Question

5. Without actual division, find which of the following rational numbers have terminating decimal expansion.

Answer 1

If the factors of denominator of the given rational number is of form 2ⁿ 5^m ,where n and m are non negative integers, then the decimal expansion of the rational number is terminating otherwise non terminating recurring.

SOLUTION:
19/125
Here, the factors of the denominator 125 are 5³ × 2^0 , which is in the form 2ⁿ 5^m .
So , 19/125 has terminating decimal expansion.

Now,
19/ 125 = 19 × 2³ / 5³ ×2³
[Make the denominator in the power of 10]
19/125 = 19 × 8 /(10)³
19/125 = 152/1000 = 0.152

Hence, 0.152 is the decimal expansion of 19/125.

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Answer 2

Solution:-

given by:-
(iii)) here we find us 19/125  a rational number or a have terminating decimal form.

According to Theorem, any given rational number of the form p/q  where p and q are co-prime, has a terminating decimal expansion if q is of the form 2^n×5^m  , where m and n are non-negative integers.

q = 125  = 5×5×5 = 5^3

Here, denominator is of the form 2^n×5^m  , where m = 3 and n = 0.

It means rational number 19/125  has a terminating decimal expansion.

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