Question

the decimal expansion of 13 /1250 terminate after
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Answer 1

This is given that the prime factorization of the denominator is of the form 2 m × 5 n . Hence, it has terminating decimal expansion which terminates after 4 places of decimal. Hence, the correct choice is (d).

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Answer 2

SOLUTION

TO DETERMINE

After how many decimal places the below rational number will terminate

$\displaystyle \sf{ \frac{13}{ 1250 } }$

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

$\displaystyle \sf{ \frac{13}{ 1250 } }$

Numerator = 13

Denominator = 1250 = 2 × 5⁴

Since the prime factorisation of the denominator contains only prime factors as 2 and 5

So the given rational number is terminating

The exponent of 2 = 1

The exponent of 5 = 4

Max{ 1 , 4 } = 4

Hence the given rational number terminates after 4 decimal places

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