### 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.