Question

Look at several examples of rational numbers in the form $\frac{p}{q}$ (q≠0),where p and q are integers with no common factors other than 1 and having terminating decimal representations (expansions). Can you guess what property q must satisfy?

Answer 1

Answer:

Let us take 1/2,1/4,7/8,37/25,8/125,17/20,31/16 etc.

which has terminating decimal expansion.

▪{ 1/2

1/4=1/2×2×1

7/8=7/2×2×2×1

37/25=37/5×5×1

8/125=8/5×5×5×1

17/20=17/2×2×5×1

31/16=31/2×2×2×2×1 }▪

Here, th denominator is either 2 or power of 2 or 5 or power of 5 or both.

Hence, in p/q ,q is either 2 or power of 2 or 5 or power of 5 or both....

Hope It Helps...☺