Comparing fractions, decimals and percents

To compare a fraction, a decimal and a percent, change them all into the same form. Percents are often easiest. Then order them.

The idea: make them all the same form

Which is biggest: 3/5, 0.58 or 61%? They look different, so they are hard to compare. But they are all numbers, and each can be written in any of the three forms.

Change every one into a percent: 3/5 = 60%, 0.58 = 58% and 61% stays 61%. Now the order is easy to see: 58%, 60%, 61%. The biggest is 61%.

See it: pictures to draw with your child

Copy these onto paper or a whiteboard. A quick sketch makes the idea concrete before any written method.

percentas a number0%025%1/437.5%3/860%0.6100%1
On one number line, 3/8 (37.5%) sits between 1/4 (25%) and 0.6 (60%).
3/5 = 60%
3/5 shades 60 squares of the grid.
0.58 = 58%
0.58 shades 58 squares, a little less than 3/5.

Which form should you change them to?

Percents are usually the easiest, because they are whole numbers out of 100. Decimals work well too, especially with a calculator. Fractions are the hardest to compare unless they share a denominator.

Ordering step by step

  1. Write every number as a percent (or every number as a decimal).
  2. Line them up and compare them like whole numbers.
  3. Write the order using the original forms, not the converted ones.

For example, order 0.4, 3/8 and 41% from smallest. As percents: 40%, 37.5% and 41%. So the order is 3/8, 0.4, 41%.

Convert any number

Type a fraction, decimal or percent to see all three forms. Use it to check your ordering.

Use a number line

A number line from 0 to 1 (or 0% to 100%) shows every form in the same place. Mark 1/2, 0.5 and 50% and they land on the same point. Children then see that the forms are just names.

Benchmarks help place a number quickly. Is it more or less than a half? More or less than a quarter? 0.45 is just under 50%, so it sits just left of the middle.

Traps to watch for

More digits does not mean bigger. 0.125 is smaller than 0.5, even though 125 looks bigger than 5. Write them as 12.5% and 50% and the trap disappears.

A bigger denominator means smaller pieces. 1/8 is smaller than 1/5, even though 8 is bigger than 5. As percents they are 12.5% and 20%.

Quiz: compare and convert

Pick the biggest number, or change a fraction or decimal to a percent.

Where this fits: percentages step by step

  1. What is a percent
  2. Percent to fraction
  3. Fraction to percent
  4. Percent to decimal
  5. Decimal to percent
  6. Comparing fractions, decimals and percents (this page)
  7. Benchmark percents
  8. Percent mental math
  9. Over 100% and under 1%
  10. Percent of a number
  11. Finding the percent
  12. Finding the whole
  13. Percent change
  14. Percent increase and decrease
  15. Discounts and sale price
  16. Sales tax
  17. Tips
  18. Simple interest
  19. Markup, commission and percent error
  20. Percent word problems

What to say to your child

A short script for teaching it the first time. Pause after each line and let your child do the next step.

  1. “Which is bigger, 0.3 or 1/4?”
  2. “Let’s change both to percents. 0.3 is …” (30%.)
  3. “And 1/4 is …” (25%.)
  4. “So which is bigger?” (0.3.)
  5. “Now put 0.3, 1/4 and 28% in order.” (1/4, 28%, 0.3.)

More worked examples

Example 1: biggest of 0.7, 2/3 and 68%

70%, about 66.7% and 68%. The biggest is 0.7.

Example 2: order 1/5, 0.25, 22%

20%, 25%, 22%. Order: 1/5, 22%, 0.25.

Example 3: equal values

3/4, 0.75 and 75% are all the same number.

Example 4: a percent over 100

1.2 is 120%, so it is bigger than 115% and 9/8 (112.5%).

Practice questions (answers below)

Ask these out loud or write them down. Check each answer, and ask “how did you get that?” for one or two.

  1. Which is bigger, 0.6 or 55%?
  2. Which is bigger, 1/4 or 0.3?
  3. Order 0.5, 45%, 3/5
  4. Is 2/5 equal to 0.4?
  5. Which is smallest, 1/8, 0.2, 15%?
  6. Order 0.09, 9.5%, 1/10
  7. Biggest of 7/10, 0.72, 69%
  8. Write 3/20 as a percent
  9. Which is bigger, 1.1 or 105%?
  10. Stretch: order 1/3, 0.33, 33.4%
Show the answers
  1. 0.6
  2. 0.3
  3. 45%, 0.5, 3/5
  4. Yes
  5. 1/8
  6. 0.09, 9.5%, 1/10
  7. 0.72
  8. 15%
  9. 1.1
  10. 0.33, 1/3, 33.4%

Common mistakes

More digits is biggerThinks 0.125 > 0.5.Fix: write both as percents: 12.5% < 50%.
Bigger denominator is biggerThinks 1/8 > 1/5.Fix: 1/8 = 12.5% and 1/5 = 20%.
Writing the order in the new formGives the answer as 30%, 40%.Fix: write the answer using the numbers as they were given.

How to teach it at home

Card order

Make cards with fractions, decimals and percents and race to order them.

Grid match

Shade grids and find the matching fraction, decimal and percent.

Best deal

Compare “1/4 off” with “20% off” on real prices.

By grade

More for each grade: Grade 6 math and the CBSE class 6 maths guide.

Worksheets and practice

Fractions, decimals and percents worksheet, page 1

Fractions, decimals and percents worksheet: printable PDF with an answer key. · Make a fresh test

Percent practice · percent calculator · fraction, decimal and percent converter · percentage quiz · percent levels · percent games · percentages for kids

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Questions parents ask

How do you compare fractions, decimals and percents?

Change them all to the same form, usually percents, then compare like whole numbers.

Which is bigger, 3/5 or 0.58?

3/5. As percents, 3/5 = 60% and 0.58 = 58%.

How do you order fractions, decimals and percents?

Convert each to a percent, put them in order, then write them back in their original forms.

Is 0.5 bigger than 0.45?

Yes. 0.5 = 50% and 0.45 = 45%.

What grade learns this?

Grade 6, under Common Core 6.RP.A.3c and 6.NS.C.7.