Numbers were first used, or so the story goes, to count what you owned, sheep, cattle etc. You didn’t really need a number till the first sheep walked past, and then the counting numbers could begin at 1 and continue as far as necessary. It wasn’t long though before there was a need to have numbers representing both positive and negative values. These are known as the integers, and the dividing point between them is known as zero, which is neither positive nor negative.
So how do you work with zero? Addition and subtraction are a cinch. Adding or subtracting zero to any integer does not change its value. Multiplication is also straightforward. You can multiply any integer, including zero itself, by zero, and the answer is always zero itself.
Division by zero is another story. One easy way to illustrate the problem with division is to use a pocket calculator. Take any integer, 5 for example. We know 5 ÷ 5 = 1,
5 ÷ 0.05 = 100, 5 ÷ 0.0005 = 10,000. You soon realize that when we divide by smaller and smaller numbers, the correct answers are larger and larger numbers. Because we can only approach zero, then it is agreed that division by zero would be considered undefined. It is possible though to divide zero by any number other than itself. The answer will always be zero.
Zero serves a useful purpose as a placeholder both for very small and very large numbers, e.g., 0.00035 or 750,000,000. Having the zeros in place enables us to read and understand the values of these numbers.
Another role that zero plays in basic mathematics is as an exponent. Most people realize that 3² =9 (the exponent indicates the number of times the 3 is to be multiplied by itself). Even negative integers can be used as exponents. 3 raised to the exponent -2 = 1/9. But what about 3°? It turns out that all integers (with the exception of zero itself) can be raised to the exponent zero, but in every case, the result is 1. That makes it pretty straightforward. 1000° = 1, 1° = 1, and (-75)° = 1. But 0° is undefined. Don’t even think about making that equal to zero.
It takes a while for people interested in math (and isn’t everyone?) to become accustomed to the use of zero. However, like most things in math, once you do understand it, it is consistent and dependable.