We will begin with multiplication, because it is the easiest thing to do in scientific notation. We will use two fundamental rules of arithmetic to help us. The first involves what happend when you multiply two numbers with exponents.
Consider what happens when we multiply together two numbers in powers of ten notation, such as 103 and 105. First, let's try breaking these two down into tens:
103 = 10 X 10 X 10
105 = 10 X 10 X 10 X 10 X 10
Now multiply them together:
(10 X 10 X 10) X (10 X 10 X 10 X 10 X 10)
Remove the parenthesis, and what do we get?
10 X 10 X 10 X 10 X 10 X 10 X 10 X 10
In powers of 10 notation, this is 108.
Look at the exponents carefully, before and after the multiplication. Can you see what is happpening?
Try the following youself, breaking things down into tens, and see if you can see a pattern:
103 X 108 = ?
104 X 104 = ?
102 X 103 X 105 = ?
Now check your answers.
Questions? Ask the designer, Jim Heath
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