GCSE Maths: How to Order Numbers Fast
Introduction
It is important to be able to know how to order numbers whether it is positive numbers, negative numbers and also decimal numbers.
Ordering positive numbers is straightforward and you should be able to order such numbers in either ascending or descending order.
Ascending means to start with the smallest number and to finish with the largest number.
Descending means to start with the largest number and to finish with the smallest number.
If you consider the following set of numbers: 76,103,13,130,67
And you wanted to put them in ascending order then you would have: 13, 67, 76, 103 and 103.
If you wanted to rank the same numbers in descending order you would have: 130, 103, 76, 67 and 13.
Dealing with negative numbers can often lead to some confusion. What is important to remember is that the “larger the number is after the negative sign”, the smaller the number actually is. For instance “-9” is smaller than “-2”.
Suppose you wanted to put the following numbers in order of size, starting with the smallest: -3,5,0,-7,-1
Here you have a combination of both positive and negative numbers.
Looking at the numbers, the smallest number is -7. Then it is -3 and then -1. This will then be followed by 0 and 5.
This can be written as: -7, -3, -1, 0 and 5.
It is important to remember that “0” is always bigger than any negative number.
Putting decimals in order can also prove to be quite tricky. If you think about 0.42 and 0.402 you might think that 0.402 is the bigger number because it has more digits but this is not the case.
To be able to correctly order decimal numbers you need to know the place value system for numbers that appear after the decimal point.
Looking at the table below you can see the place value system for those numbers that appear after the decimal point. The numbers have been inserted and so 0.42 is the bigger number and 0.402 is the smaller number.
GCSE Maths - How To Order Numbers: Example
Take a look at the following how to order numbers question:
\begin{array}{lllll} 0.72, & 0.7, & 0.072, & 0.07, & 0.702 \end{array}You want to put the above decimal numbers in order of size starting with the smallest.
The numbers have been put into a place value grid. Looking at this you can put the numbers in order of size, starting with the smallest.
0.07, 0.072, 0.7, 0.702 and 0.72.
If you don’t want to use a place value grid you can always draw a number line and see which numbers are closest to 0 and which is closer to 1 to help put the numbers in size order.
How To Order Numbers - Another Example
Take a look at the following how to order numbers question:
In questions like this, you need to simply just look at the whole numbers because they are all different. So in order of size the numbers would appear as:
0.5, 1.8, 3.71 and 12.4.
Question Practice
Take a look at the following question:
You want to list these in size order, smallest first.
These numbers need to be put in size order starting with the smallest. You can see that there is a combination of positive and negative numbers. Remember, the larger the number after a negative sign, the smaller that number is.
In this case -15 will be the smallest number, followed by -6, then -4, then 4 and then 5.
So you will have: -15, -6, -4, 4 and 5.
Question Practice
Try the following questions on your own before looking at the solution:
You want to write these in ascending order (so smallest first)
Question Practice Solution
Another way that you can determine the order is to write these as a fraction ensuring that each as the same denominator
\begin{gathered} 0.62=\frac{62}{100}=\frac{620}{1000} \\ 0.5=\frac{5}{10}=\frac{500}{1000} \\ 0.062=\frac{62}{1000} \\ 0.06=\frac{6}{100}=\frac{60}{1000} \\ 0.502=\frac{502}{1000} \end{gathered}Putting these numbers into ascending order is now much easier than just looking at the decimal numbers.
In ascending order the answer is: 0.06, 0.062, 0.5, 0.502, 0.62
Question Practice
Try the following questions on your own before looking at the solution:
Question Practice Solutions
Writing each as a fraction ensuring that the denominator is the same:
\begin{gathered} 0.51=\frac{51}{100}=\frac{510}{1000} \\ 0.017=\frac{17}{1000} \\ 0.5=\frac{5}{10}=\frac{500}{1000} \\ 0.15=\frac{15}{100}=\frac{150}{1000} \\ 0.405=\frac{405}{1000} \end{gathered}In ascending order the answer is: 0.017, 0.15, 0.405, 0.5, 0.51
When it comes to ordering numbers you need to understand how place value works and how negative numbers work. As long as you can understand this then ordering numbers for GCSE maths is very easy indeed.
There will be other numbers that you might need to place in order will be fractions or even a mixture of different types of numbers which can include fractions, decimals and percentages. The method of ordering these types of numbers is discussed in another article.