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How to Compare Numbers by Size

It is important to be able to compare numbers and understand their sizes. You must be able to answer questions like:

  • Which number is the greatest?

  • Which number is the smallest?

The numbers 1 through 6 arranged from smallest to greatest on a ladder

When answering these questions, the real number line is your best friend. It can be viewed as a ladder, which places the large numbers further up on the ladder and the small numbers further down on the ladder. If the ladder falls down to the right, you can see that the large numbers are towards the right and the low numbers towards the left.

The only thing you need to think of now, is where on the real number line the different numbers belong. For example, the number 2 sits right in between the number 1 and the number 3. Then you know that 2 is smaller than 3, but larger than 1.

When you’re learning how to compare numbers, you need to know the following:

  • Where the numbers are placed on the real line.

  • That the number to the right is larger than the number to the left.

Example 1

What does it look like when you write 23, 98, 0, 56, 19, 10, 65 and 73 in ascending order?

The following recipe works well:


Draw the real line from 0 to 100.


Mark the numbers from the exercise on the real line.

Now you can write the numbers in the same order as you marked them on the real line. They will then be in ascending order.

The number line from 0 to 100

The right order is:

0, 10, 19, 23, 56, 65, 73, 98

Think About This

What is the largest double digit number you can make with both the digits 2 and 5?

If you choose to put 2 first and 5 last, you get the number 25. If you choose to put 5 first and 2 last, you get the number 52. Since 52 is further to the right on the real line than 25, 52 is the largest number you can make with the digits 2 and 5.

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