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Comparing Decimals and Fractions

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We learned how to compare two decimals. We also learned how to compare two fractions. But can you compare a decimal and a fraction?

Yes, you can!

To compare a decimal and a fraction, you need to convert, or change, one of the numbers so that you have either two decimals or two fractions.

Remember:

A tenth (0.1) in fraction form is
1
10
.
A hundredth (0.01) in fraction form is
1
100
.
For example, three tenths (0.3) is
3
10
in fraction form, and 2.54 or two and fifty-four hundredths is 2
54
100
in fraction form.

Let's take a look at some examples.

Example 1

 
Compare 0.4 and
1
2
.
Let's change 0.4 to a fraction. This decimal is four tenths, so it is equal to
4
10
in fraction form.
Now, we need to compare
4
10
and
1
2
.
Let's write
1
2
as a fraction with 10 as the denominator.
 
1 x 5
2 x 5
=
5
10
 
Now, we can compare
4
10
and
5
10
.
As 4 < 5,
4
10
is less than
5
10
.
So, 0.4 <
1
2
 
 

Example 2

 
Lisa has
3
5
of a pizza and Andy has 0.5 of a pizza. Who has more pizza?
Let's change 0.5 to a fraction. This decimal is five tenths, so it is equal to
5
10
in fraction form.
Now, we need to compare
3
5
and
5
10
.
Let's write
3
5
as a fraction with 10 as the denominator.
 
3 x 2
5 x 2
=
6
10
 
Now, we can compare
6
10
and
5
10
.
As 6 > 5,
6
10
is greater than
5
10
.
 
3
5
is greater than 0.5.

So, Lisa has more pizza than Andy.

Summary
  • To compare a decimal and a fraction, we convert, or change, one of the numbers so that we have either two decimals or two fractions.
  • A tenth (0.1) in fraction form is
    1
    10
    .
    A hundredth (0.01) in fraction form is
    1
    100
    , and so on.

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