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 closeto 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=x 100 1 %