How did you do?
105 X 109 = 10(5+ 9) = 1014
107 X 106 X 105 = 10(7+6+5) = 1018
1027 X 1032 = 10(27+32) = 1059
102 X 10-3 X 105 = 10(2-3+5) = 104
Did you get the last one right? You should always be careful of negative exponents. Remember that adding a negative number is the same as subtracting a positive number!
The second rule of arithmentic that will help us easily multiply numbers in scientific notation is the following:
If you are just multiplying numbers together, the order of the numbers does not matter.
For example, all of these arrangements multiply together to make 120 -- prove it to yourself!
2 X 3 X 4 X 5 = 120
2 X 5 X 3 X 4 = 120
4 X 5 X 3 X 2 =120
2 X 4 X 3 X 5 =120
and so on...
We can use these two rules to help us multiply together numbers in scientific notation. Consider this:
(2.3 X 102) X (4.5 X 103)
This is essentially a bunch of numbers multiplied together, so the order doesn't matter. We can rearrange, placing the coefficients in one set of parenthesis, and the powers of 10 in the other:
(2.3 X 4.5) X (102 X 103)
In the first set of parenthesis, we simply multiply the two numbers together to get 10.35; in the second set, we follow the rule for multiplying numbers that are raised to a power. Both have the same base (10), so we simply add the exponents. So we get:
(10.35) X (102+3)
10.35 X 105
There is only one minor thing wrong with this answer. Think for awhile about what it might be and then move on for the answer.
Questions? Ask the designer, Jim Heath
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