vaivish1723 wrote:
26
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
Please explain
Oa is
Theory:Reduced fraction \(\frac{a}{b}\) (meaning that fraction is already reduced to its lowest term) can be expressed as terminating decimal
if and only \(b\) (denominator) is of the form \(2^n5^m\), where \(m\) and \(n\) are non-negative integers. For example: \(\frac{7}{250}\) is a terminating decimal \(0.028\), as \(250\) (denominator) equals to \(2*5^2\). Fraction \(\frac{3}{30}\) is also a terminating decimal, as \(\frac{3}{30}=\frac{1}{10}\) and denominator \(10=2*5\).
Question: Does the decimal equivalent of P/Q, where P and Q are positive integers, contain only
a finite number of nonzero digits?
According to the above we must determine whether the denominator (after reducing the fraction, if possible) contains only the 2-s and/or 5-s as the prime factors.
(1) P>Q, clearly insufficient.
(2) Q=8=2^3, hence denominator has only 2 as prime factor. Fraction P/Q will be terminated decimal. Sufficient.
Answer: B. (OA must be wrong)
How can we say that the fraction given is a "reduced fraction". Because if it's not than 70/8 is a non-terminating value.