3.2 X 104 = 32,000
1 / 32,000 = 0.00003125 = 3.0125 X 10-5
And 0.0003125 is not even close to 3.2 X 10-4 !
When we consider something like
1 / (3.2 X 104)
We need to remember that the denominator of this fraction is simply two numbers multiplied together, in this case 3.2 and 104. Since the two numbers are being multiplied together, we can break this fraction up into two separate fractions, just as we did with
1/8 = 1 / (2 X 4) = (1/2) X (1/4) = 0.5 X 0.25 = 0.125
WARNING!
You can only do this if the numbers in the denominator are being multiplied together! This will not work for addition, subtraction or division, so please don't try!
Using this arithmetic "trick," let's see what we get:
1 / (3.2 X 104) = (1 / 3.2) X (1 /104) = 0.3125 X 10-4
Putting this into the standard form, we get 3.125 X 10-5
We can also look at this in light of the rules we have learned about dividing numbers in scientific notation. Remember that 1 = 1 X 100 and calculate
1 / (7.5 X 10-7)
You can check your answer on the next page, and see some general guidelines.
Questions? Ask the designer, Jim Heath
Copyright 2000 Austin Community College