Converting Recurring Numbers in Fractions

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Converting a recurring decimal to vulgar fraction A decimal with recurring value is called recurring decimal.
E.g: 2/9 will give 0.22222222...... where 2 is recurring number.

Method:
a) Separate the recurring number from the decimal fraction.
b) Annex denominator with "9" as many times as the length of the recurring number.
c) Reduce the fraction to its lowest terms.

Example: Consider 0.2323232323

Step a: The recurring number is 23
Step b: 23/99 [the number 23 is of length 2 so we have added two nines]
Step c: Reducing it to lowest terms : 23/99 [it can not be reduced further].

How to Convert a mixed-recurring decimal to vulgar fraction ? A decimal with both recurring and non-recurring value is called mixed recurring decimal.
E.g: 28/25 will give 1.1199999999...... where 11 is non-recurring number and 9 is recurring number.

Method:
a) Separate the recurring number, non recurring number from the decimal fraction.
b) Round the decimal after point to the first recurring value.
c) Result of step b - non recurring number.
d) Annex as many "0" as non-recurring number length and as many "9" as recurring number length.
e) Step c / Step d
f) Add the fraction with the number before decimal point.
Example: Consider 1.11999999...

Step a: The recurring number is 11, non-recurring number is 9
Step b and c: 119-11 [rounded value of number after decimal point - non recurring value]
Step d: 900
Step e: 108/900 [c/d]
Step f: 1+¹⁰⁸/₉₀₀ [adding with number before decimal point ]
Reducing it to lowest terms : 900+108 / 900 = 1008/900 = 28/25.

This is a very important topic as time is concern.