Video Transcript
A scientist must mix the correct volumes of two liquids, liquid A and liquid B, as part of an experiment. He must mix 500 milliliters of liquid A with 200 milliliters of liquid B. He uses a measuring cylinder to measure the volume of each liquid first. The measuring cylinder has a resolution of five milliliters. He then mixes the two liquids. What is the uncertainty in the volume of the mixture?
In this scenario, we have these two liquids, liquid A and liquid B. The scientist conducting an experiment wants to measure out 500 milliliters of liquid A and 200 milliliters of liquid B. To do this, the scientist will use a measuring cylinder. The cylinder is marked with a resolution of five milliliters. This means that the smallest difference in volume indicated in the markings on the cylinder is equal to twice this amount, 10 milliliters.
If we took an up-close view at a certain section of our cylinder, we can imagine considering the markings indicating 430 and 420 milliliters of volume. If our cylinder was filled with a liquid to somewhere between these two marks, then to report the measured volume of that liquid, we would identify the marking closest to the surface of the liquid and then recognize that the actual volume of our fluid might be as much as five milliliters different from this. We would report this volume of fluid then as 430 plus or minus five milliliters.
This particular fluid volume is just an example, and it shows us that when we think about our actual liquid volumes, 500 milliliters for liquid A and 200 milliliters for liquid B, these measurements are also accurate to plus or minus five milliliters. We could write the two volumes then like this. And we’re told that as part of the experiment underway, these two liquids are to be mixed or combined. That means we are adding them together, which indicates, as we’ll see in a second, that the uncertainties in the two liquid volumes add so that the total uncertainty is their sum. 500 plus 200 is 700, and five plus five is 10.
So the final volume of our mixture is 700 plus or minus 10 milliliters. Our question, though, asks only about the uncertainty in the volume of this mixture. That uncertainty we see is 10 millimeters.
