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Converting Decimals to Mixed Numbers

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If you can convert a decimal to a fraction, you can easily convert a decimal with a whole part to a mixed number.

A decimal with digits to the left of the decimal point indicates there is a whole part and some parts of a whole.

For example, 2.75 or two and seventy-five hundredths means there are two whole parts and an additional seventy-five out of one hundred parts.

Convertingdnp1

When you are converting a number with digits both to the left and right of the decimal point, only convert the decimal part or the digits to the right of the decimal point. In other words, just leave the whole number as same and convert the decimal!

Let's take a look at some examples.

Example 1

Write 1.2 as a fraction.

Change the decimal 0.2 to a fraction.

0.2 =
2
10
 
Now, reduce the fraction
2
10
to its lowest form.
 
2 ÷ 2
10 ÷ 2
=
1
5
 
So, 1.2 = 1
1
5
 
 

Example 2

Write 3.25 as a fraction.

Change the decimal 0.25 to a fraction.

0.25 =
25
100
 
Now, reduce the fraction
25
100
to its lowest form.
 
25 ÷ 25
100 ÷ 25
=
1
4
 
So, 3.25 = 3
1
4
 
 

Example 3

Write 25.4 as a fraction.

Change the decimal 0.4 to a fraction.

0.4 =
4
10
 
Now, reduce the fraction
4
10
to its lowest form.
 
4 ÷ 2
10 ÷ 2
=
2
5
 
So, 25.4 = 25
2
5
 
 

Example 4

Write 130.21 as a fraction.

Change the decimal 0.21 to a fraction.

0.21 =
21
100
 
The fraction
21
100
is in its lowest form only, as there is no common factor of numerator and denominator.
So, 130.21 = 130
21
100
 
Summary
  • A decimal with a whole part can be written as a mixed number.
  • In decimals, the digits to the left of the decimal point represents the whole part and the digits to the right of the decimal point represents the decimal or fraction part.
  • To convert a decimal to a mixed number, leave the whole number as same and convert the decimal part.
  • Reduce fractions after changing from decimal form.

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