# Decimals To Fraction

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## How to Convert Decimal to Fraction?

Conversion of decimal to fraction can be done by following the below mentioned steps:

Step 1: Write down the decimal number that is to be converted into the fraction as
(Decimal )/1

Step 2: Multiply both numerator and denominator by 10 for each number written after the decimal point. For example, if there are two numbers after the decimal point multiply it by 100 whereas if there are three numbers after the decimal point multiply it by 1000, and so on.

Step 3: Simplify the fraction into reduced form.

### Example: Convert 0.95 to fraction.

#### Solution:

Step 1: Writing down the decimal number 0.95 as (Decimal )/1 gives (0.95 )/1

Step 2: Multiplying both numerator and denominator by 100 as numbers written after the decimal point are 2.

(0.95 × 100 )/(1× 100)= 95/100

Step 3: Simplifying the fraction into reduced form as:

(95 ÷ 5)/(100 ÷ 5) = 19/20

## How To Convert Recurring Decimals To Fraction?

To convert the given decimal number into its fractional form, follow the below steps:

Step 1: Let the given recurring decimal number be ‘x’.

Step 2: Let the number of recurring digit be ‘n’.

Step 3: Multiply the recurring decimal by 10 if there is only one recurring. For example, if there are two recurring digits multiply it by 100 whereas if there are three recurring digits multiply it by 1000, and so on.

Step 4: Subtract the equation (1) from equation (3) to eliminate the recurring part.

Step 5: Solve for x to convert it into fraction.x

### Example: Convert the recurring decimal 0.7777 to fraction.

#### Solution:

Step 1: Let x = 0.7777 …….. (1)

Step 2: Multiplying both LHS and RHS by 10 as there is only one recurring digit.

10 × x= 0.7777 × 10 …..,,(2)

10x = 7.777 ……………..(3)

Step 3: Subtracting the equation (1) from equation (3) to eliminate the recurring part gives:

10x – x = 7.777 – 0.7777

9x = 7

Step 4: Solving for x gives 7/9

Therefore, 0.7777 in fraction is equals to 7/9.

## Converting Fraction to Decimal

A fraction is made up of two parts namely numerator and denominator. It shows how many parts we have out of the total number of parts. Both numerator and denominator is separated by a line known as vinculum or bar. This line represent division. For converting fraction into decimal, divide the numerator by the denominator. This will give you an answer in decimal form.

Example:

7/5 as a decimal is 7 ÷ 5 = 1.4

65/100 as a decimal is 65 ÷ 100 = 0,65

2/4 as a decimal is 2÷ 4 = 0.5

## Another Method of Converting Fraction To Decimal

Step 1: Find a number you can multiply the denominator of the fraction to make it 10, 100, or 1000, or any 1 followed by digit ‘0’.

Step 2: Multiply both numerator and denominator by that number.

Step 3: Then just write the numerator part by placing the decimal point in a correct place. Place the decimal point one space from the right side for every 0 written in the denominator.

### Example: Convert 7/4 to fraction.

#### Solution:

Step 1: We can multiply 4 by 25 to make it 100.

Step 2: Multiply both numerator and denominator by 100 as shown below.

(7 × 25)/(4 × 25) = 175/100

Step 3: Write down 175 with the decimal point two places from the right side as the digit 100 has 2 zeroes.

Therefore, 7/4 = 1.75