### Video Transcript

What is negative 40 degrees
Celsius in degrees Fahrenheit?

In this exercise then, we’re
doing a temperature conversion from a temperature in degrees Celsius to one in
degrees Fahrenheit. Whenever we do that, it’s
helpful to recall the conversion relationship between these two separate
temperature scales. Given a temperature in degrees
Celsius, we can call it 𝑇 sub C, if we multiply that temperature by nine-fifths
and then add 32 to that result, we get the corresponding temperature in degrees
Fahrenheit, we’ll call it 𝑇 sub F.

So, what we want to do is solve
for 𝑇 sub F, given an input temperature of negative 40 degrees Celsius. To do that, we’ll use this
conversion relationship, and we’ll insert negative 40 for our temperature in
degrees Celsius. Multiplying negative 40 by
nine-fifths, we get negative 360 divided by five. And that fraction is equal to
negative 72. When we add positive 32 to
negative 72, we get a result of negative 40. And it’s now that we put the
correct units onto this result. That’s degrees Fahrenheit.

Now, at first this may seem
strange. We started out with negative 40
in degrees Celsius, and we found that, apparently, that’s negative 40 in degrees
Fahrenheit. In fact, there is nothing wrong
with what we’ve done. Rather, what we’ve discovered
is the one single temperature at which that temperature value in degrees Celsius
is equal to the same temperature value in degrees Fahrenheit. There is no other temperature
for which this is true, but it is true for negative 40. So, negative 40 degrees Celsius
is negative 40 degrees Fahrenheit.