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Chapter Overview
Learning Goals
Learning Goals
Maths
Types of numbers
Number calculations
Fractions, decimals and percentages
Algebraic manipulation
Formulae and equations
Straight line graphs
Other graphs
Ratio
Proportion
Rates of change
Shapes
Properties of shapes
Lines and angles
Drawing shapes
Trigonometry
Probability
Maths
Summary
Ordering both whole numbers and decimal numbers requires the use of place values.
To order whole numbers, follow this procedure:
1.  Group the numbers by how many digits each number has. 
2.  Sort the numbers in each group by comparing the leftmost digits first. 
3.  Write the sorted numbers in a list without the groups. 
Sort the following numbers from largest to smallest:
$13$  $528$  $99$  $428$  $3$  $91$  $5142$  $5$  $3125$ 
First, group the numbers by number of digits. Because the question asks from largest to smallest, put the numbers with the most digits to the left.
4 digits  3 digits  2 digits  1 digit  




Then, sort the numbers in each group from largest the smallest by comparing the leftmost digit:
For the 4 digit group:
$5142$ is bigger than $3125$ because $5$ is bigger than $3$.
For the 3 digit group:
$528$ is bigger than $428$ because $5$ is bigger than $4$.
For the 2 digit group:
$13$ is the smallest. $99$ and $91$ have the same tens digit.
So, move on to the next digit and compare:
$99$ is bigger than $91$ because $9$ is bigger than $1$.
For the 1 digit group:
$5$ is bigger than $3$.
Hence, the table should now look like this:
4 digits  3 digits  2 digits  1 digit  




Remove the groups to get the ordered list:
$\underline{5142}$  $\underline{3125}$  $\underline{528}$  $\underline{428}$  $\underline{99}$  $\underline{91}$  $\underline{13}$  $\underline{5}$  $\underline3$ 
To order numbers that have decimals, use this method:
1.  Sort the whole number parts. 
2.  Group the numbers that have the same "whole number parts" by how many initial zeroes are to the right of the decimal point. 
3.  Sort each group by comparing the first non zero digits. 
4.  Write the sorted numbers without the groups. 
Sort the following numbers from smallest to largest:
$0.0028$  $4.01$  $0.01$  $0.005$  $0.089$  $12.0001$  $4.2$  $0.0023$ 
First, sort the numbers by their integer parts:
between $0$ and $1$  Between $1$ and $9$  between $10$ and $99$  



There are only two numbers that begin with $4$, so they can be compared easily:
$4.01$ is smaller than $4.2$ because $0$ is smaller than $2$.
Next, sort the numbers between $0$ and $1$ by how many zeroes come after the decimal point:
2 initial zeroes  1 initial zero  


Note: Because this is from smallest to largest, put the numbers with the most zeroes to the left as they're inherently smaller.
Sort each smaller group:
2 initial zeroes:
$0.005$ is the largest because $5$ is bigger than $2$.
$0.0023$ is smaller than $0.0028$ because $3$ is smaller than $8$.
1 initial zero:
$0.01$ is smaller than $0.089$ because $1$ is less than $8$.
Hence, the table becomes:
between 0 and 1  between 1 and 9  between 10 and 99  



Therefore, the numbers sorted from smallest to biggest are:
$\underline{0.0023}$  $\underline{0.0028}$  $\underline{0.005}$  $\underline{0.01}$  $\underline{0.089}$  $\underline{4.01}$  $\underline{4.2}$  $\underline{12.0001}$ 
Ordering both whole numbers and decimal numbers requires the use of place values.
To order whole numbers, follow this procedure:
1.  Group the numbers by how many digits each number has. 
2.  Sort the numbers in each group by comparing the leftmost digits first. 
3.  Write the sorted numbers in a list without the groups. 
Sort the following numbers from largest to smallest:
$13$  $528$  $99$  $428$  $3$  $91$  $5142$  $5$  $3125$ 
First, group the numbers by number of digits. Because the question asks from largest to smallest, put the numbers with the most digits to the left.
4 digits  3 digits  2 digits  1 digit  




Then, sort the numbers in each group from largest the smallest by comparing the leftmost digit:
For the 4 digit group:
$5142$ is bigger than $3125$ because $5$ is bigger than $3$.
For the 3 digit group:
$528$ is bigger than $428$ because $5$ is bigger than $4$.
For the 2 digit group:
$13$ is the smallest. $99$ and $91$ have the same tens digit.
So, move on to the next digit and compare:
$99$ is bigger than $91$ because $9$ is bigger than $1$.
For the 1 digit group:
$5$ is bigger than $3$.
Hence, the table should now look like this:
4 digits  3 digits  2 digits  1 digit  




Remove the groups to get the ordered list:
$\underline{5142}$ 