## Without actually performing the long division , state whether the following rational no. will have a terminating decimal expansion or non-te

Question

Without actually performing the long division , state whether the following rational no. will have a terminating decimal expansion or non-terminating repeating decimal expansion.
(a)6/15​

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1 month 2021-09-16T16:43:54+00:00 2 Answers 0 views 0

1. SOLUTION: Here, prime factors of 5 = 5¹ × 2⁰ which is in form So, it will have a terminating decimal expansion.

. Here is a theorem on the decimal expansion of a rational number.

Let ‘x’ be a rational number whose decimal expansion terminates.

Then, ‘x’ can be expressed in the form (p/q), where ‘p’ and ‘q’ are coprime and the prime factorization of ‘q’ is in the form , where n and m are non-integers.

Here is the decimal expansion of  It terminates after one decimal place.

2. To check it whether 6/15 is a terminating decimal place or not.

We will so prime factorization,

6 = 2*3

and 15 = 3*5

3 will be cancelled

the fraction becomes simple

2/5 here 5 is the denominator which is in the form 2^n * 5^m, where 2^0 is there.

SO it is a terminating decimal place