Question

Which of the following rational numbers have a terminating decimal expansion?

• A. $\frac{125}{441}$
• B. $\frac{77}{210}$
• C. $\frac{15}{1600}$
• D. $\frac{129}{2^2\times 5^2\times 7^2}$

Answer 1

Answer: (C)

$\frac{15}{1600}$

If numerator and denominator are co-prime then fraction will terminate only if denominator will be of type $2^m{5}^n$ .

Now let see the denominator of each option one by one

A. 441 cannot be expressed in the form of $2^m{5}^n$ .

B. 210 = 7x3x2x5 ;cannot be expressed in the form of $2^m{5}^n$

C. 1600= .$2^6{5}^2$

D. Cannot be expressed in the form of $2^m{5}^n$ .

So the correct answer will option C