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.