Question

The decimal expansion of the rational number 658/25 will terminate after how many places of decimal?
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Answer 1

Answer:

26.32. will be the decimal expansion

Answer 2

SOLUTION

TO DETERMINE

The decimal expansion of the rational number 658/25 will terminate after how many places of decimal ?

CONCEPT TO BE IMPLEMENTED

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

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 }

EVALUATION

Here the given rational number is

$\displaystyle\sf{ \frac{658}{25} }$

So denominator = 25

Now 25 = 5 × 5 = 5²

Since the prime factorisation of the denominator contains only prime factors as 5

So the given rational number is terminating

Since the exponent of 5 = 2

Hence the given rational number terminates after 2 decimal places

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