Question

The smallest number by which 1/13 should be multiplied so that is decimal expansion terminator after 2 decima place is​

Answer 1

SOLUTION

TO DETERMINE

The smallest number by which $\displaystyle\sf \: \frac{1}{13}$ should be multiplied so that is decimal expansion terminates after 2 decimal place is

EVALUATION

We know that ,

$\displaystyle\sf{Fraction = \frac{Numerator}{Denominator} }$

A fraction is said to be terminating if prime factorisation of the denominator contains only prime factors 2 and 5

If the denominator is of the form

$\sf{Denominator = {2}^{m} \times {5}^{n} }$

Then the fraction terminates after N decimal places

Where N = max { m , n }

Here the given number is

$\displaystyle\sf \: \frac{1}{13}$

In order to get the number which should terminates after 2 decimal place we need to multiply the numerator by 13 and denominator by 2² × 5²

Hence the required number

$\displaystyle\sf = \frac{13}{ {2}^{2} \times {5}^{2} }$

$\displaystyle\sf = \frac{13}{4 \times 25 }$

$\displaystyle\bf = \frac{13}{100 }$

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