Lesson 1 — Activity 3:

Comparing and Ordering Whole Numbers


Would you rather win $25 or $30?

Is $30 more or less than $25?

Most of us could answer these questions without thinking too hard. Ordering numbers is something we do by organizing numbers from smallest to largest or largest to smallest.



Because you understand place value, you can order large numbers easily either from smallest to largest (also known as ascending order) or from largest to smallest (also known as descending order).


Follow the steps below to determine if a number is larger than or smaller than another number.

Compare 9,875 and 9,654.

  1. Both numbers have 9 in the thousands place, so you need to go to the next place to the right.
  2. In this case, that is the hundreds place.
  3. One number (9,875) has an 8 in the hundreds place; the other number (9654) has a 6 in the hundreds place.
  4. Because 800 is larger than 600, you can now make statements to compare these numbers.
    • 9,875 is larger than 9,654.
    • 9,654 is smaller than 9,875.



A better way to write this is to use the signs greater than and less than.

greater than (>)

  

less than (<)

In the greater than sign (>), the larger end of the sign comes first as you read from left to right.

Example: 50 > 25

In the smaller than sign (<), the smaller end of the sign comes first as you read from left to right.

Example: 25 < 50



Remember: You know immediately when numbers are equal to each other — they are exactly the same!

Example: 450 = 450



Comparing and Ordering Larger Numbers

Follow these steps to compare and order the numbers

below from smallest to largest.

9,875, 65,842, 9,654, 103,270, 65,361

1. Count how many digits are in each number.
There are two numbers, each with four digits, that read as thousands. These are the smallest numbers in this group.
9,875 and 9,654
2. Look at the first digit in each number.
Both have 9 in the thousands place, so you need to look further to know which one is smaller.
 9,875 and 9,654
3. Move to the next column to the right.
The next column is in the hundreds place. One number has 8 hundred, and the other has only 6 hundred.
9,875 and 9,654
4. Determine which of these numbers is smaller.
Obviously, 6 hundred is smaller than 8 hundred.
9,654 is smaller than 9,875
5. Record these two numbers as the smallest in the group.
You now have the two smallest numbers. Remove from the list above.

9,654

 9,875


Repeat these steps to find the next lowest number among the numbers remaining.


1. Count how many digits are in each number.
Two numbers have five digits, which means they read as tens of thousands.
 65,842 and
65,361
2. Look at the first digit in each number.
Both have 6 in the ten thousands place, so look further to know which is smaller.
65,842 and
65,361
3. Move to the next column to the right.
The next column is the thousands. Both numbers have 5 in the thousands, so you need to look further.
 65,842 and 65,361
4. Move to the next column to the right.
The next column is the hundreds.  One number has 8 hundred, and the other one has only 3 hundred.
65,842 and
65,361
5. Determine which of these numbers is smaller.
Obviously, 3 hundred is smaller than 8 hundred.
65,361 is smaller than 65,842
6. Record these two numbers as the next smallest in the group.
You now have the next two smallest numbers, so remove them from the list above.

65,361

65,842

 
Now, the list from smallest to largest  is:

9,654, 9,875, 65,361, 65,842

 
1. Count how many digits are in each number.
Only one number remains, and it has five digits.

103,270

 
Now you have arranged all the numbers in order from smallest to largest.
 

9,654, 9,875, 65,361, 65,842, 103,270

If you need to arrange numbers from largest to smallest, you follow the same steps, but you begin with the number that has the most digits and work back to the one with the fewest digits. The numbers below, when ordered from largest to smallest, look like this:


103,270, 65,842, 65,361, 9,875, 9,654


Self-check!

Try this!


Order the following numbers from smallest to largest.

50     125     123     75     1,234




Extra Practice!

Click here to download extra practice questions (with answers)!