Ordering and Comparing numbers up to 10,000,000

Key vocabulary:

Ascending  -  Numbers going from smallest to largest

Descending  - Numbers going from largest to smallest

Sometimes we need to figure out which number is bigger or smaller than another number.

For example, we might want to know which of two cities has a bigger population or which of a group of people is taller.

When we have a lot of numbers, it can be helpful to put them in order to make it easier to look at and understand them.

When we do math, like adding, subtracting, multiplying or dividing, we sometimes need to order numbers to make it easier to solve problems. It's like putting together a puzzle with the pieces in the right order - it makes it much easier to see how everything fits together!

To do this, we need to order the numbers from smallest to largest (ascending)  or from largest to smallest (descending).

Let's say we have a set of numbers:

Our first job is to label the numbers so we can accurately see which numbers are in each column:

We have labelled these numbers into the correct place value column starting from the far right with:

O = Ones

T = Tens

H = Hundreds

th = Thousands

Tth = Ten Thousands

Hth = Hundren Thousands

M = Millions

It is important to know that each column is ten times larger than the column to its right.

For example a 1 in the ‘Ones’ column holds the value of just 1

However, a 1 in the ‘Tens’ column holds the value of 10 (10 times larger than the 1 in the Ones column)

A 1 in the ‘Hundreds’ column holds the value of 100 (10 times the 10 that is to its right in the ‘tens’ column)

And so on.. all the way up the place value chart

When ordering numbers we start by looking at the leftmost digit of each number (the one that's the farthest to the left).

We do this because this will always be the largest value and therefore the most important when ordering and comparing.

In this case, we compare the digit 5, the digit 8 and the digit 7 because these are in the ‘millions’ column and hold the largest value.

By looking at these numbers we can see that 8 is the largest number and therefore 8,765,432 is the largest number. It does not matter what the numbers are in the other columns. They can never be larger than 8 million.

Next we can see that 7 in larger than 5 so therefore 7,353, 928 is our next largest number.

Therefore our ordered numbers will be:

As this list goes from largest to smallest it is called a ‘descending’ order

Example 2

Sometimes we might need to compare just two numbers. To do this we will use our comparison symbols:

Let's use these symbols to compare these two numbers:

When we look in the ‘Millions’ column we can see that they both have a 6 and therefore have the same value

Now we must look in the next largest column to the right because this will be the next largest value column, so let’s check our ‘hundred thousands’ column

When we look in the ‘Hundred thousands’ column we can see that they both have a 2 and therefore have the same value

Again, this is the same value so we look at the next largest value..

When we look in the ‘Ten thousands’ column we can see that they both have a 4 and therefore have the same value

Again, this is the same value so we look at the next largest value..

When we look in the ‘Thousands’ column we can see that they both have a 2 and therefore have the same value

Again, this is the same value so we look at the next largest value..

When we look in the ‘Hundreds’ column we can see that there is a 5 and a 4.

Therefore the number with the 5 in the hundreds column will be larger so we can write our answer like this:

Or we could write it like this:

Both of these answers would be correct.