Question

Which one of the following has a terminating decimal expansion?
A. $\dfrac{5}{{32}}$
B. $\dfrac{7}{9}$
C. $\dfrac{8}{{15}}$
D. $\dfrac{1}{{12}}$

Answer 1

Hint: In order to solve this problem we will use the basic definition of terminating rational number which states that a rational number which terminates after a finite number of steps in the process of division is called a terminating decimal. Example, 1.25, 5.365 etc

Complete step-by-step answer:
We know that a terminating decimal is a decimal that ends. It is a decimal with a finite number of digits. For example $\dfrac{1}{4} = 0.25$ , it has only two decimal digits.

Now consider the fraction $\dfrac{5}{{32}}$​ whose decimal form will be:

$\dfrac{5}{{32}} = 0.15625$

The resulting decimal number ends with five decimal digits and therefore, it is terminating decimal.
Hence, $\dfrac{5}{{32}}$​ has a terminating decimal expansion.

Note: In order to solve these types of problems be familiar with the concept of terminating and non-terminating numbers. A non-terminating, non-repeating decimal is a decimal number that continues endlessly, with no group of digits repeating endlessly. Decimals of this type cannot be represented as fractions, and as a result are irrational numbers. Pi is a non-terminating, non-repeating decimal.