Question

Page 1.5
A real number
$\frac{ {7}^{2} \times {3}^{2} \times {2}^{2} }{7 \times {5}^{3} \times {3}^{2} \times {2}^{5} }$
will have :
a) terminating decimal
b) non-terminating
c) terminating repeating decimal
d) none of these

Answer 1

Solution : 

--> Cancelling out the few terms of the Numerator and the Denominator :
$It's \ \ \frac{7}{2^3 * 5^3} = \frac{7}{1000}$

Well obviously, the question doesn't ask to write the decimal Expansion so it's fine if one can just see that the DENOMINATOR consists only of '2's and '5's and hence, will give a Terminating Decimal Expansion !! 

Note : Just so you know -> Option ( c ) must've been non-terminating repeating decimal ☺☺☺

Answer 2

hey mate !!


here is your answer !!

look this attachment :-


when the rational number , such that the prime factorization of denominator ( q ) is in the form of

$2 ^{m} \times 2 ^{n}$

where , m and n are non negative integer


then the number have
TERMINATING DECIMAL expansion .



hence , Option number (A ) is correct !!!