Question

. Without performing division, state whether the following rational numbers will
have a terminating decimal form or a non-terminating, repeating decimal form.
13/3125​

Answer 1

10101010101010101010101

Answer 2

Answer:

Theorem: Let x=  p/q be a rational number, such that the prime factorization of q is of the form 2^n 5^m, where n, m are non-negative integers. Then, x has a decimal expansion which terminates.  

​13/3125

Factorize the denominator, we get

3125=5×5×5×5×5=5^5

So, denominator is in form of 5^m so, 13/3125 is terminating.

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