Sorting Whole Numbers
Hi there. This math education post is on sorting whole numbers. This post is a follow up from my sorting names post from a week ago.
Topics
- Place Value Review
- Simple Sorting Cases
- First Digit Is Same
- Checking The Next Digits
- Practice Problems
- Solutions To Practice Problems
Place Value Review
In a whole number, the number digit is the ones place. The ones place contain how many ones are there in a number. On the left side of the ones place is the tens places. The tens place contains how many tens there are in a number. After the tens place is the hundreds place.
A good visual for understanding place value is with the use of blocks for ones, sticks for tens, flat squares for one hundred, and a cube of 1000 little cubes.
The picture below displays the place value for one million, five hundred sixty-four thousand, seven hundred ninety-eight. Its number form is 1,564,798 or 1 564 798.
The number 12 has a two in the ones place and a one in the tens place. You can represent the number 12 in expanded form as 10 + 2.
Simple Sorting Cases
When it comes to sorting, learning how to sort can take time but once you know how to sort numbers it can be fast and easy.
Sorting Single Digit Numbers
This case is easy as you have the numbers from 0 to 9 in order. That is from 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. Given three numbers such as 7, 1, and 2 ordering these three numbers from smallest to largest would give 1, 2 and 7.
Sorting Double Digit Numbers
When it comes to sorting double digit numbers make sure that the first digits from each two digit number are being compared. The number 38 is before 60 as the first digit 3 in 38 is before the 6 in 60. Ties for the first digit will be dealt with in a later section.
Higher Numbers Case
With numbers such as 100, 177, 1888 and such, do compare the first digit as usual. Another thing to keep in mind is to watch for the number of digits in each number. For example, the number 31 is less than 200 even though the first digit 3 in 11 is greater than 2 in 200. The number 31 has a zero in the hundreds place which is less than the 2 located in the hundreds place for 200.
First "Digit" Is Same
When the first digit of two numbers are the same in place value, we have to check the next digit on its right and compare. As an example, the two numbers 801 and 827 have the same first digit being 8 in the hundreds place. Since there is a tie, the next digit on the right side of 8 is used. The 0 from 801 is less than the 2 from 827. It is concluded that 801 is less than 827.
Warning
Be careful once again with cases like 7 and 72. The first digit on the left is the same but the sevens are different in place value. The first 7 is just 7 as in seven ones with 0 tens while the 7 in 72 represent 7 tens as in 70. The number 7 is less than 72.
Checking The Next Digits
If the first two or even three digits between numbers are the same in place value check the digit(s) after. The numbers 555 and 551 both contain the same leading two fives (in place value). After checking the third digit the number 551 is less than 555 since the 1 from 551 is less than the third 5 in 555.
Practice Problems
Sort each number list in order from smallest to largest. (Optional Bonus: Sort again from largest to smallest)
18, 9, 12, 21, 13
27, 32, 39, 2, 3
100, 1020, 130, 1001, 10, 102
37, 331, 31, 300, 321, 308, 310
Solutions To Practice Problems
9, 12, 13, 18, 21
2, 3, 27, 32, 39
10, 100, 102, 130, 1001, 1020
31, 37, 300, 308, 310, 321, 331
