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Maths

# Ordering numbers: Whole numbers and decimals  0%

Summary

# Ordering numbers: Whole numbers and decimals

## ​​In a nutshell

Ordering both whole numbers and decimal numbers requires the use of place values.

## Ordering whole numbers

To order whole numbers, follow this procedure:

#### 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.

##### Example 1

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.

#### 1 digit

 $3125$​​ $5142$​​
 ​$528$​​ $428$​​
 $13$​​ $99$​​ $91$​​
 $3$​​ ​$5$​​

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:

#### 1 digit

 ​​$5142$​​ $3125$​​
 $528$​​ $428$​​
 $99$​​ $91$​​ $13$​​
 $5$​​ $3$​​

Remove the groups to get the ordered list:

 ​​$\underline{5142}$​​ $\underline{3125}$​​ $\underline{528}$​​ $\underline{428}$​​ $\underline{99}$​​ $\underline{91}$​​ $\underline{13}$​​ ​$\underline{5}$​​ $\underline3$​​

## Ordering numbers with decimals

To order numbers that have decimals, use this method:

#### procedure

 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.

##### Example 2

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 $10$​ and $99$​​

 $0.0028$​​ $0.01$​​ $0.005$​​ $0.089$​​ $0.0023$​​
 ​​$4.01$​​ $4.2$​​
 ​​$12.0001$​​

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:

#### 1 initial zero

 $0.0028$​​ $0.005$​​ ​$0.0023$​​
 $0.01$​​ $0.089$​​

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:

#### 1 initial zero

 $0.0023$​​ ​$0.0028$​​ $0.005$​​
 $0.01$​​ $0.089$​​
 ​$4.01$​​ ​$4.2$​​
 $12.0001$​​

Therefore, the numbers sorted from smallest to biggest are:

 $\underline{0.0023}$​​ $\underline{0.0028}$​​ $\underline{0.005}$​​​​ ​$\underline{0.01}$​​ $\underline{0.089}$​​ ​$\underline{4.01}$​​ ​$\underline{4.2}$​​ ​$\underline{12.0001}$​​