Up to a discussion of significant zeros.

Scientific Notation

To write a number in scientific notation, rewrite it so that there is exactly one digit to the left of the decimal point. Of course, you will have to multiply this rewritten number by an appropriate power of ten in order to make it equal to the original number.

When we do this, we are able to distinguish between zeros that are significant figures and zeros that are simply "place holders" - the ones that are just there to give the number the correct size (remember the 50 million years from the joke in the introduction? Most of those zeros are just place holders).

A few examples might make this clearer:

NumberIn scientific notationNumber of sig. figures
18001.8 x 10^2two
18001.80 x 10^2three
18001.800 x 10^2four

Remember the example from the last page? We can now write down the two different measurements in scientific notation and clear up the issue of which is more precise.

Your measurement:1.000 x 10^3 m
Your partner's measurement:1 x 10^3 m

It is now obvious which measurement is more precise.

Now that we can state any measurement with the correct number of significant figures, it is time to learn how do calculations with these quantities.

On to Calculations with significant figures.
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