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Scientific Notation 25559 Views
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Description:
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.
Transcript
- 00:08
Scientific Notation, a la Shmoop. Congratulations! You just won a ton of money
- 00:17
in the lottery! Ay caramba. You're excited to tell the world
- 00:22
about your good fortune, but will that number even fit in a tweet?
- 00:29
Well, you'll need an easier way to express it. Thank goodness for Scientific Notation.
- 00:37
In short, Scientific Notation is a way of abbreviating numbers.
Full Transcript
- 00:43
Unlike names and words, you can't just trim out a few characters and expect it to mean
- 00:47
the same thing. It may sometimes seem like you have a ridiculous
- 00:50
amount of zeros, but each one is pretty important. You can't just remove them willy-nilly.
- 01:01
So we need the Scientific Notation to show how many zeros there are without actually
- 01:05
"showing" them. Here's how we do it...
- 01:11
Let's take that amount you won in the lottery... and simplify it.
- 01:16
First we have to grab all non-zero numbers -- in this case, "25."
- 01:22
Next, we have to convert this number to one that is greater than "1" but less than "10."
- 01:29
Send in the decimals. By plunking down a decimal in between the
- 01:34
2 and the 5, we get the number 2.5, which totally works
- 01:38
This number is referred to as our "coefficient." Our next job is to look at the number as a
- 01:45
whole... ...and count up the number of places to the
- 01:48
right of the decimal point.
- 01:53
Notice that we are not just counting up the zeros -- we also have to factor in the 5,
- 01:58
which is now also to the right of the decimal point
- 02:07
After some exhaustive counting, we see that there are 34 decimal places.
- 02:11
In Scientific Notation, we would write our complete number this way:
- 02:16
We've already established that "2.5" is our coefficient.
- 02:19
Because we are working in base 10, the "10" in our abbreviation is -- not surprisingly
- 02:23
-- called the "base." Finally, the 34 on the end that has been shrunken
- 02:28
down and raised up slightly is called..."the exponent."
- 02:35
And there you have it.
- 02:36
Remember, if given a number in Scientific Notation, you can always work backwards as
- 02:40
well. Or, you can just pay someone to do all the
- 02:42
work for you.
- 02:42
After all, you did just win two-point-five times ten to the thirty-fourth power dollars.
- 02:45
(GREAT NO CHANGES)
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