# Video: Units of Measured Quantities

Which of the following is an appropriate symbol for the unit of a quantity found by dividing a temperature by a distance? [A] mK [B] K/m [C] K⋅m [D] km [E] K/m²

04:15

### Video Transcript

Which of the following is an appropriate symbol for the unit of a quantity found by dividing a temperature by a distance?

Now, as we look over the five answer options, we see these different symbols representing different physical quantities. And we need to be careful not to confuse these quantities with one another.

For example, the m in option A is different from the m in option B. Those don’t represent the same thing. Notice also that the k in option D is lowercase, whereas the Ks in other options are uppercase. This difference is intentional, and these symbols mean different things.

Now our question asks us, which symbol correctly represents a temperature divided by a distance? As a starting point, we can establish that we’re working with a particular system of units. That’s called the SI or international system. The reason it’s important to know what system we’re working with is because temperatures and distances are represented differently in different unit systems.

Within the SI system, temperature is represented using a unit called a Kelvin. So the temperature of an object would be reported in these units. We would say it’s 10 Kelvin or 87 Kelvin or something like that. This unit is abbreviated using a capital K. And looking back at our answer choices, we see this capital K in four of our five answer options.

Now moving on to distance, in the international system, the SI system for short, the unit of distance is the meter. And we abbreviate this unit using a lowercase m. Along with measuring distances in units of meters, we can also measure distances in units of kilometers, abbreviated km. And specifically, this is a lowercase k that comes in front of the m for meters.

Now that we know this, that solves the mystery of why this k in answer option D is different from all the other Ks. This lowercase k refers to the kilo in kilometers, whereas these uppercase Ks in the other options refer to a temperature in Kelvin. This means, by the way, that answer option D does have a distance in it. But it has no temperature. Therefore, it won’t be our answer to this question.

Now that we know that temperature in Kelvin is abbreviated capital K and distance in meters is abbreviated lowercase m, we can see what the symbol will look like when we divide a temperature by a distance. Our answer then should show us capital K divided by lowercase m. That’s a temperature divided by a distance in the SI system.

Looking at option A, we might think that this is a distance in meters multiplied by a temperature in Kelvin. But actually, this m is a prefix. It stands for “milli” or one thousandth. The reason we know this m is not a distance in meters is because there’s no multiplication sign between these two letters. If there were, this would be a distance in meters multiplied by a temperature in Kelvin. But because there’s not, we know that that m stands for “milli.” So we’re talking about thousandths of a Kelvin. In other words, this answer option has a temperature, but it has no distance involved. Therefore, it also won’t be our answer.

Moving on to option B, this shows us a temperature in Kelvin divided by a distance in meters. This matches the symbol that we were looking for. So option B looks like it might be our answer. Before we make it our final choice though, let’s look at options C and E.

Option C has a temperature in Kelvin multiplied by a distance in meters. Because there’s no division involved here, we won’t choose that. And then, in option E, we have a temperature in Kelvin divided not by a distance in meters, but by a quantity in meters times meters.

Now if we think about it, if we have a distance of one meter and then we multiply that by a distance of one meter, then the result is not a distance along a line, but rather an area. And the area is one meter squared. It’s this unit, square meters, that we see in the denominator of option E. So E is not showing us a temperature divided by a distance. But it’s showing us a temperature divided by an area. Therefore, it also isn’t the symbol we’re looking for.

So then option B really is our final answer. The symbol for the quantity found by dividing a temperature by a distance in the SI system is capital K for Kelvin, divided by lowercase m for meters.