Question

 of the following has terminating decimal fraction?Full Marks : 2 37/45  11/625  17/49  89/36​

Answer 1

Step-by-step explanation:

Step-by-step explanation:

To find : Which of the following numbers has terminating decimal expansion ?

Solution :

A rational number terminates only when its denominator is in the form 2^m\times 5^n2m×5n and doesn't include any other prime factor in it's standard form.

Now, We factories the denominator to get in the form

a) \frac{37}{45}4537

\frac{37}{45}=\frac{37}{3^2\times 5^1}4537=32×5137

It is not terminating.

b) \frac{21}{2^35^6}235621

\frac{21}{2^3\times 5^6}23×5621

It is terminating.

c) \frac{17}{49}4917

\frac{17}{49}=\frac{17}{7^2}4917=7217

It is not terminating.

d) \frac{89}{2^33^2}233289

\frac{89}{2^3\times 3^2}23×3289

It is not terminating