Question

The decimal form of 129225775 is

(a) terminating (b) non-termining.

(c) non-terminating non-repeating (d) none of the above​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

$\displaystyle \sf{ The \: decimal \: form \: of \: \: \frac{129}{ {2}^{2} \times {5}^{7} \times {7}^{5} } }$

(a) terminating

(b) non terminating

(c) non-terminating non-repeating

(d) none of the above

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 fraction is

$\displaystyle \sf{ \: \frac{129}{ {2}^{2} \times {5}^{7} \times {7}^{5} } }$

Numerator = 129

$\displaystyle \sf{ Denominator\: = {2}^{2} \times {5}^{7} \times {7}^{5} }$

Since the prime factorisation of the denominator contains prime factors as 7 other than 2 and 5

So the given fraction is non terminating

FINAL ANSWER

Hence the correct option is

(b) non terminating

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Answer 2

Answer:

non terminating

Step-by-step explanation: