KEY CONCEPTS: WHAT IS MEANT BY UNCERTAINTY? HOW DO WE DEAL WITH UNCERTAINTY IN OUR MEASUREMENTS? KEY TERMS: UNCERTAINTY ESTIMATED UNCERTAINTY PERCENT UNCERTAINTY Introduction to Uncertainty

Uncertainty of Measurement? Every measurement we make is subject to some level of uncertainty.  A given measurement isn’t complete until it also includes its degree of uncertainty. Where does uncertainty come from?  Uncertainty of measurement can come from  the measuring instrument,  the item being measured,  the environment,  the operator,  and other sources as well.

Uncertainty? But what is uncertainty of measurement?  It’s the doubt that exists about the result of any measurement.  Even the most careful measurements have a slight margin of doubt.  There are two types of measurement uncertainty we can have  Accuracy The nearness of a measurement to the standard or true value  Precision The degree to which several measurements provide answers very close to each other.

Estimated Uncertainty Let’s say we were trying to measure the length of this pencil.  There are a lot of challenges to this measurement, but we’ll do the best we can.  We can see that the pencil ends at the second line after the 8 cm mark on the ruler. So that will be our base measurement. We can write it as 8.2 cm or as 82 mm.  Now we need to add our estimated uncertainty. Our ruler only measures to the nearest millimeter. So our uncertainty will be half of that interval.  So our total measurement is 8.2 ± 0.05 cm or 82 ± 0.5 mm.

Percent Uncertainty Sometimes we want to express our uncertainty of measurement in terms of a percentage of the base measurement.  To do this we figure out what the uncertainty is.  Our string could be just 81.5 mm or it could be 82.5 mm. So, our percentage uncertainty is 82.5 – 81.5 = 1 mm.  Now we divide this by our base measurement and multiply by 100 to find the percent. 1 mm 82 mm =x1001 %