Question

after how many places the decimal expansion of 13÷2³×5² terminates​

Answer 1

Answer:

after 3 decimal places as 3>2

Answer 2

SOLUTION

TO DETERMINE

After how many decimal places the below rational number will terminate

$\displaystyle \sf{ \frac{13}{ {2}^{3} \times {5}^{2} } }$

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

$\displaystyle \sf{ \frac{13}{ {2}^{3} \times {5}^{2} } }$

Numerator = 13

Denominator = 2³ × 5²

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 = 3

The exponent of 5 = 2

Max{ 3 , 2 } = 3

Hence the given rational number terminates after 3 decimal places

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