Question

How much is 42 divided by 0?

Answer 1

Hint: We start solving the problem by dividing 42 with the numbers that were closer to 0 from the right-hand side of the number line. We then extrapolate the result by using these obtained values when we move towards zero from the right-hand side of the number line. We then divide 42 with the numbers that were closer to 0 from the left-hand side of the number line. We then extrapolate the result by using these obtained values when we move towards zero from the left-hand side of the number line. We then check whether both the extrapolated results are the same or not to get the required answer.


Complete step by step answer:
According to the problem, we are asked to find the result when 42 is divided by 0.
Let us find the value when 42 divided by 0.1.
So, we get \[\dfrac{42}{0.1}=420\] ---(1).
Now, let us find the value when 42 divided by 0.01.
So, we get \[\dfrac{42}{0.01}=4200\] ---(2).
Now, let us find the value when 42 is divided by 0.0001.
So, we get \[\dfrac{42}{0.0001}=420000\] ---(3).
Now, let us find the value when 42 is divided by 0.000001.
So, we get \[\dfrac{42}{0.000001}=42000000\] ---(4).
From equations (1), (2), (3), and (4), we can see that the result is increasing and moving towards $ +\infty $ as we move closer to 0 from the right-hand side of the number line.
Now, let us find the value when 42 divided by -0.1.
So, we get \[\dfrac{42}{-0.1}=-420\] ---(5).
Now, let us find the value when 42 is divided by -0.01.
So, we get \[\dfrac{42}{-0.01}=-4200\] ---(6).
Now, let us find the value when 42 is divided by -0.0001.
So, we get \[\dfrac{42}{-0.0001}=-420000\] ---(7).
Now, let us find the value when 42 is divided by -0.000001.
So, we get \[\dfrac{42}{-0.0001}=-42000000\] ---(8).
From equations (5), (6), (7), and (8), we can see that the result is decreasing and moving towards $ -\infty $ as we move closer to 0 from the left-hand side of the number line.
So, we can see that the final results are not the same as we move towards zero. So, we get the result when 42 divided by 0 is undefined.
  $\therefore$ The result when 42 divided by 0 is undefined.

Note:
 We know that division of 42 with 0 can be represented as $ \dfrac{42}{0} $ , which clearly not satisfies the definition of rational numbers $ \dfrac{p}{q} $ , $ \left( q\ne 0 \right) $ which makes the answer undefined. We can also solve this problem by assuming $ \displaystyle \lim_{x \to 0}\dfrac{42}{x} $ which gives a similar answer. We can also perform the division process manually in standard ways but the results will not be unique as we go on. Similarly, we can expect problems to find the value when 42 is divided by $ \infty $.