Do you feel in difficulty in converting a pure recurring decimal to a vulgar fraction? If so, this is the right place for you where you will get a complete idea of the procedure for conversion of a pure recurring decimal into vulgar fractions. Refer to Worked Out Examples on Converting Pure Recurring Decimal into a Vulgar Fraction for a better understanding of the concept.

Do Read: Repeating or Recurring Decimal

## How to Convert a Pure Recurring Decimal into Vulgar Fraction?

Follow the simple and easy process listed below to change from a pure recurring decimal to a vulgar fraction. They are in the following fashion

- Firstly note down the decimal form and remove the bar from the top and place it equal to variable n.(1)
- Check the number of digits having bars on the heads.
- If the repeating decimal has 1 digit multiply both sides with 10. If the repeating decimal has 2 digits multiply both sides with 100. …..(2)
- Subtract number obtained in step 1 from step 2.
- Divide both sides of the equation with the coefficient of n.
- Thus, we obtain the required vulgar fraction in the lowest form.

### Worked Out Examples for Converting a Pure Recurring Decimal into Vulgar Fraction

1. Express 0.\(\overline{5}\) as a Vulgar Fraction?

Solution:

Let n = 0.\(\overline{5}\)

n = 0.555555……..(1)

Since you have only one digit repeated after the decimal point we will multiply with 10 on both the sides

Therefore, 10n=5.555555……(2)

Subtracting (1) from (2) we have

10n-n=5.55555……-0.5555….

9n=5

n = \(\frac { 5 }{ 9 } \)

Therefore, Vulgar Fraction is \(\frac { 5 }{ 9 } \)

2. Express 0.\(\overline{45}\) as a vulgar fraction?

Solution:

Let n = 0.\(\overline{5}\)

n = 0.454545……..(1)

Since you have only one digit repeated after the decimal point we will multiply with 10 on both the sides

Therefore, 100n=45.454545……(2)

Subtracting (1) from (2) we have

100n-n=45.454545……-0.454545……..

99n=45

n = \(\frac { 45 }{ 99 } \)

Therefore, Vulgar Fraction is \(\frac { 45 }{ 99 } \)

### Shortcut Method for Converting a Pure Recurring Decimal to Vulgar Fraction

- In this method, you need to write the recurring digits only once in the numerator.
- In the denominator write as many nines as in the number of repeating digits.
- Reduce the fraction to the lowest terms possible and that is the resultant vulgar fraction.

### Conversion of Pure Recurring Decimal to Vulgar Fraction Examples

**1. Write 0.353535….. as Vulgar Fraction?**

Solution:

Given Decimal is 0.353535…..

Numerator = Period = 35

In the numerator, place the recurring digits once, and in the denominator write as many nines as in the number of the repeating digits

The denominator is 99 as the number of repeating digits are two.

= \(\frac { 35 }{ 99 } \)

Therefore, 0.353535….. expressed as a vulgar fraction is \(\frac { 35 }{ 99 } \)

**2. What is 0.333…… expressed as a Vulgar Fraction?**

Solution:

Given Decimal is 0.3333……

In the Numerator, place the recurring digits once as the numerator and as many nines as in the repeating digits as the denominator.

Numerator = Period = 3

Number of repeating digits = one therefore, the denominator will have only one 9

Expressing numerator by denominator we have

= \(\frac { 3 }{ 9 } \)

Therefore, 0.3333…… expressed as vulgar fraction is \(\frac { 3 }{ 9 } \)

### FAQs on Conversion of a Pure Recurring Decimal into Vulgar Fraction

**1. What is meant by a Vulgar Fraction?**

Vulgar Fraction is the other name for a common fraction. It is the fraction in which both the numerator and denominator are integers.

**2. How do you Convert a Pure Recurring Decimal into a Vulgar Fraction?**

Simply place the recurring digits once in the numerator and as many nines as in the number of repeating digits as the denominator. Reduce the fraction to the lowest terms if possible and that is the resultant vulgar fraction.

**3. What is 0.2323….. as a vulgar fraction?**

0.2323…. is written as \(\frac { 23 }{ 99 } \) in vulgar fraction.