Question

The product of any number and “0” is ___
A. 1
B. 0
C. number itself
D. none of these

Answer 1

Hint: We use the concept that any number multiplied with zero gives the value zero. Be it a natural number, whole number, rational number, integers, irrational number or a complex number. We check the possibility for each type of number and write our final answer.

Complete answer:
We have to find the product of any number and “0”.
Let us write different cases for natural numbers, whole numbers, rational numbers, integers, irrational numbers or complex numbers.
Natural number:
We know the set of natural numbers contains 1, 2, 3, 4, 5 …
When we multiply any of the natural numbers to the digit 0, we get the value 0.
Whole number:
We know the set of whole numbers contains 0, 1, 2, 3, 4, 5 …
When we multiply any of the whole numbers to the digit 0, we get the value 0.
Rational number:
We know a set of natural numbers contains numbers of the form where p and q both are integers.
When we multiply any of the rational numbers to the digit 0, we get the value 0.
Integers:
We know the set of integers contains … -3, -2, -1, 0, 1, 2, 3, 4, 5 …
When we multiply any of the integers to the digit 0, we get the value 0.
Irrational number:
We know a set of irrational numbers contains numbers of the form where x is a positive integer.
When we multiply any of the irrational numbers to the digit 0, we get the value 0.
Complex number:
We know a set of complex numbers contains numbers of the form where i is imaginary.
When we multiply any of the complex numbers to the digit 0, we get the value 0.
From all the above cases we can say that any number multiplied with 0 is always equal to 0.

Correct option is B.

Note: Many students make mistake of writing the value of product of any number with 0 as 1 as they think when taking case of rational number where they assume denominator can be 0 and they will cancel off and write the value as number itself or 1, which is wrong as rational number has denominator where the denominator has to be non-zero.