A number - X - was found to be represented in the simplest p - q form- The decimal expansion of this number was found to be 5-3333333333 - The value of p - q is

A number ' X ...

Question

A number ' $x$ ' was found to be represented in the simplest $\frac{p}{q}$ form. The decimal expansion of this number was found to be 5.3333333333..... .The value of $p - q$ is ___

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Solution

We have $x = 5.3333333......$ ------ (i)
Therefore, $10 x = 53.33333333....$ ---- (ii)
Subtracting (i) from (ii), we get, $10 x - x = 48$
i.e. $x = \frac{48}{9} = \frac{16}{3}$
So, $p - q = 13$

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