Question: Without using the long division method, identify which of the following common fractions represent recurring decimals. 1. 5/6

Posted by: Lakshya G. on 17.01.2021

One of the factors of denominator 6 of a fraction 5/6 is 3 which gives recurring decimal as 1/3=0.333...
5/6 as denominator 6=2 x 3, that means (2.5)/3 is a non-terminating recurring decimal.

The denominator of the given fraction is 6 which has factors 2&3. We know that any rational number whose denominator is not in the form of" 2^n*5^m "will have a recurring decimal expansion.As the denominator of the given fracrion 5/6 contains a factor "3" which is different from "2" and "5" ,the decimal expansion  is recurring and non terminating.

The denominator of 5/6 having the factors 2x3 this having other than 2 aand 5 because 3 is a factor of 6 so it represent a recurring decimals
Write the fraction in lowest terms Factories the denominator using prime numbers If the factors include only 2or 5 or a combination of both then it is non recurring otherwise recurring Here the factors of 6 are 2×3 So it is recurring
Simplify the fraction first, Write the prime factorisation of denominator, if it is other than a 2 or 5 or combination of both, fraction will be recurring. 5/6= 0.8333.... (6=2×3) Other examples- 2/3= 0.666.... (3 makes it recurring) 5/9= 0.555... (9=3×3)

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