# 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

## Decimal ---> Proper Fraction

A decimal number can be converted to a proper fraction, if the value of the decimal number is less than 1.

Example :

0.7

The decimal number 0.7 is less than 1. So, it can be converted to a proper fraction.

Since there is one digit after the decimal in 0.7, it can be written as a fraction with denominator 10.

Therefore,

0.7 = 7/10

In a decimal number, if there is more than one digit after the decimal point, the decimal number can be written as a fraction with denominator 100, 1000 etc.,

two digits ----> denominator ----> 100

three digits ----> denominator ----> 1000

four digits ----> denominator ----> 10000

## Decimal ---> Improper Fraction

A decimal number can be converted to an improper fraction, if the value of the decimal number is greater than 1.

Example :

1.3

The decimal number 1.7 is greater than 1. So, it can be converted to an improper fraction.

Since there is one digit after the decimal in 1.3, it can be written as a fraction with denominator 10.

Therefore,

1.3 = 13/10

If you have more than one digit after the decimal point, you can take the denominator 100, 1000, etc., as explained above.

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

A decimal number can be converted to a mixed number or mixed fraction, if the value of the decimal number is greater than 1.

Example :

1.3

To convert 1.3 as a mixed number, write 1.3 as shown below.

1.3 = 1 + 0.3

0.3 is a decimal number less than 1. So, it can converted to a proper fraction. Since there is one digit after the decimal point in 0.3, it can be written as a fraction with denominator 10.

= 1 + ³⁄₁₀

= 1³⁄₁₀

## 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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