This is a short video about measurement uncertainty. There's a part of the lab
report that asks you to explain your measurement uncertainty, so we're going to talk about what
that means here. Measurement uncertainty is the result of imprecision in measuring devices. All
measuring devices have some degree of imprecision, and therefore some degree of uncertainty.
Measurement uncertainty is always the larger of these two choices, either the limit of the
instrument which is half of the smallest increment multiplied by the number of measurements taken,
or a justified estimation of the limit of the measurement procedure as done by the
experimenter. So let's see what that looks like in real life. We can imagine that we're measuring a
pencil and we're comparing it to a ruler, so we need to use the limit of the instrument,
half of the smallest increment multiplied by the number of measurements taken. I can
see that half of the smallest increment here, the smallest increment is 0.5 centimeters, I know this
because I can see that there are lines for every centimeter and lines for every half centimeter,
so the smallest space between two points that this ruler measures is one half of a centimeter,
so that's the smallest increment. So I'm going to end up using that in my equation. I now need
to know how many measurements are being taken here, this is the part that confuses students
a lot because they assume we're just taking one measurement, we're measuring the pencil once,
but a measurement doesn't just mean measuring the actual pencil. When we're dealing with measurement
uncertainty a measurement is when we use the instrument and compare the instrument to the
object, and when you think about that we actually have to do that at 2 points on the pencil. We need
to see how far it goes this way to the right, and how far it goes this way to the left,
so we're technically comparing 2 points on the pencil to the instrument. So we're taking 2
measurements here rather than 1, so therefore the uncertainty is going to be that number of
measurements times half of the smallest increment, which just turns out to be 0.5 centimeters again.
So we would say that the measurement uncertainty of this ruler is one half of a centimeter,
and whenever we recorded any values that we measured for this ruler we would record the
values and add an uncertainty of plus or minus 0.5 centimeters to the end. As an example, if I
recorded the length of this pencil I would eyeball it and say it seems to be around 4.30 centimeters,
so I would say that's 4.3 plus or minus 0.5 centimeters. So that's how we would record
that based on the measurement uncertainty rules. Readings on a meter like this can also be a little
strange. I can see that the smallest increment here is 0.2 volts V stands for volts here so
0.2 is the smallest space between two lines and this is a little counterintuitive, but we would
also say that we're taking two measurements here because we're comparing either side of this meter
to the background measurements, so that's a little strange but we would say that we're also taking
two measurements in this situation. So for a lot of situations that you deal with we would say that
it's going to be half of the smallest increment times two measurements which will just become the
smallest increment again, so the uncertainty here would be 0.2 volts. So if I were to record this
voltage I can see that that line is around 3.3 or so. I'm not exactly sure, so I would record
it as 3.3 plus or minus 0.2 volts. If you're working with a digital reading the uncertainty
will be at least plus or minus one digit of the last significant figure of the reading. As an
example we can imagine we have this digital scale, and right away I can see that the scale goes down
to the tenth spot there's one number after the decimal, so when I put this apple on it I get a
recording of a certain value: 163.4. In this case this is grams, and so the uncertainty here would
be plus or minus 0.1 because it's plus or minus one digit of the last significant figure, and here
that last significant figure is the 4 after the decimal point so I would say it's mass is 136.4
plus or minus 0.1 grams, so if you're writing a lab report and need to fill out the section
"explain the measurement uncertainty in the IV or DV" just write about how you follow this method.