# Order Fractions, Decimals and Percentages

In this worksheet, students will put groups of fractions, decimals and percentages into ascending or descending orders by converting them into decimals for easier comparison.

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   Pearson Edexcel, OCR, Eduqas, AQA

Curriculum topic:   Number, Fractions, Decimals and Percentages

Curriculum subtopic:   Structure and Calculation, Ordering Fractions, Decimals and Percentages

Difficulty level:

### QUESTION 1 of 10

When you want to compare fractions, decimals and percentages, you need to convert them all into the same form.

The easiest method is to convert them to decimals.

To convert percentages into decimals: divide by 100.

To convert fractions into decimals: convert them to a fraction over 10, 100 or 1000 and then divide.

e.g. Put the following into ascending order.

41% , 2/5 , 038

Step 1: Change them all to decimals.

41%: Divide by 100 -> 41/100 = 0.41

2/5: Convert the denominator -> 4/10 = 0.4

Step 2: Put the decimals in ascending order.

From smallest to largest, this decimal sequence will be:

0.38 , 0.4 , 0.41

Step 3: Rewrite the decimals in their original form.

0.38 , 2/5 , 41%

Now let's give some similar challenges a try.

IMPORTANT: In this activity, write fractions in the form a/b and do not leave a space between a number and a percentage sign.

Put the following fractions, decimals and percentages into ascending order:

42%, 3/10, 0.61

Put the following group into descending order:

22%, 1/5, 0.21

Which of the following numbers would you change if you wanted to compare them?

0.72, 76%, 3/4

0.72

76%

3/4

Look at the figures below.

0.28, 27%, 1/4

Place them into ascending order.

0.72

76%

3/4

Which of the following numbers would come last if we put them into descending order?

32%, 3/10, 0.34

In ascending order, which one of these values would come first?

1/2, 47%, 0.52

1/2

47

0.52

47%

Put the following fractions, decimals and percentages into order in your head or on paper:

37%, 7/20, 0.31

Then complete the sentence below.

1/2

47

0.52

47%

Put the following fractions, decimals and percentages into ascending order:

48%, 1/2, 0.49

Which number will come first?

48%

1/2

0.49

Consider this final group:

48%, 0.5, 49%

If you were putting the numbers above into sequence, what could you change all the numbers into before comparing them?

Decimals

Percentages

Fractions

Which of these three proportions is the largest

2/5, 45%, 0.42

Start by changing them all into the same form.

2/5

45%

0.42

• Question 1

Put the following fractions, decimals and percentages into ascending order:

42%, 3/10, 0.61

EDDIE SAYS
Firstly, we need to convert all these numbers into decimals. We convert 42% by dividing it by 100. 3/10 can be easily converted as it already has a multiple of 10 as its denominator. As decimals, these numbers would be: 0.42, 0.30, 0.61 If we put these into ascending order, this will be: 0.30, 0.42. 0.61 Remember to change the numbers back to their original form (fraction or percentage) before you write them as your answer. Good effort!
• Question 2

Put the following group into descending order:

22%, 1/5, 0.21

EDDIE SAYS
Did you notice that we switched to descending order? As decimals, these numbers would be: 0.22, 0.20, 0.21 In descending order, these are arranged: 0.22, 0.21, 0.20 Don't forget that descending means getting smaller, or moving to the left on a number line.
• Question 3

Which of the following numbers would you change if you wanted to compare them?

0.72, 76%, 3/4

76%
3/4
EDDIE SAYS
We said in the intro that it is easiest to change them all to decimals. Therefore, the only one we don't have to change is 0.72 as it's already a decimal. Reminder: In order to convert percentages into decimals you divide by 100. In order to convert fractions into decimals, convert them to a number over 10, 100 or 1000 then divide. Great work so far, keep it up!
• Question 4

Look at the figures below.

0.28, 27%, 1/4

Place them into ascending order.

EDDIE SAYS
We said that we need to change each figure into decimals. This gives us the numbers: 0.28, 0.27, 0.25 We can now just look at the numbers after the decimals to decide which is smallest (and so on). Great work if you got this one right!
• Question 5

Which of the following numbers would come last if we put them into descending order?

32%, 3/10, 0.34

3/10
EDDIE SAYS
Descending means getting smaller, so we're looking for the smallest number with the smallest value. As decimals, these numbers would be: 0.32, 0.30, 0.34 It is then easier to see which value is the smallest. That's right, it's 0.30 which corresponds to 3/10 in our original trio of numbers.
• Question 6

In ascending order, which one of these values would come first?

1/2, 47%, 0.52

47%
EDDIE SAYS
If we convert the three numbers to decimals, we have: 0.50, 0.47, 0.52 If we put these in ascending order, we get: 0.47, 0.50, 0.52 Did you choose option b? Don't forget that when we are dealing with percentages, the sign is vital. Sneaky options like this can trip you up, so be on the lookout! Well done if you spotted that, maths genius!
• Question 7

Put the following fractions, decimals and percentages into order in your head or on paper:

37%, 7/20, 0.31

Then complete the sentence below.

EDDIE SAYS
Remember that if we want to compare these numbers, we need to change them all to decimals as follows: 0.37, 0.35, 0.31 In ascending order, the sequence is: 0.31, 0.35, 0.37 -> 0.31, 7/20, 37% In descending order, the sequence is: 0.37, 0.35, 0.31 -> 37% , 7/20, 0.31 In both these sequences, 0.35 which represents 7/20 is the middle. Is this getting easier?
• Question 8

Put the following fractions, decimals and percentages into ascending order:

48%, 1/2, 0.49

Which number will come first?

48%
EDDIE SAYS
In ascending order, we are looking for the smallest number which will be in the first position in the sequence. If you change them all to decimals, we would have: 0.48, 0.50, 0.49 It's much easier to spot the correct answer now, which is 48%. Always change values back to their original form when writing your answer in any exam!
• Question 9

Consider this final group:

48%, 0.5, 49%

If you were putting the numbers above into sequence, what could you change all the numbers into before comparing them?

Decimals
Percentages
EDDIE SAYS
For this, the only one you shouldn't change to is fractions, as you'd have to change all three and they're harder to compare. It's much easier to compare them when they are all shown in relation to 100. You could change them all to decimals because you are used to doing that. Or you could change them all to percentages because you only have to change 1 of them. Well done, that's another activity completed!
• Question 10

Which of these three proportions is the largest

2/5, 45%, 0.42

Start by changing them all into the same form.

45%
EDDIE SAYS
If we changed all of these into decimals, we would have: 0.40, 0.45, 0.42 We can see here that 0.45 is the largest. Which original proportion does this decimal represent? That's correct, it is 45%.
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