# Conversion of Pure Recurring Decimal into Vulgar Fraction

Follow the steps for the conversion of pure recurring decimal into vulgar fraction:

(i) First write the decimal form by removing the bar from the top and put it equal to n (any variable).

(ii) Then write the repeating digits at least twice.

(iii) Now find the number of digits having bars on their heads.

If the repeating decimal has 1 place repetition, then multiply both sides by 10.

If the repeating decimal has 2 place repetitions, then multiply both sides by 100.

If the repeating decimal has 3 place repetitions, then multiply both sides by 1000 and so on.

(iv) Then subtract the number obtained in step (i) from the number obtained in step (ii).

(v) Then divide both the sides of the equation by the coefficient of n.

(vi) Therefore, we get the required vulgar fraction in the lowest form.

Worked-out examples for the conversion of pure recurring decimal into vulgar fraction:

1. Express 0.4 as a vulgar fraction.

Solution:

Let n = 0.4

n = 0.444 ----------- (i)

Since, one digit is repeated after the decimal point, so we multiply both sides by 10.

Therefore, 10n = 4.44 ----------- (ii)

Subtracting (i) from (ii) we get;

10n - n = 4.44 - 0.44

9n = 4

n = 4/9 [dividing both the sides of the equation by 9]

Therefore, the vulgar fraction = 4/9

2. Express 0.38 as a vulgar fraction.

Solution:

Let n = 0.38

n = 0.3838 ----------------- (i)

Since, two digits are repeated after the decimal point, so we multiply both sides by 100.

Therefore, 100n = 38.38 ----------------- (ii)

Subtracting (i) from (ii) we get;

100n - n = 38.38 - 0.38

99n = 38

n = 38/99

Therefore, the vulgar fraction = 38/99

3. Express 0.532 as a vulgar fraction.

Solution:

Let n = 0.532

n = 0.532532 ----------------- (i)

Since, three digits are repeated after the decimal point, so we multiply both sides by 1000.

Therefore, 1000n = 532.532 ----------------- (ii)

Subtracting (i) from (ii) we get;

1000n - n = 532.532 - 0.532

999n = 532

n = 532/999

Therefore, the vulgar fraction = 532/999

Shortcut method for solving the problems on conversion of pure recurring decimal into vulgar fraction:

Write the recurring digits only once in the numerator and write as many nines in the denominator as is the number of digits repeated.

For example;

(a) 0.5

Here numerator is the period (5) and the denominator is 9 because there is one digit in the period.

= 5/9

(b) 0.45

Numerator = period = 45

Denominator = as many nines as the number of digits in the denominator

= 45/99

Related Concept

From Conversion of Pure Recurring Decimal into Vulgar Fraction to HOME PAGE

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

## Recent Articles

1. ### Expanded form of Decimal Fractions |How to Write a Decimal in Expanded

Jul 22, 24 03:27 PM

Decimal numbers can be expressed in expanded form using the place-value chart. In expanded form of decimal fractions we will learn how to read and write the decimal numbers. Note: When a decimal is mi…

2. ### Worksheet on Decimal Numbers | Decimals Number Concepts | Answers

Jul 22, 24 02:41 PM

Practice different types of math questions given in the worksheet on decimal numbers, these math problems will help the students to review decimals number concepts.

3. ### Decimal Place Value Chart |Tenths Place |Hundredths Place |Thousandths

Jul 21, 24 02:14 PM

Decimal place value chart are discussed here: The first place after the decimal is got by dividing the number by 10; it is called the tenths place.

4. ### Thousandths Place in Decimals | Decimal Place Value | Decimal Numbers

Jul 20, 24 03:45 PM

When we write a decimal number with three places, we are representing the thousandths place. Each part in the given figure represents one-thousandth of the whole. It is written as 1/1000. In the decim…