Lesson 4: Scientific Notation
In the last section you learned how to use sig digs in your calculations.
•
What do you do if you multiply numbers like 537 x 269 = 144 453... you are supposed to only
have three sig digs, but your answer sure has more than three sig digs!
We need a way to show the
correct number of sig digs.
•
What if you have a large number like
4 500 000 000
km (the distance from Neptune to the sun),
or a small number like
0.000 000 010
cm (the diameter of an atom) and you don't want to be
bothered with writing out all those zeros?
We need a way to show really big and really small
numbers.
To get around these problems, we use
Scientific Notation
(sometimes called Exponential Notation).
•
This system makes use of "powers of 10", raising 10 to whatever value you need.
•
You can get either really big numbers by using positive powers like 105 = 100 000
•
You can also show really small numbers by using negative powers like 105 = 0.00001
Example 1:
10
5
= 10 x 10 x 10 x 10 x10 = 100 000
10
5
= 1/10 x 1/10 x 1/10 x 1/10 x 1/10 = 0.00001
Don't worry about spending half a minute using your calculator to figure out what 105 equals.
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 Spring '09
 Knott
 Physics, Scientific Notation, Elementary arithmetic, Exponentiation, Mathematical notation, sig digs

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