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Comparing decimals

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Tutor: Alice

Summary

Comparing decimals

​​In a nutshell

Being able to compare the sizes of different decimals allows them to be placed in order. A number line can be useful to help visualise this process.



Which is bigger?

In order to decide which number is larger, its placement and position on a number line can be looked at. The further up the number line it is, the bigger its size.


Example 1

Which is bigger: 4.24.2 or 4.74.7?


44.14.24.34.44.54.64.74.84.95\begin{array}{cccccccccccccc}&&&& \\& &&&\downarrow &&&&&&&&&&\downarrow &&&&\\\bold4&&4.1&&\underline{4.2}&&4.3&&4.4&&4.5&&4.6&&\underline{4.7}&&4.8 &&4.9&&\bold5\\|&&|&&|&&|&&|&&|&&|&&|&&|&&|&&| \\ \hline\end{array}​​


Notice how 4.74.7 is positioned further up the number line than 4.24.2.​


What's more, 4.24.2 and 4.74.7 both share the same digit in their ones column whilst the digits in the tenths column differ. 


77​ is greater than 22 and so:

4.74.7 is greater than 4.24.2.



Ordering decimals

To order a set of decimals, compare them with each other and decide which are bigger.


Procedure

1.

Look at the digits in each place value column, one at a time from left to right.

2.

  • If the digits are the same, move on to the next place value column.
  • If the digits are different, place them (and the number associated with them) in order the required order.

3. 

Continue the process until all the decimals are arranged in order.


Example 2

Place the numbers 1.72,2.52,1.681.72, 2.52, 1.68  and 1.731.73 in order from smallest to largest.


Look at the digits in the ones column: 1,2,11,2,1 and 11.

22​ is the only differing digit. It is bigger than 11so 2.522.52 is the largest number.


Look at the remaining digits in the tenths column: 7,67,6 and 7.7.

66​ is the only differing digit. It is smaller than 77​, so 1.681.68 is less than 1.721.72 and 1.731.73.


Look at the remaining digits in the hundredths column: 22 and 33.

33​ is bigger than 22​ so 1.731.73 is greater than 1.721.72.


Using the information gathered, place all four numbers in order.

1.68,1.72,1.73,2.52\underline{1.68,1.72,1.73,2.52}


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Exercises

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FAQs - Frequently Asked Questions

How can I use a number line to decide which decimal is bigger?

How do I order decimals?

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