You've been working with numbers ever since you learned your 1s, 2s, and 3s. (Hopefully you've got those down by now or the rest of this is going to be a blur.) For years, you've been seeing the same old numbers pop up again and again, and you might suspect that not much has changed in the world of mathematics since Euclid broke onto the scene. But, in reality, numbers as we know them today are the result of many centuries of problem-solving. As problems have gotten more complex, we've actually had to invent new kinds of numbers in order to solve the new kinds of problems. To keep written math short and sweet given the introduction of all these new numbers, mathematicians have also devised a large number of acronyms and abbreviations - so many of them, in fact, that one has to imagine these guys would have been some pretty phenomenal texters. (e > 32 - 4i(2x) + loljk(omg!))
There are different ways of writing numbers depending on the situation, such as fractions and decimals. It's okay to say you're going to down "1/2 a gallon of milk" (although we don't recommend actually doing it), but to say you're going to drink "0.50 gallons of milk" will probably get you some strange looks. On the other hand, asking your mom for $0.50 (you find she's more generous when you keep it realistic) makes more sense than requesting 1/2 a dollar.
It's amazing what we can get to from thinking about numbers. On the practical side of things, numbers and operations allow us to tip the waiter, bake cupcakes, calculate sales tax, and balance a checkbook. On the impractical side of things, they allow us to concoct a secret potion that is exactly the right parts eye of newt to toe of frog. You can't just wing those secret potions.