
Comparing Decimals 

Unit 12 > Lesson 3 of 12 
Example 1: 
Polygon Pizza Place caters children's parties with squareshaped pizza. Each
pizza is exactly the same size and is divided
into equal parts called slices. At Sam's party, each child had 2
out of 10 slices from a single pizza. At Elena's party, each child had 15
out of 100 slices from a single pizza. At which party
did each child have more pizza?


Analysis: 
We can write a fraction to represent each party:


Party 
Fraction 
Sam's 

Elena's 




Using our knowledge of decimals, we get:


Party 
Fraction 
Decimal 
Sam's 

0.2X 
Elena's 

0.15 


Answer: 
Each child got more pizza at Sam's Party.

In Example 1, we compared two decimal numbers and found that 0.2 is greater
than 0.15. Some students would argue that 0.15 is a longer decimal with more
digits, and is therefore greater than 0.2. However, if we think about money, we
know that 20 cents is greater than 15 cents. Thus, our answer in Example 1 is
correct.

Decimal numbers are compared in the same way as other numbers: by comparing the
different place values from left to right. We use the symbols <, > and
= to compare decimals as shown below.

Example 1: 
Comparison 
Meaning 
0.2 > 0.15 
0.2 is greater than 0.15 
0.15 < 0.2 
0.15 is less than 0.2 
0.2 = 0.2 
0.2 is equal to 0.2 
0.15 = 0.15 
0.15 is equal to 0.15 

When comparing two decimals, it is helpful to write one below the other. This
is shown in the next example.

Example 2: 
Which is greater, 0.57 or 0.549?

Analysis: 
Let's compare these decimals using a placevalue chart.





Answer: 
0.57 is greater than 0.549.

Notation: 
0.57 > 0.549

As you can see in the example above, 0.57 has fewer decimal digits than
0.549. It is easier to compare two decimals when
you have the same number of decimal digits, so an extra zero
was written to the right of the digit 7 in the decimal 0.57. We are able to do this because 0.57 and 0.570 are equivalent decimals.

Use Caution With Writing Extra Zeros
It is easier to compare decimals when you have the same number of decimal
digits. Thus, we often write extra zeros to the right of the last digit of one
of the decimals being compared. These
extra zeros are place holders and do not change the value of the decimal. However,
if you inserted a zero between the decimal point and a decimal digit, that
would change the value of the decimal. This is shown in the table below:

0.57 
= 
0.570 
= 
0.5700 

Writing extra zeros to the right of the last digit of a
decimal does not change its value. 
0.57 
≠ 
0.507 
≠ 
0.057 

Inserting a zero between the decimal point and a decimal digit does
change the value of a decimal. 
Let's look at some more examples of comparing decimals.
Example 3: Compare each pair of decimals using the symbols <,
> or =.
Example 4: Compare each pair of decimals using the symbols <,
> or =.
In Examples 3 and 4, there were some problems in which the two decimals being
compared did not have the same number of decimal digits. In these problems, we
wrote one or more extra zeros to the right of the last digit of one decimal so that both decimals would have the same
number of decimal digits. In the examples above, we used placevalue charts to help us compare
decimals. Let's try some examples without placevalue charts.

Example 5: 
Compare each pair of decimals using the symbols <,
> or =. 


0.1379 

0.01379 
2.4896 

2.4986 
7.914 

791.4 
$2.39 

2.39 
0.81734 

0.08174 



Problem 

Answer 

0.13790 

0.1379 
> 
0.01379 
0.01379 


2.4896 

2.4896 
< 
2.4986 
2.4986 


7.914 

7.914 
< 
791.4 
791.400 


$2.39 

$2.39 
= 
2.39 
2.39 


0.81734 

0.81734 
> 
0.08174 
0.08174 



Example 6: 
Compare each pair of decimals using the symbols <,
> or =. 


1.46197 

1.046197 
15.317965 

15.317965 
4.7293 

4.7923 
0.78154 

0.78514 
$0.96 

$0.91 



Problem 

Answer 

1.461970 

1.46197 
> 
1.046197 
1.046197 


15.317965 

15.317965 
= 
15.317965 
15.317965 


4.7293 

4.7293 
< 
4.7923 
4.7923 


0.78154 

0.78154 
< 
0.78514 
0.78514 


$0.96 

$0.96 
> 
$0.91 
$0.91 



Summary: 
To compare two decimals, start
at the left and compare digits in the same placevalue position. It is
helpful to write one decimal below the other. It is also easier to compare decimals when
you have the same number of decimal digits. Thus, when comparing two decimals,
we can write one or more extra zeros to the right of the last digit of
one decimal so that both decimals have the same number of decimal digits.

This lesson is by Gisele Glosser. You can find me on Google.
Exercises
Directions: Compare each pair of decimals below using the symbols <. >
or =. You may write one decimal below the other on paper to help
you compare. Click once in an ANSWER BOX and type in your answer; then click ENTER.
After you click ENTER, a message will appear in the RESULTS BOX to indicate whether your answer is correct or incorrect.
To start over, click CLEAR.

1.

Compare these decimals and enter <, > or = in the space provided.

2.

Compare these decimals and enter <, > or = in the space provided.

3.

Compare these decimals and enter <, > or = in the space provided.

4.

Compare these decimals and enter <, > or = in the space provided.

5.

Compare these decimals and enter <, > or = in the space provided.

This lesson is by Gisele Glosser. You can find me on Google.
