Question

The decimal representation of 23/2³×5² will be -
(a) Terminating
(b) Non-terminating
(c) Non-terminating and repeating
(d) Non-terminating and non-repeating​

Answer 1

Answer:

(a) Terminating

Step-by-step explanation:

Hope This Helped You

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

The decimal representation of 23/2³×5² will be

(a) Terminating

(b) Non-terminating

(c) Non-terminating and repeating

(d) Non-terminating and non-repeating

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 number is

$\displaystyle\sf \: \frac{23}{ {2}^{3} \times {5}^{2} }$

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

So the fraction is terminating

Again max { 2 , 3 } = 3

So the fraction terminates after 3 decimal places

FINAL ANSWER

Hence the correct option is (a) Terminating

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