Hello my name is Doctor
Kevin Conley and I'm a faculty member at Forsyth Tech and I would like to cover
some fundamentals of mathematics with you in today's lecture we're going to be taking a look at
unit conversions
we'll take a look at an advanced application
where we will be doing a translation from mile-per-hour
to meter-per-second basically if you can do this
you can do anything that you'll be seeing in chemistry or in physics
I like this example because it's a translation between something
mile-per-hour that you see on signs all over the place and meter-per-second
which is a very common way of expressing speeds and velocities
in the SI or metric system let's say for example
you're driving down the road and you're doing fifty-five miles an hour
let's say we want to translate that into meter per second
so the problem then is we have 55
mile-per-hour and we want to take this to
meter-per-second there are a number of steps we have to go through
we have to do a number of different unit conversions
we have to deal with the distance and we also have to deal with the time
and this takes a number of steps but if we slow down
and do each step individually using the same procedure
we can do this first of all we're going to have to convert
miles to kilometers
miles to kms
then we convert kms to meters
we also need to convert hours to seconds
hours of course relate to minutes
and in turn minutes relate to
seconds so first of all
let's take a look at these conversions you can either look up these conversions
or be familiar with them 1 mile is equivalent to 1.61
kms 1 km
by definition as k is a thousand is equal to 1000 meters
1 hour
is equal to 60 minutes and 1 minute
will equal 60 seconds so
if we take a look at our problem again we will have
55 mile-
per-hour and this shows why the expression of mph isn't really useful
because it cannot be used in the mathematical context if you write units
out as fraction such as this
you can actually manipulate them 55 mile-per-hour
can then be operated on we want to leave
miles and go to meters so let's begin by doing that we need to have miles down
stairs
in a conversion factor so let's divide both sides by the side that actually has
miles 1 mile goes home
and we have
1 on the left as we saw before and
this conversion factor on right so
we have 1.61 kms
and this goes over one mile once we've left miles for kms
what we're gonna need to do is leave kms for meters
so now we put this down and we have one km downstairs
and 1000 meters upstairs so now
we've successfully gone from miles to meters
miles miles kms kms to arrive at meters upstairs
which is our unit destination for the numerator now for the denominator we
have hours
and things are going to be a little bit different here commonly when people go
through unit conversions they say
well I just have to multiply by 60 or I just have to divide by 60
sometimes that works but if one carefully goes through these conversions
it takes out the guesswork clearly if we have hours downstairs
think do we want hours to be downstairs or do we want
hours to be upstairs in our unit conversion we want hours to be upstairs
that then means we need to divide by the side
that doesn't have hours in it we need to divide by the side
that has minutes in it because we ultimately want the minutes
downstairs
minutes go home and 60 goes home and there's our unit conversion in this
case
the unit conversion will be 1 hour
all over 60
minutes for the next conversion
I'm obviously going to need a little bit more room so I will rewrite this
over here and I will have
1 minute set equal to 60 seconds
and as we saw before if the hours are cancelled out
I have minutes downstairs if I have minutes and I want to go to seconds
then think to yourself do I want minutes upstairs in my conversion factor
or do I want minutes downstairs in my conversion factor to do the canceling
minutes must remain upstairs so I must divide both sides by the side
that has seconds
the 60s cancel the seconds cancel
and I'm left with this conversion factor I have 1 minute over 60 seconds
and then my unit conversion by units
should be complete hours cancel with hours minutes cancel with minutes
I'm now left with seconds minutes over seconds that is the destination unit that I have
now to complete the calculation what I simply do is
I multiply straight across and then divide
I divide by each individual element
downstairs I can do this in a calculator as follows:
55 times 1.61
times 1000 all over
60 times 60 and my result then will be in meter
over second so
once your calculator is used to get a final result
you'll see that the answer is 24.6
meter per second
so a good estimate then going back and forth between mile-per-hour
and meter-per-second it's basically divide by two but with a calculation
such as this
one can methodically go through any number of calculations
and you'll see this not only in mathematics but also in chemistry
and physics thank you for your attention