Let p be a prime number other than 2 or 5 One would like to express the vulgar fraction 1 p in the f...........

Quantitative Aptitude (CDS) Number System

Let p be a prime number other than 2 or 5. One would like to express the vulgar fraction 1 / p in the form of a recurring decimal. Then the decimal will be

a pure recurring decimal and its period will be necessarily (p - 1)

a mixed recurring decimal and its period will be necessarily ( p - 1)

a pure recurring decimal and its period will be some factor of (p - 1)

a mixed recurring decimal and its period will be some factor of (p - 1)

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Explanation:

A decimal fraction in which all the digits after the decimal point are repeated is called a pure recurring decimal whereas a decimal fraction in which some digits after the decimal point do not repeat and some digits do is called a mixed recurring decimal.
The period of the decimal representation of 1/p is a division of p−1
Thus, the decimal form of the vulgar fraction 1/p is a pure recurring decimal and its period will be some factor of (p−1)