For measurements we want to be sure we convey the precision (repeatability) of our measurements using significant figures. [covered in lab & Discussion problem set] You should note a couple of aspects of significant figures:
What is the reading (clicker question for last digit)? (0.18±0.01)
What is the measured value (clicker question for last digit)? (1.72±0.01)
Dimensional (Unit) Analysis and Problem Solving
A convenient check on your work, or even a way to determine the best approach to a problem, is to use dimensional analysis. This simply means to include all of the units for each factor in an equation, and then to check to see that the units on both sides of the equation are equal.
Example: How many centimeters are there in one foot?
Known: 1 ft = 12 inches (defined, therefore exactly); 2.54 cm = 1 inch (defined).
Set up: (1 ft)(12 inches/ft)(2.54 cm/inch)
note that ft cancels ft and inches cancels inches to give cm!
Solve: (1 ft)(12 inches/ft)(2.54 cm/inch) = 30.48 cm.
How about sig figs? In this problem there are no significant figures the way its set up, because there are no measurements! That is, all of the numbers are part of definitions, so they are exact, and that means the answer is exact as well.
Extra Example: Assume it is 293 miles to your destination in the Bay Area. If you are driving a car that gets 27 miles per gallon and gas costs an average of $3.45/gallon for the trip, how much will it cost you to drive there and back?
Again, look at units. Want answer in dollars, so
$3.45/gallon ?? = $
So we have $ on both sides, but we need to get rid of (/gallon), so let's try dividing by 27 miles/gallon:
We can now cancel gallons, as shown, and all we need to do now is multiply by miles to cancel miles:
We now have the same units on each side, and can do the math, which I will leave to you.
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© R A Paselk
Last modified 26 January 2015