To order fractions, decimals and percentages together, convert everything into the same form — decimals work best for comparing — then arrange from smallest to largest (or as the question directs) and rewrite the final answer in the original forms given. Trying to compare ¾, 0.7 and 65% directly causes errors; converting first removes all the ambiguity.
Why does mixing forms cause confusion?
Fractions, decimals and percentages are three different ways of writing the same kind of number — a part of a whole. Because they look so different, it is almost impossible to compare them reliably by eye. Is 5/8 more or less than 0.65? Is 72% greater than ¾? Converting everything to decimals puts all the numbers on the same scale, so the comparison is straightforward.
How do you convert a fraction to a decimal?
Divide the numerator by the denominator.
- 3/4 = 3 ÷ 4 = 0.75
- 2/5 = 2 ÷ 5 = 0.4
- 7/8 = 7 ÷ 8 = 0.875
- 1/3 = 1 ÷ 3 = 0.333… (recurring)
Some fractions are worth memorising because they appear frequently:
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/8 | 0.125 | 12.5% |
| 1/3 | 0.333… | 33.3…% |
| 2/3 | 0.666… | 66.6…% |
How do you convert a percentage to a decimal?
Divide the percentage by 100.
- 65% = 65 ÷ 100 = 0.65
- 7% = 7 ÷ 100 = 0.07
- 130% = 130 ÷ 100 = 1.3 (percentages can exceed 100%)
Full worked example: order ¾, 65%, 0.7, 3/5 and 70% from smallest to largest
| Original value | Decimal conversion |
|---|---|
| ¾ | 0.75 |
| 65% | 0.65 |
| 0.7 | 0.70 (already a decimal) |
| 3/5 | 0.60 |
| 70% | 0.70 |
Decimals in order: 0.60, 0.65, 0.70 = 0.70, 0.75
Answer: 3/5, 65%, 0.7, 70%, ¾
Notice that 0.7 and 70% are equal — both appear in the same position. If the question asks you to list all five separately, write them in the order they appeared originally. If it asks for distinct values, note they are equal.
How do you handle negative fractions and decimals?
Negative numbers work the same way: convert to decimals and compare. Remember that on the number line, more negative means smaller.
Example: order −1/4, −0.3 and −30% from smallest to largest.
| Value | Decimal |
|---|---|
| −1/4 | −0.25 |
| −0.3 | −0.30 |
| −30% | −0.30 |
Decimals in order: −0.30, −0.30, −0.25
Answer: −0.3 and −30% are equal (smallest), then −1/4
What are the most common mistakes?
- Forgetting to convert back. The question gives values in their original form; your answer should list them in that form, not as decimals.
- Converting percentage by dividing by 10 instead of 100. 65% ÷ 10 = 6.5, which is wrong. Always divide by 100.
- Assuming that a larger numerator means a larger fraction. 3/7 > 2/5 is not obvious by looking at the numerators; convert both (3/7 ≈ 0.43, 2/5 = 0.40) to confirm 3/7 is larger.
- Not writing enough decimal places for recurring fractions. When comparing 1/3 and 0.34, use 0.333… to see that 0.34 is slightly larger.
Frequently asked questions
Is it always best to convert to decimals, or can I use fractions or percentages instead?
Converting to decimals is usually quickest because decimals share the same place-value structure and can be compared digit by digit. Converting to fractions requires finding a common denominator, which is slower when the fractions have different denominators. Converting to percentages works fine but some fractions (like 1/7) give untidy percentages.
What if the question asks me to place the values on a number line?
The method is the same: convert to decimals first, locate each decimal on the line, then label the point with the original form. Space the points accurately — 0.65 is 65% of the way between 0 and 1, not halfway between 0.6 and 0.7.
How do I compare a mixed number with a decimal?
Convert the mixed number to a decimal: 2¾ = 2.75, then compare directly. Alternatively, convert the decimal to a mixed number: 2.8 = 2 4/5. Which approach is easier depends on the numbers.
Can I use a calculator to convert fractions?
Yes — and in non-calculator exams, long division gives exact decimal equivalents for many fractions. For recurring decimals, write enough digits (at least three or four) to make the comparison reliable.
For KS3 number practice with Professor Pi, visit aitutors.me.