Question

Without actual division find which of the following rational number are terminating decimal 40/ 300

Answer 1

Answer:

It's not a terminating decimal

Explanation :

We know that if the denominator of a rational number has no prime factors other than 2 or 5, then it is expressible as a terminating, otherwise it has non - terminating repeating decimal representation. Thus, we will have to check the prime factors of the denominators of each of the given rational numbers.

In the 40/300 he denominator is 300

300 = 2 × 2 × 3 × 5 × 5

Since we have 3 as a factor other than 2 and 5, it has non - terminating repeating decimal representation.

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Answer 2

Answer:

It is a recurring decimal

Step-by-step explanation:

denominator = 300 = 3 *2^2 * 5^2

numerator is not a multiple of 3.

so denominator cannot be expressed in the form 2^m *5^n where m and n are integers.(because three is neither 2^m nor 5^n)

so it is not a terminating decimal