# An Introduction to Physics - Lesson 2

Precision versus Accuracy and Significant Digits

In Science, we take measurements of data when conducting experiments. Three of the important concepts in our analysis and problem solving will be precision, accuracy, and significant digits. Precision is our ability to obtain consistent results over and over again. It is often a function of quality of the instruments used and the user's ability to use the instrument effectively. When performing a measurement, you may get a really crappy value. Precision is the ability to obtain that same crappy value over and over again. Accuracy, on the other hand, is a measure of how close we determine a value to it's actual value. An effective way to picture this is to consider a dart board. Darts around the center are accurate. Darts clustered in another region are precise, but not accurate. Darts that are clustered around the center are accurate and precise.

Significant Figures are the number of reliably known digits in a number. We use these in conjunction with accuracy and precision to give us an answer that represents our true ability to know the accuracy of our answer. Calculators make it easy to find numbers to several decimal places. But our answer cannot be any more accurate than the least accurate measurement we take. For example,if we measure length in meters and time in hundredths of a second, we could find a velocity of 1 meter/3.00 seconds and come up with an answer of 333333333 m/s. This is obviously more accurate than we can measure, so we say that we have 1 significant digit and express our answer as 0.3 m/s. Leading and trailing zeros generally count only as placeholders, not as significant figures for accuracy.

Placing our numbers in *scientific notation* (3 x 10^{-1}) can
help us recognize the number of significant figures in a number. Again,let's not beat around the bush here - YOU WILL LOSE POINTS ON ASSIGNMENTS FOR USING MORE SIGNIFICANT DIGITS THAN AN ANSWER
MERITS. I'm not a complete jerk - I'll give you an extra digit for free!

Click here to practice converting to Scientific Notation. If you are having difficulty with this, I strongly suggest that you take a look at this website and practice some of the material.

Click herefor a great visual demonstration of powers of 10.

Quick and Dirty Approximations

Occasionally we will do quick approximations to get order of magnitude answers to see if we are in the ballpark. We will consider an order of magnitude to be something within a factor of ten of
the real value. For example, you could approximate your volume by assuming you are a cylinder with a circumference of your waist size and your height. Use your circumference to determine your
"radius", and then use the volume formula, *V*_{cyl}
=*pr ^{2}h*.
Or, we could estimate the amount of water in the lower reach of Torsey Pond: Assume an average length (l) of 1 km, an average width (w) of .5 kilometer, and an average depth (d) of 2 meters. Also
assume it is mostly the shape of a rectangular prism. Then, Volume = lwd = (1000m)(500m)(2m) = 1 x 10

^{6}m

^{3}. There are 1000 liters in 1 m

^{3}, so there are approximately 1 x 10

^{9}liters in that part of the pond.