Question

without actual division find out if 13/125 is rational or irrational.

Answer 1

Answer:

Rational

Step-by-step explanation:

Given Check whether 13/125 is terminating or non terminating repeating decimal without performing actual division

Without actually performing division we need to find whether the given rational number is terminating or not.

So p/q will be terminating if p and q are co – prime and q is of the form 2^n 5^m where m and n are non-negative numbers.

First checking whether they are co-prime.

13 and 125 do not have common factors and hence they are co – prime.

Now factors of denominator will be 5 x 5 x 5 = 5^3

   We can write this as 1 x 5^3

                                       = 2^0 x 5^3

So denominator is of the form 2^n 5^m where n = 0 and m = 3  

so 13 / 125 = 0.104 and it is a terminating decimal.

So, 13/125 is rational.

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