Functional Skills: Ordering Numbers

Ordering Large Numbers

You may also be asked to order large numbers. To order large numbers look at each number in turn and compare the digits, starting with the first.

Example: Put the following numbers in order from largest to smallest.

$3456, ,,, 5364, ,,, 3465, ,, 5634$

Step 1: Split the numbers into positive and negative. There are only positive numbers here, so we do not need to do this.

Step 2: Put the numbers into groups with the same number of digits. They all have $4$ digits, so we do not need to do this.

Step 3: Look at the first digit for each number and compare them:

$xcancel{textcolor{blue}{3}456}, ,,, overset{downarrow}{textcolor{blue}{5}}364, ,,, xcancel{textcolor{blue}{3}465},  ,,, overset{downarrow}{textcolor{blue}{5}}634$

$2$ numbers start with $3$. Since we are looking for the largest first, we can eliminate those $2$ numbers.

Step 4: Look at the second digits.

$5 xcancel{textcolor{blue}{3}64}, ,,,  5overset{downarrow}{textcolor{blue}{6}}34$

$6$ is bigger than $3$, so eliminate the first number.

So, $5634$ is the largest and $5364$ is the second largest.

Step 5: Look at the other numbers.

$3 xcancel{textcolor{blue}{4}textcolor{red}{5}6}, ,,,  3 textcolor{blue}{4}overset{downarrow}{textcolor{red}{6}} 5$

The second digit is the same in each number, so compare the third digit. $6$ is bigger than $5$ so eliminate the first number.

So, $3465$ is the third largest and $3456$ is the smallest.

Step 6: Finally, write down the correct order:

$5634, ,,, 5364, ,,, 3465, ,,, 3456$

Ordering Negative Numbers

When ordering negative numbers, you need to be careful – for negative numbers, the bigger the number after the minus $(-)$ sign, the smaller the negative number.

Example: Put the following numbers in order from largest to smallest.

$23, ,,, -23, ,,, 32, ,,, -32$

Step 1: Split the numbers into positive and negative.

$23, ,,, 32$     and    $-23, ,,, -32$

Step 2: Put the numbers into groups with the same number of digits. They all have $2$ digits, so we do not need to do this.

Step 3: Then, look at the first digit for each number and compare them.

$xcancel{textcolor{blue}{2}3}, ,,,  overset{downarrow}{textcolor{blue}{3}}2$

$3$ is greater than $2$, so $32$ is the largest and $23$ is the second largest.

Step 4: Now, look at the negative numbers and compare the first digit of each.

$– overset{downarrow}{textcolor{blue}{2}}3, ,,,  – xcancel{textcolor{blue}{3}2}$

$-3$ is smaller than $– 2$, since the bigger the number after the minus sign, the smaller the negative number.

So, $-23$ is the third largest and $-32$  is the smallest.

Step 5: Finally, write down the correct order:

$32, ,,, 23, ,,, -23, ,,, -32$