How to order fractions, decimals and percents from least to greatest
When a list mixes fractions, decimals and percents, convert everything to decimals first. Then the order is easy to see, and you only write the numbers back in their original form at the end.
The three conversions
- Fraction to decimal. Divide the top by the bottom. 3/4 = 3 ÷ 4 = 0.75.
- Percent to decimal. Divide by 100. 65% = 0.65.
- Decimal. Already done.
Worked example
Order 3/4, 0.7, 65%, 7/8 and 0.8 from least to greatest.
| Original | As a decimal |
|---|---|
| 3/4 | 0.75 |
| 0.7 | 0.7 |
| 65% | 0.65 |
| 7/8 | 0.875 |
| 0.8 | 0.8 |
Sorted by the decimal column, the answer is 65%, 0.7, 3/4, 0.8, 7/8.
Line the decimals up to the same number of places (0.650, 0.700, 0.750, 0.800, 0.875) so that a number like 0.7 does not look smaller than 0.65 because it has fewer digits.
Comparing two fractions by cross-multiplying
For two fractions only, skip the decimals. To compare 5/8 with 3/5, multiply across diagonally, 5 × 5 = 25 and 3 × 8 = 24. The larger product sits on the side of the larger fraction, so 5/8 is greater than 3/5. This works when both denominators are positive.
Fractions that do not end
2/3 as a decimal is 0.6667 (rounded). To order 2/3, 0.67, 66% and 5/8, write each to four places: 0.6667, 0.6700, 0.6600 and 0.6250. The order is 5/8, 66%, 2/3, 0.67.
Including negatives
A negative number is always less than a positive one, and among negatives the one closer to zero is greater. −1/2 = −0.5 is greater than −0.6, so −0.6 comes first. Order the negatives by flipping their sign, ordering, then reversing the result.
Common mistakes
- Comparing numerators or denominators alone. 1/3 has a bigger denominator than 1/2 but is smaller.
- Reading 0.7 as less than 0.65 because 7 < 65. Compare digit by digit from the left.
- Forgetting that 65% means 0.65, not 6.5.
- Putting the numbers back in decimal form in the final answer when the question gave fractions.
To skip the conversions, paste the list straight into the least to greatest calculator, which handles fractions, mixed numbers and negatives.
Related calculators
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Least to greatest calculator
Paste any list, including fractions and negatives, and get it sorted.
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Fractions calculator
Convert, simplify and compare fractions.
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Percentage calculator
Turn percents into decimals and back.
Common questions
How do you order fractions, decimals and percents from least to greatest?
Convert every number to a decimal, compare the decimals, then write the numbers back in their original form. A fraction becomes a decimal by dividing top by bottom; a percent by dividing by 100.
How do I compare two fractions without a calculator?
Cross-multiply. For 5/8 and 3/5, compare 5 × 5 = 25 with 3 × 8 = 24. The side with the larger product is the larger fraction, so 5/8 > 3/5.
Which is less, −0.6 or −1/2?
−0.6 is less. On the number line it sits further left than −0.5. With negatives, the number with the larger absolute value is the smaller number.
What if the decimal never ends?
Compare enough digits to tell them apart. 2/3 is 0.6667, which is above 0.66 but below 0.67. Write each number to four places (0.6600, 0.6667, 0.6700) before deciding.
