(narrator)

Now dimensional analysis

is also really handy when we have a problem

like this one that’s gonna involve

unit conversion. So a bicycle is traveling

15 miles per hour. How many feet will it cover

in 20 seconds? So the problem here,

of course, is that, uh…this measurement

is in hours, while this measurement

is in seconds. This measurement

is in miles, while this measurement

is in feet. And so we’re gonna need

to do some conversion. Uh…so let’s start

with our quantity–20 seconds. So to convert this

into some other units, um…I’m gonna multiply

by an equivalence. And in this case,

I wanna get rid of seconds, uh…and introduce

something else to replace it. And the immediate conversion

that comes to mind is I know that 1 minute

is 60 seconds. Uh…and minutes

are better than seconds, but I really want hours. So I’m gonna do

the same thing again. I’m gonna

eliminate minutes. Notice that this is

in the numerator. This is in the denominator,

so they will cancel…or reduce. Uh…and,

uh…let’s see, I know that 1 hour

is 60 minutes. Uh…and so now,

the seconds are gonna reduce. The minutes

are gonna reduce. Let’s see,

multiplying, I’m gonna end up

with 20 over 3600 is 1 over 180…

1 over 180. And this is now

in*hours*as the units. So the time we’re talking about

is 1 over 180 hours. So I’ve got 1 over 180–

and again that’s hours. And…but I’m really interested

in distance. And so I’ve got to multiply this

by another equivalence, and the equivalence

I’m gonna use is this one– in this case,

coming from the speed that the bike

is traveling. So I want to eliminate hours,

introduce miles, uh…and this tells me that

the bicycle is traveling 50 miles in one hour… Hours are gonna get

reduced. We’re gonna be left

with miles. We’re gonna be left

with 15 over 180, uh…is…one-twelfth

of a mile. So in those 20 seconds, the bicycle travels

one-twelfth of a mile. And now all we need to do

is convert into feet. So to do that, we’re going to eliminate miles,

introduce feet. Uh…and looking on my…

looking it up, um… it looks like 1 mile

is 5,280 feet. And so…we end up

with 5,280, uh…feet divided by 12 is…

let’s see, is…440 feet. So in those 20 seconds, the bicycle

will travel 440 feet. Uh…and now this conversion

works just fine. Um…and notice

that we sort of did it in three different steps here. We converted the time. Then we converted it

to a distance, and then we converted

the distance into feet. Um…if we

were really wanting to do this sort of…

as quickly as possible, we actually could’ve done

this a little bit differently by, uh…just stringing

all these conversions… into one. So notice that this conversion

now is here. This conversion

now is here. And if we multiply all

of our numerators and all of our denominators

and divide them, we would end up

with exactly the same 440 feet that we came up with doing it

in three different steps.

In a testing environment, how would you work out the miles to feet conversion without looking it up?