Question

Which of the following will not represent zero:-
(a). \[0\times 0~~~~~~~~~~~\]
(b). \[~~{{5}^{0}}-1~\]
(c). \[\dfrac{0}{3}\]
(d.) \[\dfrac{6}{2}\]

Answer 1

HINT:- Before solving this question, we must know the following things:-
1.) If the numerator of any fraction is zero, then the whole fraction becomes zero.
2.) When the denominator of a fraction is less than the numerator, then the fraction is an improper fraction and can be converted into a mixed fraction, which is the combination of whole number and a proper fraction.
3.) If the power of any integer is 0, the integer represents 1.
4.) If any number is multiplied by 0, then the product will always be 0.

Complete step-by-step solution -
Let us now solve the question.
a). We will consider every option.
 \[0\times 0\]
As mentioned in the hint provided above, if any number is multiplied by 0, then the product will always be 0. So, \[0\times 0\] will represent zero.
Hence, this is a wrong option.

b). \[~~{{5}^{0}}-1~\]
   As mentioned in the hint provided above, if the power of any integer is 0, the integer represents 1. Therefore, \[~~{{5}^{0}}-1~\] equal to 1 – 1, which is again 0. So, \[~~{{5}^{0}}-1~\]will represent zero.
     Hence, this is a wrong option.

c). \[\dfrac{0}{3}\]
As mentioned in the hint provided above, if the numerator of any fraction is zero, then the whole fraction becomes zero. So, \[\dfrac{0}{3}\] is equal to zero.
Hence, this is a wrong option.

d). \[\dfrac{6}{2}\]
We can see that the above fraction can be simplified further. So, we will firstly simplify this fraction. After simplification, the fraction we get is \[\dfrac{3}{1}\], which is equal to 3. As 3 does not represent zero, therefore, \[\dfrac{6}{2}\] will also not represent 0.
Hence, this is the correct option.
So, the correct option for this question is (d) \[\dfrac{6}{2}\] .

NOTE:- One must do all the calculations very carefully in this question. And not only in this question, the student should be very careful while solving any such question as any mistake in the calculations can make the answer wrong.