Does the decimal equivalent of P/Q, where P and Q are positive integers, contain only
a finite number of nonzero digits?
(1) P>Q
(2) Q=8
a finite number of nonzero digits?
(1) P>Q
(2) Q=8
I feel the answer should be Bradhika1306 wrote:Does the decimal equivalent of P/Q, where P and Q are positive integers, contain only
a finite number of nonzero digits?
(1) P>Q
(2) Q=8
If you consider statement 1 alone P can be 23 and Q can be 3. This will produe a recurring decimal number. However if P is 21 and Q is 3 it will contain only finite numbers of non zero digits.
Now consider statement two - The denominator is 8. To produce a recurring number the denominator should be a prime number ex - 2 and 5. See rule below. So for any value of P, P/Q will be a finite number.
I found this rule on the net:
A fraction in lowest terms with a prime denominator other than 2 or 5 (i.e. coprime to 10) always produces a recurring decimal. The period of the recurring decimal, 1/ p, where p is prime, is either p − 1 (the first group) or a divisor of p − 1 (the second group)
Please confirm if my logic is correct.
