Question

Without using long division show that the rational no. 21/1120 has the terminating decimal expansion

Answer 1

Since 7 is common between the numerator and denominator, we divide both numerator and denominator by 7.

So, 21/1120 will become 3/160

Now for 3/160 to be a terminating decimal 1/160 needs to be a terminating decimal. Also, it needs to be in the form $2^{x} . 5^{y}$

160 can be written as $2^{5}*5$.

Hence 21/1120 will be a terminating decimal.