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Scientific Notation 25556 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.

Language:
English Language

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.

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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