Put decimal numbers in order

key notes:

Comparing decimals means determining which decimal represents a larger number, and which represents a smaller number.

 Ordering decimals means putting them in order from the least to the greatest, or from the greatest to the least.

=	When two values are equal, we use the “equals” sign	example: 0.2+0.2 = 0.4
<	When one value is smaller than another, we can use a “less than” sign.	example: 0.3 < 0.5
>	When one value is bigger than another, we can use a “greater than” sign	example: 0.9 > 0.6

How to Tell Which Decimal is Bigger

When given two decimal numbers, how can someone tell which decimal is bigger? The process is similar to what is done when words are alphabetized. If the first letter of each word is the same, look at the second letter. If the second letter is the same, look at the third letter. Here is how to tell which decimal number is bigger:

• Write the numbers with the decimal points lined up.
• Starting at the far left, which is the largest place value, compare the numbers.
• If the first-place value is the same in both numbers, move one spot to the right and compare again.
• If the second place value is the same in both numbers, move one spot to the right and compare again.
• Continue until the place value digits are different. The number with the larger digit is the larger number.

Here is an example. Which number is bigger, 8.019 or 8.03? Follow the steps:

• Write the numbers with the decimal points lined up.

8	.	0	1	9
8	.	0	3

• Starting at the far left, which is the largest place value, compare the numbers.

The digit in the ones place in both numbers is an 8.

• If the first-place value is the same in both numbers, move one spot to the right and compare again.

The digit in the tenth place in both numbers is a 0.

• If the second place value is the same in both numbers, move one spot to the right and compare again.

The digit in the hundredth place in the top number is a 1, and it is a 3 in the bottom number.

• The number with the larger digit is the larger number.

Since 3 is bigger than 1, then 8.03 > 8.019

8.03 > 8.019

Ordering Decimals

What is the process for ordering decimal numbers? The process is very similar to the previous example. Here is how to put decimals in order:

How do you order decimals from smallest to largest?

To order decimals from smallest to largest:

• Write the decimal numbers with the decimal points lined up.
• Starting at the far left, compare the digit’s place value by place value.
• Continue comparing place values as you move to the right, ordering the decimals as you go.

Example of ordering decimals.

Decimals can be ordered from least to greatest or from greatest to least. Consider the decimals 5.8, 5.067, and 5.154. From greatest to least, the order is 5.8, 5.154, and 5.067.

• 0.2<0.3<0.4<0.5<0.6
• 5.2<6.1<7.1<7.8<9.8<9.9
• 7.8>6.2>6.1>5.2>5.19>4.56>4.50>3.2
• 7.8>5.5>5.1>5>4.2>3.2>1.5>1.45

Learn with an example

let’s practice: