Decimal fraction: A fraction in which denominator is 10 or it is 10²,10³ etc. i.e. power of 10 is called decimal fraction e.g. 3/10, 3/100 they can be represented as 0.3, 0.03 etc.

1. Non-recurring or terminating Decimal: As the name suggests, non-recurring means which do not reoccur or repeat i.e. they terminate or come to end e.g. 0.5, 0.25, and 0.125 etc. In order to convert these fractions, just the numerator is divided by the denominator. For example if you need to convert 1/4 into decimal, divide 1 by 4 and get the answer as 0.25.

2. Recurring or non-terminating Decimal: As the name suggests recurring means which reoccur or repeat i.e. they do not terminate or come to end e.g. 0.333…, 0.545454…. etc. In order to convert these fractions, just the numerator is divided by the denominator. For example if you need to convert 1/3 into decimal, divide 1 by 3 and get the answer as 0.333…

Let us discuss each of them one by one:

1. Pure recurring decimals: This is the type of recurring decimal in which all digits or set of digits (after decimal point) repeat .e.g. 0.7777…0r 2.373737….. . It can be simply written as  or 
2. Mixed recurring decimals: This is the type of recurring decimal in which one or more digits after the decimal do not repeat while remaining digits or set of digits (after decimal point ) repeat .e.g. 1.4232323…

To convert mixed recurring decimal fraction into vulgar fraction

Shortcut:

1. In numerator: Write the complete number after decimal digits and subtract from it the digits which are repeated. i.e. in  subtract 2 from 217 to get 215 in numerator.
2. In denominator: Check the number of digits repeated and not repeated then write the number of nines in the denominator equal to number of digits repeated followed by number of zeros equal to number of digits not repeated i.e. in  , two digits 17 are repeated so two nines are there followed by one zero as only one digit 2 that is not repeated. So we get 990 in denominator. So the answer of  is 215/990