Conversions of a Decimal Into Vulgar Fraction

Vulgar Fraction:- x/y is an example of a vulgar fraction. There are no decimal places in this equation, thus x and y are both integers. There can’t be a zero in the denominator (y) like there can be in other fractions. There was a time when the name was used to differentiate this form of fraction from that employed in astronomy.

Positive and negative common fractions, as well as proper and improper fractions, are all possibilities. Unless irrational, fractions such as compound fractions, complex fractions, mixed numerals, and decimals cannot be evaluated as fractions.

What are decimal fractions?

A decimal fraction is a fraction that expresses the fraction in decimal values is called a decimal fraction. For example, 3/2 can be considered as 1.5 in decimal fractions. That is the decimal result of dividing the given fraction.

How to Convert a Decimal Fraction to a Vulgar/Common Fraction:

Steps to Convert:-

1. a) Start with counting of decimals aftr the point.
2. b) Once you know how the total decimal numbers then go for the denominator by adding 1.
3. c) All of the denominator in this type of conversion should start from 1; then keep adding zeros as the “total number of decimals”
4. d) In this step, a fraction is formed. 
5. e) Now reduce the fraction to its lowest form.

 Example: 

1. Convert 0.68 to Vulgar fraction –

Step 1. Now in this step, after the decimal we have 68, i.e. two numbers

Step 2. Considering the given sum as 0.68 and adding one in denominator, we will get as 

68/1..

Step 3. But here we still need to add zeros. as there are two numbers after decimal by fraction will be 68/100

Step 4. Now we will go for reducing the fraction

Step 5. Thus my answer will be 17/25.

1. Convert 0.30 into Vulgar fraction –

Step 1. Now in this step, after the decimal we have 30, i.e. two numbers

Step 2. Considering the given sum as 0.30 and adding one in denominator, we will get as 

30/1..

Step 3. But here we still need to add zeros. as there are two numbers after decimal by fraction will be 30/100

Step 4. Now we will go for reducing the fraction

Step 5. Thus my answer will be 1/3.

Solved Examples:

(1)5.8 + 6 + 0.3 + 0.4 = ?  

=12.5

=125/10

=25/2

(2)6.2 + 4=?

= 10.2

=102/10

=51/5

(3)1.255

= 1255/1000

= 251/200

Converting a recurring decimal to a vulgar fraction

Repeating decimals are the decimals that have same value over and over again, so they are called repeating or recurring decimals.

E.g. 20/30 will give 0.66666…… where 6 is a recurring number.

Method: 

6. a) Our first step is to just focus on that recurring number, which is given as 6.
7. b) Now count for the times that “6” number has been repeated. Which in the above example is five times.
8. c) While converting from recurring decimal to vulgar fraction, here number 9 is added in the denominator.
9. d) As only one number “6” is recurring, thus we will be adding 9 in the denominator only one time.
10. e) The fraction formed will be 6/9. And now we will reduce this fraction to it’s lowest form. 
11. f) Thus, ⅔ will be my answer.

Example: 

• 0.6363636363

• Step a: Here the recurring no is 63 
• Step b: So the next step will be 63/99, as the number 63 is of length 2, so it has been added two times.
• Step c: Then it should be reduced to the lowest terms, which results in 7/11, and this is the last reduction, which can be done with this number. 

• Conclusion

  We can conclude by saying that vulgar fractions are nothing new but the commonest or lowest form of a fraction that existed. We have learned how to convert any decimal to a fraction form and find its lowest possible way to express it in the form of numerator and denominator.