kommagetallen, procenten", the same triangle, in the Dutch order |
The six mistakes behind most wrong answers
- 5% written as 0.5. Five per hundred is 0.05. The check: 50% is a half, so 5% must be much smaller than a half.
- 0.5 and 0.05 and 0.55 treated as "about the same". Line the decimals up with the same number of places (0.50, 0.05, 0.55) before comparing.
- 1/3 written as 0.3 or 33%. It is 0.333… recurring and 33⅓%. On a calculator, 0.33 × 3 = 0.99, not 1; that is the proof.
- Comparing a fraction with a percentage without converting. "Which is bigger, 3/5 or 55%?" Convert both to the same form (60% vs 55%) and then decide. Children guess from the size of the numbers otherwise.
- Moving the decimal point the wrong way. Bigger number, digits move left (decimal to percentage). Smaller number, digits move right (percentage to decimal).
- Not simplifying. 45/100 is correct but loses the mark that says "in its simplest form". Divide by 5 or 2 or 10 until nothing divides both.
How to practise it at home, ten minutes a day
Pick three lines from the chart each evening and ask them both ways, out of order ("what is 3/8 as a decimal? what is 60% as a fraction?"). Do it for a fortnight and the chart is in. Then use the worksheet: 30 questions in three blocks of ten (conversions, comparing and ordering, percent-of problems), 25 minutes, no calculator, mark it together with the answer page. The questions a child gets wrong in block 1 tell you which conversion to reteach; block 2 wrong with block 1 right means the child can convert but does not compare; block 3 wrong is about the method for "30% of 240", which is a separate lesson (10% first, then multiply).
Download the chart and worksheet (PDF)
Where to get help
A 1-on-1 online maths class with a tutor who holds a master's in mathematics and teaches the Year 5 and 6 curriculum, the KS2 SATs, US Grade 4 to 6 and CBSE Class 6 and 7 every week: fractions, decimals and percentages taught as one idea, the chart learnt with games rather than by rote, and a marked worksheet after every class. The KS2 SATs page has the arithmetic and reasoning paper details; the free 30-minute first class is a real lesson on this week's topic. If long division is the sticking point before the decimals, that method is here.
Questions parents ask
1How do you convert a fraction to a decimal to a percentage?
2How do you convert a percentage back to a fraction?
3Which fraction, decimal and percentage equivalents should a child know by heart?
4What year do children learn fractions, decimals and percentages?
See how we teach this, 1-on-1 online →
Shobha
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Teaching maths, science and English to children online since 2018. 500+ students, 20+ tutors, families in nine countries.