This question really highlights the true science of mathematics. Yes, it is very useful- we can calculate practical real-life problems such as how much a bag of apples costs, or even the distance from the earth to the moon. But it also requires us to think in a much more abstract way, such as in dimensions of more than 4 used in things like higher equations. Interestingly, multiple dimensions is also a fundemental concept of string theory!
When numbers first were in use, zero had not even been considered. The ancient Chinese could not accept the idea of nothing as being an amount of something. They also struggled with using zero in even simple calculations. For example, 0 – 10 = -10. Simple but a whole new system had to be introduced; negative numbers. Now negative numbers are widely accepted, we can think of them in terms of debts to rationalise them, but at the time this was a radical new way of thinking about numbers. Once they had negative numbers, zero was properly accepted and we now use it in graphical equations and solving simultaneous equations, basic fundamentals in maths. Looking back, it seems strange that we didn’t think of zero as even a number. There wasn’t even a symbol of it until thousands of years after numbers were introduced!
You may think we are pretty advanced in mathematics, but there still remains another basic calculation that zero does not fit so easily into; division. Well, the proper answer to dividing a number by zero is infinity. Infinity? That’s not a number is it? You may not think of infinity as a number, just as we didn’t use to think of zero as a number, but we must learn to think of maths abstractly. If zero is an abstract number, when you calculate with it you should expect to get an abstract number as an answer.
But there is a practical way of rationalising things. Think of the number you are dividing as an apple. When the apple = 1, if you divide by one you get the whole apple. If you divide by 0.1 you get the apple in 10 slices. If you divide by 0.01 you get 100 slices. As you get closer to 0 you get more and more slices, and the slices get smaller and smaller. Therefore at 0 the number of slices is infinity, and the size of each slice will be 0. Hence, you can divide by zero you just have to accept infinity as an abstract number, just as zero and negative numbers have been in the past. Who knows, someday we may be accepting multiple dimensions!