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:
387/800
Here, the factors of the denominator 800 are 2^5 × 5² ,which is in the form 2ⁿ 5^m .
So , 387/800 has terminating decimal expansion.

Now,
387/800 = 387 × 5³ / (5² ×2^5) 5³
[Make the denominator in the power of 10]
387/800 = 387 × 125 /(10)5
19/125 = 48375 /100000 = 0.48375

Hence, 0.48375 is the decimal expansion of 387/800.

HOPE THIS WILL HELP YOU

Answer 2

solution:-

(v) here we find us 387/800 a terminating decimal form or a non-terminating, repeating 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 = 800  = 2×2×2×2×2×5×5 = 2^5×5^5


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

desimal form 0.48375 of 387/800
It means rational number 387/800  has a terminating decimal expansion.


■I HOPE ITS HELP■