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You need to be able to handle numbers of this sort without a calculator.
Basically, you need to remember the following.
For multiplication, add exponents, and for division, subtract exponents.
Example
(4.5x10^{5})(3.0x10^{8}).
Explanation
The answer is 1.35x10^{14} (or
rounded, 1.4x10^{14}). In
solving this, think: 3 x 5 = 15, and
then add the exponents: 5 + 8 = 13. Move the decimal to the right of the
first nonzero digit, or one place to the left.
Example
Try another one: .
Explanation
The answer is 3.4 x10 ^{12}. In
solving this, think: 6.8/2 = 3.4, and then subtract the exponents: (2) 
(10) = 12.
