Scientific Notation

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These tutorials will take you through using scientific notation.

Why should you care about scientific notation?

Because it's hard to keep track of really big or really small numbers.

Suppose you have to figure out how many bacteria are in Lake Michigan.

You know there are 1732000 bacteria/liter

and there are 4920000000000000 liters in Lake Michigan

It's just a simple little multiplication problem, right?

Easy to do -- if you can keep track of all those zeroes. But you probably can't, unless you count them. In fact, I bet you counted them just to copy the problem down, didn't you?

Scientific notation is just a way of counting the zeroes for you.

Whenever you multiply a number by 10, you move the decimal point to the right, don't you?

2.0 x 10 = 20.0

2.0 x 10 x 10 = 200.0

Scientific notation just tells you how many times you multiplied a number by 10 - that is, it counts the number of spaces you moved the decimal point right..

2.0 x 10 = 20.0 = 2 x 101
(we usually don't bother writing the 1, but just say this is 2 x 10).

2.0 x 10 x 10 = 200.0 = 2 x 102

So, what about those 4920000000000000.0 liters in Lake Michigan?

The decimal point is 15 places to the right of the 4, so you could write this as

4.92 x 1015

Now, how would you write the number of bacteria in scientific notation? After you've tried it, put your cursor in the black box below to see the answer.

Click 'forward' to go on.

the decimal point is 6 places to the right of the 1, so you could write this as
1.732 x 10 6 bacteria/L