Question

out of the following number which number has non-terminating recurring decimal form?
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Answer 1

Answer:

Option 3 is correct, it is of a non terminating recurring decimal form.

Step-by-step explanation:

A rational number whose denominator is of the form (2^m) × (5^n) will always have a terminating decimal form.

Here, we must check for each option,

(1)

(13/5)

Here the denominator is 5.

We can write 5 as,

5 = 2⁰ × 5¹

Since 2⁰ is 1 it won't change the value.

Thus, the denominator is of the form (2^m) × (5^n) where m = 0 and n = 1

So, it is of terminating decimal form.

(2)

(23/25)

Denominator = 25

25 = 5²

It can also be written as

25 = 2⁰ × 5²

Thus,

the denominator is of the form (2^m) × (5^n) where m = 0 and n = 2

So, it is of terminating decimal form.

(3)

17/6

Denominator = 6

6 = 2¹ × 3¹

It can also be written as,

6 = 2¹ × 3¹ × 5⁰

But here, the denominator is not of the form (2^m) × (5^n), because a 3 is also there. It should only be of the form (2^m) × (5^n).

Hence,

it is of a non terminating recurring decimal form.

Let's just check for 4 also,

(4)

19/8

Denominator = 8

8 = 2³

Also written as,

8 = 2³ × 5⁰

Thus,

the denominator is of the form (2^m) × (5^n) where m = 3 and n = 0

So, it is of terminating decimal form.

Hence,

Option 3 is correct