HOW TO CONVERT DECIMALS TO FRACTIONS

Depending on the decimal number, it can be converted to a proper fraction or improper fraction or mixed fraction.

If the value of a decimal is less than 1, it can be converted to a proper fraction.

If the value of a decimal is greater than 1, it can be converted to an improper fraction or a mixed fraction (mixed number).

Decimal < 1 -----> Proper Fraction

Decimal > 1 -----> Improper Fraction

Decimal > 1 -----> Mixed Fraction or Mixed Number

Solved Problems

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

Problem 1 :

0.5

Solution :

Since 0.5 < 1, it can be converted to a proper fraction.

There is one digit after the decimal point in 0.5. So, 0.5 can be written as a fraction with denominator 10.

0.5 = 5/10

Simplify.

= 1/2

Problem 2 :

0.36

Solution :

Since 0.36 < 1, it can be converted to a proper fraction.

There are two digits after the decimal point in 0.36. So, 0.36 can be written as a fraction with denominator 100.

0.36 = 36/100

Simplify.

= 9/25

Problem 3 :

0.075

Solution :

Since 0.075 < 1. it can be converted to a proper fraction.

There are three digits after the decimal point in 0.075. So, 0.075 can be written as a fraction with denominator 1000.

0.075 = 75/1000

Simplify.

= 3/40

Problem 4 :

0.0004

Solution :

Since 0.0004 < 1. it can be converted to a proper fraction.

There are four digits after the decimal point in 0.0004. So, 0.0004 can be written as a fraction with denominator 10000.

0.0004 = 4/10000

Simplify.

= 1/2500

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

Problem 5 :

1.1

Solution :

Since 1.1 > 1. it can be converted to an improper fraction.

There is one digit after the decimal point in 1.1. So, 1.1 can be written as a fraction with denominator 10.

1.1 = 11/10

Problem 6 :

3.45

Solution :

Since 3.45 > 1. it can be converted to an improper fraction.

There are two digits after the decimal point in 3.45. So, 3.45 can be written as a fraction with denominator 100.

3.45 = 345/100

Simplify.

= 69/20

Problem 7 :

9.025

Solution :

Since 9.025 > 1. it can be converted to an improper fraction.

There are three digits after the decimal point in 9.025. So, 9.025 can be written as a fraction with denominator 1000.

9.025 = 9025/1000

Simplify.

= 361/40

Problem 8 :

2.0008

Solution :

Since 2.0008 > 1, it can be converted to an improper fraction.

There are four digits after the decimal point in 2.0008. So, 2.0008 can be written as a fraction with denominator 10000.

= 20008/10000

Simplify.

= 2501/1250

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

Problem 9 :

1.9

Solution :

Since 1.9 > 1, it can be converted to a mixed number.

To convert 1.9 to a mixed number, write 1.9 as shown below.

1.9 = 1 + 0.9

There is one digit after the decimal point in 0.9. So, 0.9 can be written as a fraction with denominator 10.

= 1 + ⁹⁄₁₀

= 1⁹⁄₁₀

Problem 10 :

5.75

Solution :

Since 5.75 > 1, it can be converted to a mixed number.

To convert 5.75 to a mixed number, write 5.75 as shown below.

5.75 = 5 + 0.75

There are two digits after the decimal point in 0.75. So, 0.75 can be written as a fraction with denominator 100.

= 5 + ⁷⁵⁄₁₀₀

Simplify.

= 3 + ¾

= 3¾

Problem 11 :

1.006

Solution :

Since 1.006 > 1, it can be converted to a mixed number.

To convert 1.006 to a mixed number, write 1.006 as shown below.

1.006 = 1 + 0.006

There are three digits after the decimal point in 0.006. So, 0.006 can be written as a fraction with denominator 1000.

= 1 + ⁶⁄₁₀₀₀

Simplify.

= 1 + ³⁄₅₀₀

= 1³⁄₅₀₀

Problem 12 :

12.0098

Solution :

Since 12.0098 > 1, it can be converted to a mixed number.

To convert 12.0098 to a mixed number, write 12.0098 as shown below.

12.0098 = 12 + 0.0098

There are four digits after the decimal point in 12.0098. So, 12.0098 can be written as a fraction with denominator 10000.

= 12 + ⁹⁸⁄₁₀₀₀₀

Simplify.

= 12 + ⁴⁹⁄₅₀₀₀

= 12⁴⁹⁄₅₀₀₀

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