Question

The product of a non-zero rational number with an irrational number is always:
A. Irrational number
B. Rational number
C. Whole number
D. Natural number

Answer 1

Hint: To determine the answer, we refer to the definitions of rational and irrational numbers respectively. Then we observe what a product of these two numbers becomes.

Complete step-by-step answer:
By definition, an irrational number in decimal form goes on forever without repeating (i.e. a non-repeating, non-terminating decimal).

By definition, a rational number in decimal form either terminates or repeats the numbers in the decimal part.

By multiplying a non-repeating, non-terminating number to a repeating or terminating/repeating number, the result will always be a non-terminating, non-repeating number.

So, option A is the correct answer.

Note: In order to solve questions of this type the key is to understand the definitions of all the given numbers and the types of numbers in the options.
Whole number - An integer is a number that can be written without a fractional component. The set of integers consists of zero, the positive natural numbers is called whole numbers or counting numbers
Natural Number - The natural numbers are those used for counting and ordering.