Bunuel wrote:
I should think so... Infact.. If it had been given as postive numbers, P could be any irrational number such as \(\sqrt{2},\sqrt{3}, \sqrt{5}\)
So, the answer would be only 1 & 3.
Kudos Please... If my post helped.
As long as the denominator can be expressed as powers of prime factors, the fraction will always be finite...[/quote]
That's not true. Any positive integer can be expressed as powers of primes.
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 \(10=2*5\).
Note that if denominator already has only 2-s and/or 5-s then it doesn't matter whether the fraction is reduced or not.
For example \(\frac{x}{2^n5^m}\), (where x, n and m are integers) will always be the terminating decimal.
We need reducing in case when we have the prime in denominator other then 2 or 5 to see whether it could be reduced. For example fraction \(\frac{6}{15}\) has 3 as prime in denominator and we need to know if it can be reduced.
Questions testing this concept:
https://gmatclub.com/forum/does-the-dec ... 89566.htmlhttps://gmatclub.com/forum/any-decimal- ... 01964.htmlhttps://gmatclub.com/forum/if-a-b-c-d-a ... 25789.htmlhttps://gmatclub.com/forum/700-question-94641.htmlhttps://gmatclub.com/forum/is-r-s2-is-a ... 91360.htmlhttps://gmatclub.com/forum/pl-explain-89566.htmlhttps://gmatclub.com/forum/which-of-the ... 88937.htmlHope it helps.[/quote]
Just to clarify does the fraction need to have either 2 or 5 (or both) ONLY in its denominator or it can have other primes in there as well e.g. 2 * 7 or 5*11