Give a way to count all rational numbers where the denominator is a power of 2;

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let the rank of a rational number p/q (p>0 ,q>0) be 3^p*2^q...clearly this is unique for each rational number when the rational number is in its lowest form...So this is one of the way of counting Rational numbers....as I found a map from Rationals to Natural numbers... So by this map I can count the number of positive rational numbers...hence by symmetricity total number of rational numbers are twice the number of positive rational numbers...So the map 3^p.2^q gives a way of counting rational number by assigning it a positive integer value.... Although Rational numbers are infinite....but this map shows that they are countable........the first few numbers in my counting are 1 ,1/2,2,1/3.....please do rate and reward .. :) If you found it helpful...atleast rate helpful..and if you are not satisfied then you can tell that directly... :)

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