Ever wish you didn't have to write out all those zeros when you counted your mounds of money? Well, there's a solution for that: scientific notation. It shortens those numbers down for your convenience.
|Basic Operations||Scientific Notation|
Unlike names and words, you can't just trim out a few characters and expect it to mean
the same thing. It may sometimes seem like you have a ridiculous
amount of zeros, but each one is pretty important. You can't just remove them willy-nilly.
So we need the Scientific Notation to show how many zeros there are without actually
"showing" them. Here's how we do it...
Let's take that amount you won in the lottery... and simplify it.
First we have to grab all non-zero numbers -- in this case, "25."
Next, we have to convert this number to one that is greater than "1" but less than "10."
Send in the decimals. By plunking down a decimal in between the
2 and the 5, we get the number 2.5, which totally works
This number is referred to as our "coefficient." Our next job is to look at the number as a
whole... ...and count up the number of places to the
right of the decimal point.
Notice that we are not just counting up the zeros -- we also have to factor in the 5,
which is now also to the right of the decimal point
After some exhaustive counting, we see that there are 34 decimal places.
In Scientific Notation, we would write our complete number this way:
We've already established that "2.5" is our coefficient.
Because we are working in base 10, the "10" in our abbreviation is -- not surprisingly
-- called the "base." Finally, the 34 on the end that has been shrunken
down and raised up slightly is called..."the exponent."
And there you have it.
Remember, if given a number in Scientific Notation, you can always work backwards as
well. Or, you can just pay someone to do all the
work for you.
After all, you did just win two-point-five times ten to the thirty-fourth power dollars.
(GREAT NO CHANGES)