Question

Without actual division, show that each of the following rational numbers is a terminating decimal. Express each in decimal form: i) 24/125 (ii) 171/800​

Answer 1

Answer:

The rule is any rational number which has 5 and 2 in the denominator is terminating.

24/125=24/5^3=24/(5^3×2^0) this has both 5 and 2 in the denominator, so this is terminating, also since highest power is 3 (5^3), so it will terminate at 3rd place of decimal

Similarly 171/800=171/(5^2×2^5) Here both 2 and 5 are present in the denominator. So it is terminating and will go upto 5 place of decimal because highest power is 5