Question

Which of the following numbers has terminating decimal expansion
a. 37/45 b. 21/2356 c. 17/49 d. 89/2332

Answer 1

37/45 is terminating decimal but recurring also

Answer 2

Answer:

Option b - $\frac{21}{2^35^6}$ is terminating.

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 $2^m\times 5^n$ and doesn't include any other prime factor in it's standard form.

Now, We factories the denominator to get in the form

a) $\frac{37}{45}$

$\frac{37}{45}=\frac{37}{3^2\times 5^1}$

It is not terminating.

b) $\frac{21}{2^35^6}$

$\frac{21}{2^3\times 5^6}$

It is terminating.

c) $\frac{17}{49}$

$\frac{17}{49}=\frac{17}{7^2}$

It is not terminating.

d) $\frac{89}{2^33^2}$

$\frac{89}{2^3\times 3^2}$

It is not terminating.