Question

What is \[0\] divided by \[0\] ?

Answer 1

Hint: In the given question, we are required to find the value of zero divided by zero. We know that \[\dfrac{3}{3}\] , \[\dfrac{8}{8}\] , \[\dfrac{{ - 4}}{{ - 4}}\] are of the form \[\dfrac{a}{a}\] which gives the result \[1\] . Every fraction is the form of \[\dfrac{a}{a}\] gives \[1\] . But it does not hold for \[a\] is equal to zero, as \[\dfrac{0}{0}\] is undefined. We will also see some common misconceptions regarding the division by zero in the problem.

Complete step-by-step answer:
Division means to into equal parts or groups. To symbolize divide we use the \[' \div '\] symbol or sometimes we use \['/'\] symbol. Division is the opposite of multiplying. As we have to find the value of zero divided by zero.
For this first we should know what is division by zero. Division by zero is the type of division where the denominator is zero, that is the divisor is zero.
Suppose that division by zero is of the form \[\dfrac{a}{0}\] where \[a\] is a non-zero and is called a dividend. Now this division has no meaning because there is no number which when multiplied by zero gives \[a\] . So, the expression \[\dfrac{a}{0}\] is undefined.
 If we put \[a\] is equal to zero then the expression \[\dfrac{0}{0}\] is also undefined because any number multiplied by zero is zero.
Hence, zero divided by zero is undefined.
So, the correct answer is “undefined”.

Note: Some of us have the misconception that any number dividing by zero gives zero and zero divided by zero is equal to one. But this is not true. We know that \[\dfrac{0}{8} = 0\] due to which we assume that \[\dfrac{8}{0}\] is also equal to zero but it is not like that so, as \[\dfrac{8}{0}\] is undefined. There are some division properties of zero you should know given as follows:
\[0\] divided by any non-zero number is always equal to \[0\] .
\[0\] divided by \[0\] is undefined.
Any number divided by \[0\] is also undefined as it is meaningless.