Different Ways to Represent Numbers
You may not realize it, but you're already pretty good at recognizing a variety of different symbols that all represent the same number or concept. For example, the thing in parentheses (4) isn't actually the number four. It's just a symbol that represents the concept of the number four. To further illustrate this point, take a gander at these symbols:
(8 ÷ 2)
Each of these symbols is different, but they're all symbolic representations of the number four. Same deal with the Roman numeral IV. They're just different ways of saying the same thing.
Along the same lines, an amount can be expressed by either a fraction, decimal or percentage. For example, we're really saying the same thing whether we write or 75%. We can even draw a picture:
In each case, the symbol represents having three out of four equal parts, or 75% of the whole. If this were a football game, we'd be ready to head into the fourth quarter. If this were a dollar, we'd be 25 cents shy of being able to dry our laundry.
When you're dealing with a particular problem or situation, choose the representation that best goes with the situation. When working with money, $0.75 usually makes more sense than "three-fourths of a dollar." When running a poll, "three-fourths of those polled" makes more sense than saying "0.75 of those polled." If you're saying that "three-fourths of those polled feel that $0.75 a week is enough to live on," then you could also say that there's a "100% chance that the polling methods are flawed."
Writing real numbers as decimals allows us to separate the real numbers into rational and irrational numbers. This is important, 'cause they'll often start to tussle when left alone together.
That brings us to the decimal versions of rational numbers. We already know that a rational number is anything we can write as a fraction of two integers, right? Well, here's another definition: rational numbers are decimals that end or repeat. Here are some examples of decimals that are rational numbers:
Irrational numbers are decimals that go on forever without repeating. That's pretty amazing when you think about it, considering that most of our politicians can't go more than about two minutes without repeating.