CONVERTING DECIMALS TO FRACTIONS

In the process of converting decimal numbers in to fractions, we may have the following situations.

Decimal -----> Proper Fraction

Decimal -----> Improper Fraction

Decimal -----> Mixed Fraction or Mixed Number

Note :

We will have the first and second situations, if the value of the decimal number is greater than 1.

We will have the third situation, if the value of the decimal number is less than 1.

Solved Problems

Problems 1-4 : Convert each decimal number to a proper fraction.

Problem 1 :

0.2

Solution :

The decimal number 0.2 is less than 1. So, it can be converted to a proper fraction.

Since there is one digit after the decimal point in 0.2, write it as a fraction with denominator 10.

= 2/10

Simplify.

= 1/5

Problem 2 :

0.75

Solution :

The decimal number 0.75 is less than 1. So, it can be converted to a proper fraction.

Since there are two digits digits after the decimal point in 0.75, write it as a fraction with denominator 100.

= 75/100

Simplify.

= 3/4

Problem 3 :

0.025

Solution :

The decimal number 0.025 is less than 1. So, it can be converted to a proper fraction.

Since there are three digits after the decimal point in 0.025, write it as a fraction with denominator 1000.

= 25/1000

Simplify.

= 1/40

Problem 4 :

0.005

Solution :

The decimal number 0.005 is less than 1. So, it can be converted to a proper fraction.

Since there are three digits after the decimal point in 0.005, write it as a fraction with denominator 1000.

= 5/1000

Simplify.

= 1/200

Problems 5-8 : Convert each decimal number to an improper fraction.

Problem 5 :

1.5

Solution :

The decimal number 1.5 is greater than 1. So, it can be converted to an improper fraction.

Since there is one digit after the decimal point in 1.5, write it as a fraction with denominator 10.

= 15/10

Simplify.

= 3/2

Problem 6 :

2.75

Solution :

The decimal number 2.75 is greater than 1. So, it can be converted to an improper fraction.

Since there are two digits digits after the decimal point in 2.75, write it as a fraction with denominator 100.

= 275/100

Simplify.

= 11/4

Problem 7 :

5.036

Solution :

The decimal number 5.036 is greater than 1. So, it can be converted to an improper fraction.

Since, there are three digits after the decimal point in 5.036, write it as a fraction with denominator 1000.

= 5036/1000

Simplify.

= 1259/250

Problem 8 :

7.008

Solution :

The decimal number 7.008 is greater than 1. So, it can be converted to an improper fraction.

Since there are three digits after the decimal point in 7.008, write it as a fraction with denominator 1000.

= 7008/1000

Simplify.

= 876/125

Problems 9-12 : Convert each decimal number to a mixed number.

Problem 9 :

1.3

Solution :

The decimal number 1.3 is greater than 1. So, it can be converted to a mixed number.

Write the given decimal number 1.3 as shown below.

1.3 = 1 + 0.3

Since there is one digit after the decimal point in 0.3, write it as a fraction with denominator 10.

= 1 + 3/10

= 1³⁄₁₀

Problem 10 :

3.25

Solution :

The decimal number 3.25 is greater than 1. So, it can be converted to a mixed number.

Write the given decimal number 3.25 as shown below.

3.25 = 3 + 0.25

Since there are two digits after the decimal point in 0.25, write it as a fraction with denominator 100.

= 3 + 25/100

Simplify.

= 3 + 1/4

= 3¼

Problem 11 :

2.05

Solution :

The decimal number 2.05 is greater than 1. So, it can be converted to a mixed number.

Write the given decimal number 3.25 as shown below.

2.05 = 2 + 0.05

Since there are two digits after the decimal point in 0.05, write it as a fraction with denominator 100.

= 2 + 5/100

Simplify.

= 2 + 1/20

= 2¹⁄₂₀

Problem 12 :

7.0025

Solution :

The decimal number 7.0025 is greater than 1. So, it can be converted to a mixed number.

Write the given decimal number 7.0025 as shown below.

7.0025 = 7 + 0.0025

Since there are four digits after the decimal point in 0.0025, write it as a fraction with denominator 10000.

= 7 + 25/1000

Simplify.

= 7 + 1/40

= 7¹⁄₄₀

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