 # Order Decimals

In this worksheet, students will practice ordering decimals into ascending or descending sequences using place value. 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 ordering decimals, the first step is to always make sure that the decimals have the same number of decimal places.

e.g. Put the following decimals in ascending order:

0.4 , 0.21 , 0.401 , 0.32 , 0.61

The longest decimal here has three decimal places so we need to convert them all to have three decimal places.

We do this by adding zeros onto the end of any which have less than 3 numbers after the decimal place, as below:

0.400 , 0.210 , 0.401 , 0.320 , 0.610

We can then simply read the numbers as we would normal numbers, and put them in order:

0.210 , 0.320 , 0.400 , 0.401 , 0.610

The final answer should always use the same numbers as the original question, so we need to take off all the zeros which we added, leaving us with:

0.21 , 0.32 , 0.4 , 0.401 , 0.61

In this activity, you will order groups of decimal numbers into either ascending or descending order and locate numbers in specific positions in the resulting sequences.

Now let's attempt some questions together!

Look at the decimals below and place them in ascending order in your head or on a piece of paper:

0.3, 0.21, 0.8, 0.57

Then complete the sentence below.

Put the following numbers in descending order:

0.23, 0.2, 0.25, 0.251

Don't forget you can add 0s to give the same number of decimal places.

In ascending order, which of these numbers would come last?

4.1, 0.41, 4.01, 4.11

Look at this group of numbers:

0.85, 8.5, 0.8, 0.805

Now complete the sentence below.

Put the numbers below in ascending order:

0.207, 0.27, 0.2, 0.2077

Remember, you can always add 0s so that each number has the same amount of decimal places.

Now consider this group:

4.02, 4.2, 4.22, 4

Put the following numbers in ascending order:

3.7, 0.307, 0.37, 0.0307

Then complete the sentence below.

Put the following numbers in descending order:

45, 0.45, 4.5, 0.405

Then complete the sentence below.

If we want to put these numbers in sequence, which numbers do we have to add extra 0s to?

0.61, 0.601, 6.1, 6.11

0.61

0.601

6.1

6.11

Put the following numbers in ascending order:

0.251, 2.51, 25.01, 25.1

Then complete the sentence below.

0.61

0.601

6.1

6.11

• Question 1

Look at the decimals below and place them in ascending order in your head or on a piece of paper:

0.3, 0.21, 0.8, 0.57

Then complete the sentence below.

EDDIE SAYS
The longest decimal here has two decimal places, so we need to convert them all to have same by adding 0s: 0.30, 0.21, 0.80, 0.57 We can read them without the decimals to order them: 21, 30, 57, 80 However, don't forget to convert them back to decimals: 0.21, 0.30, 0.57, 0.80 Also, remember to take those extra zeros off at the end for full marks: 0.21, 0.3, 0.57, 0.8 This is good work so far, keep it up!
• Question 2

Put the following numbers in descending order:

0.23, 0.2, 0.25, 0.251

Don't forget you can add 0s to give the same number of decimal places.

EDDIE SAYS
Did you notice the question is asking for descending order now? That means we would be going from right to left on our number line, decreasing in value. The longest decimal here has three decimal places, so we need to make them all have the same number of decimal places by adding zeroes: 0.230, 0.200, 0.250, 0.251 Don't forget to remove the extra decimal places once you have found the correct order. Don't panic if you found this one difficult; we will keep practising!
• Question 3

In ascending order, which of these numbers would come last?

4.1, 0.41, 4.01, 4.11

4.11
EDDIE SAYS
Does it matter that we now have numbers in front of the decimals? Not really, just remember to make the numbers all the same length so we can compare them easily: 4.10, 0.41, 4.01 , 4.11 If we now place these in ascending order, we have: 0.41, 4.01, 4.10, 4.11 Don't let all those 4's and 1's confuse you! 4.11 is obviously bigger than 4.10, and adding 0s made this clear. Don't forget to remove the 0s when writing your answers. Keep up the great work!
• Question 4

Look at this group of numbers:

0.85, 8.5, 0.8, 0.805

Now complete the sentence below.

EDDIE SAYS
Think first about which number has to come last. (Hint: it's the only one that doesn't start with a zero!) For the rest, we need to convert them to all have 3 decimal places in order to compare them with ease: 0.800, 0.805, 0.850, 8.500 Is this becoming less daunting as you practise?
• Question 5

Put the numbers below in ascending order:

0.207, 0.27, 0.2, 0.2077

Remember, you can always add 0s so that each number has the same amount of decimal places.

EDDIE SAYS
The longest decimal here has four decimal places, so we need to convert all the options to have the same number of places: 0.2070 , 0.2700 , 0.2000, 0.2077 If we now ignore the first number (they're all zero), we can see the order more clearly: 0.2000, 0.2070, 0.2077, 0.2700 Don't forget to remove those extra decimal places before giving your answer. How did you do?
• Question 6

Now consider this group:

4.02, 4.2, 4.22, 4

EDDIE SAYS
The longest decimal here has two decimal places, so we have to convert them all to have the same to compare them: 4.02, 4.20, 4.22, 4.00 Don't let the solitary '4' trick you - just add two decimal places as normal. Now if we place these in ascending order, we will have: 4.00, 4.02, 4.20, 4.22 As we can see, 4.02 is second in this sequence. You're making great progress!
• Question 7

Put the following numbers in ascending order:

3.7, 0.307, 0.37, 0.0307

Then complete the sentence below.

EDDIE SAYS
The longest decimal here has four decimal places, so we have to convert them all to have the same: 3.7000, 0.3070, 0.3700, 0.0307 Now we can compare them more easily and put them into ascending order: 0.0307, 0.3070, 0.3700, 3.7000 Don't forget to take off the extra zeros when you write your answer.
• Question 8

Put the following numbers in descending order:

45, 0.45, 4.5, 0.405

Then complete the sentence below.

EDDIE SAYS
Examiners may try to trick you, so watch out. We need to be descending here! Did you spot that? The longest decimal here has three decimal places, so we need to convert all the numbers to have the same: 45.000, 0.450, 4.500, 0.405 Don't forget to remove the extra decimal places you have added before writing your answer. Good effort, maths whizz!
• Question 9

If we want to put these numbers in sequence, which numbers do we have to add extra 0s to?

0.61, 0.601, 6.1, 6.11

0.61
6.1
6.11
EDDIE SAYS
The longest decimal here has three decimal places, so we have to add zeros to all the ones that don't have this, like so: 0.610, 0.601, 6.100, 6.110 Try to order these numbers in your head now or write them down - how did you find that?
• Question 10

Put the following numbers in ascending order:

0.251, 2.51, 25.01, 25.1

Then complete the sentence below.

EDDIE SAYS
And we're back to ascending! The longest decimal here has three decimal places. Let's go ahead and add the extra zeros: 0.251, 2.510, 25.010, 25.100 Can you order these in your head now? Great work, you've completed another activity! How about attempting another one, so you feel super confident with ordering decimals?
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