Mixed Recurring Decimal into Vulgar Fraction

A pure recurring decimal is a repeating decimal in which all the digits are periodic, i.e. the periodicity starts at the decimal point. A mixed recurring decimal is any repeating decimal which is not pure, i.e. the digits after the decimal point consist of a nonperiodic portion followed by a periodic portion. For example, a non-repeating infinite decimal has an infinite number of digits to the right of the decimal point, but the digits never become periodic.

This can easily be understood with an example 

(i) Lets change 0.18 into a vulgar fraction:- 

Solution:

Let’s consider x = 0.18

Now, let’s multiply both sides by 10 10x = 1.8

10x = 1.88… (i)

10 × 10x = 1.88… × 10 

100x = 18.8… (ii)

Subtracting (i) from (ii)

100x – 10x = 18.8 – 1.8

90x = 17

x = 17/90

Therefore, the final expression in vulgar fraction is = 17/90 (Answer)

3. Let’s change 0.43213 into a vulgar fraction

Solution:

(ii) Let’s consider x = 0.43213213213…

Multiply both sides by 100 

100x = 43.213

100x = 43.213213… (i)

100 × 1000x = 43.213… × 1000 

100000x = 43213.213… (ii)

Subtracting (i) from (ii)

100000x – 100x = 43213.213 – 43.213213

99900x = 43170

x = 43170/99900

x = 4317/9990

Therefore, the vulgar fraction = 4317/9990

As this method is a bit lengthy an easier way to convert is shown below,

Vulgar fractions are the fractions expressed by numerator and denominator, not decimal. Proper fractions are the fractions where the numerator is less than the denominator. It has a value of less than 1. Improper fraction- is a fraction in which the denominator is greater than the numerator and has a value of 1 or more than 1

For example: Converting 0.123 into a vulgar fraction.

So, the numerator becomes = 123 – 12 = 111

Now the denominator becomes equal to one nine followed by the other two zeros = 900

Now, the required fraction becomes = 111/900 

Therefore, the vulgar fraction results to 37/300 (Answer)

This is a straightforward and short method to solve the problem, but the first method is the more relevant as it explains the right way and order of doing and equating numbers to get to the proper answer. 

Conclusion:

We can conclude by saying that pure and mixed recurring decimals are two forms of decimals that can be converted into fraction forms using the easy method given above. So now you must be through with the concept of conversion to vulgar fraction and also solved problems will help you get more ideas. So this article would have helped you understand and apply this knowledge in the future.