Ordering Numbers (Cambridge (CIE) IGCSE Maths)

Revision Note

Test yourself

Ordering Numbers

How do I put numbers in order (including decimals and negatives)?

  • Use place value in the number to help

    • Write the numbers underneath each other, lining up their place-value columns

    • e.g.  For the numbers 1 453 427 and 454 316

1

4

5

3

4

2

7

 

4

5

4

3

1

6

  • Start from the highest place value (furthest left) to compare the numbers

  • For decimals, numbers further to the right of the decimal point are worth less

    • e.g.  14 is more than 8 but 0.14 is less than 0.8

    • It can help to write the two numbers with the same number of decimal places to compare them

      • e.g.  12.115 and 12.15 are easier to compare when written as 12.115 and 12.150

  • For negative numbers, larger values are smaller numbers

    • e.g.  14 is more than 8 but -14 is less than -8

    • If there is a mixture, first order the positive numbers and negative numbers separately

  • Ascending order means in increasing order

    • Start with the smallest (most negative) number

  • Descending order means in decreasing order

    • Start with the largest (most positive) number

Examiner Tips and Tricks

  • Comparing numbers is easier if you rewrite them with the same number of place-value columns and in neat rows

    • e.g.  To compare 213.3 and 12.245 rewrite as

2

1

3

.

3

0

0

0

1

2

.

2

4

5

Worked Example

Write these numbers in order, with the smallest first

0.7,  -0.7,  0.2991,  -0.2991,  1.05,  -1.05,  1.508,  -1.508,  0.58,  -0.58.  2.4,  -2.4 

Starting with the positive numbers only
Rewrite them with the same number of place-value columns and underneath each other

0 . 7 0 0 0

0 . 2 9 9 1

1 . 0 5 0 0

1 . 5 0 8 0

0 . 5 8 0 0

2 . 4 0 0 0

Looking at the highest place value, there are three values starting with 0 (the smallest digit) 
These are 0.7000, 0.2991 and 0.5800
Comparing their second digits gives

0.2991, 0.5800, 0.7000

Similarly, there are two values with a 1 in the highest place value column
These are 1.0500 and 1.5080
Comparing their second digits gives

1.0500, 1.5080

There is only one number with the highest place value of 2, so the list of positive numbers can now be put into order
Start with the smallest and write them as they originally appeared (without extra zeros)

0.2991, 0.58, 0.7, 1.05, 1.508, 2.4

For the negative numbers

- 0 . 7 0 0 0

- 0 . 2 9 9 1

- 1 . 0 5 0 0

- 1 . 5 0 8 0

- 0 . 5 8 0 0

- 2 . 4 0 0 0

Remembering that -2 is smaller than -1 etc
Repeat the method above to give

-2.4, -1.508, -1.05, -0.7, -0.58, -0.2991

Put both lists together, starting with the smallest (the most negative)

-2.4,  -1.508,  -1.05,  -0.7,  -0.58,  -0.2991,  0.2991,  0.58,  0.7,  1.05,  1.508,  2.4

Last updated:

You've read 0 of your 5 free revision notes this week

Sign up now. It’s free!

Join the 100,000+ Students that ❤️ Save My Exams

the (exam) results speak for themselves:

Did this page help you?

Jamie Wood

Author: Jamie Wood

Expertise: Maths

Jamie graduated in 2014 from the University of Bristol with a degree in Electronic and Communications Engineering. He has worked as a teacher for 8 years, in secondary schools and in further education; teaching GCSE and A Level. He is passionate about helping students fulfil their potential through easy-to-use resources and high-quality questions and solutions.

Dan Finlay

Author: Dan Finlay

Expertise: Maths Lead

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.