Question

Let X = 3/8 be a Rational number then find the number of decimals that X terminates ?

Answer 1

Answer:

Let x=p/q be a rational number such that the prime factorization of q is of the form 2

m

5

n

, where n, m are positive integers.

Then x has a decimal expansion which terminates.

Example:

500

49

×

2

2

×5

3

49

Since the denominator is of the form 2

m

×5

n

, the rational number has a terminating decimal expansion.