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.