Video Transcript
The resolution of a measuring
instrument is five units. What is the uncertainty in the
measurements made by the instrument? Plus or minus one units, plus or
minus 2.5 units, plus or minus five units, plus or minus 10 units.
The question gives us the
resolution of a measuring instrument and asks us to determine the resulting
uncertainty in measurements made by the instrument.
If we recall that the uncertainty
in a measurement is half of the resolution of the measuring instrument, then since
the resolution of the measuring instrument is five units, we can write that the
uncertainty is plus or minus five units divided by two, which is plus or minus 2.5
units. And this is our answer. The uncertainty in the measurements
made by this instrument is plus or minus 2.5 units.
It’s worth taking a moment to
understand why the uncertainty of a measurement is half of the resolution of the
measuring instrument. The resolution of a measuring
instrument is the minimum difference between two different values of
measurement. Now, let’s say one possible value
for a measurement made by this instrument is 10 units. Then, because the resolution of
this instrument is five units, then the next smallest possible value for measurement
is five units and the next largest possible value is 15 units. Note that the measuring instrument
cannot return a value between five and 10 units nor between 10 and 15 units.
But what if the exact value of what
we’re measuring is in fact between five and 10 units? Then, the result that we get will
be the exact number rounded to the nearest five units. That is, if the value we are trying
to measure is anywhere in this blue portion of the number line, which is closer to
10 than it is to five or 15, then the value that we measure will be 10 because the
value that we measure is rounded to the nearest five units.
The edges of this marked portion of
the line are 7.5 on the left and 12.5 on the right. This is because on the left
anything greater than 7.5 is closer to 10 than it is to five, and on the right
anything less than 12.5 is closer to 10 than it is to 15. What this means is that a measured
value of 10 could actually be as small as 7.5, which is 10 minus 2.5, or as large as
12.5, which is 10 plus 2.5. We call this amount the maximum
amount by which the true value can differ from the measured value and still be
consistent with that measured value, the uncertainty. And as we can see, resolution is
the full difference between values of measurement and uncertainty is half of that
difference, which is why uncertainty should be half of measurement resolution.
