How to convert between units | Unit conversion | Dimensional analysis – Dr K

In this, we’ll go through how to
convert between units. When you try to convert between units, do you struggle to decide between whether to multiply or to divide the values? I will share with you
a foolproof method in converting between units. It will be your go-to method
whenever you need to convert between units like kg to pounds, atm to Torr,
moles to grams for stoichiometric calculation, cm cubed to liter for volume
and lots more. The foolproof method we will use is
called dimensional analysis. You may heard of it go by a different name like
unit factor method or factor label method or maybe unit conversion. So what is dimensional analysis? It’s a method that is used to convert one unit to
another using conversion factors. Well, the best way to explain is through
examples, so let’s start with our first example. Here we have Maria, she weighs
115 pounds and the question wants us to find her weight in kg so that means the
question is asking us to convert from pounds to kilograms. Pounds is
abbreviated as lb. It’s a US system of measurement. Kilogram on the other hand is a metric system. We can convert between these two systems of measurement
as long as we know what is the relationship between them. So in this
case if you look it up online or in your book, the relationship is 1 kilogram is
equals to 2.2 pounds. To perform the conversion, let’s start with what we are
given which is 115 pounds. Then we multiply and draw a line across. Now what we’re gonna do is we’re gonna use basic algebra to do the conversion so since we
are converting from pounds to kg, that means we want to get rid of pounds, so
we’ll place pounds which is lb on the bottom and then we’ll place kg on the
top, that way we can cancel out pounds like this and that will leave us with kg.
Then next what we’ll do is we’ll place in the numbers so we will place in 1 in
front of kg and 2.2 in front of pounds. Now let’s do the math, so we have 115 multiply by 1 divided by 2. 2. That whole thing will
give us 52.3 kilogram. Don’t forget to include the unit in your
final answer. Let’s look through how we did that conversion. We started out by
writing out the given value along with its given unit which is pounds and then
we placed the given unit at the bottom so that we can cancel them off. Then we
placed the desired unit on the top. As for the values, we inserted the numbers we
got from the relationship between the two units in fact this thing one
kilogram over 2.2 pounds that is called a conversion factor. Let’s try
using the same method on a second example. The question is asking us to
convert from psi to kPa. Both are units for pressure and if we look it up we’ll
find that one psi is equals to 6.895 kilo Pascal. So let’s start by writing out what we need to find which is pressure and the value
that is given which is 33.5. The unit is psi. Then we
multiply and draw a line across, we placed psi at the bottom because that’s the
unit we need to get rid of. Now the psi will cancel off each other. Then we placed
the unit that we want which is kPa on the top and then finally we place in the
numbers from the conversion factor which is 1 in front of psi and 6.895 in front of kPa. After that we’ll just do the math, so we have 33.5 times 6.895 divided by one. That will give us 231 kPa. So you might be wondering, for the conversion factor must
the bottom value always be one? The answer is no. As long as you set
it up in a way where the unit’s cancel off, you can plug in any value for the
conversion factor. Here’s what I mean, so sometimes when you look up the
relationship between psi and kPa you get something like 1 psi is equal to 6.895 kPa, right? Well, sometimes if you look it out you may
also get a different values like 0.145 psi is equals to 1 kPa. In fact, actually these two conversion factors are the same numerically, but you shouldn’t take my word for it, so let’s
solve it together. So we need to find the pressure. Start off with 33.5 psi that’s what we are given, multiply and draw a line across. Put psi
at the bottom so it cancels off, kPa on the top and then we place in the value.
So now instead of placing 1 for psi and 6.895 for kPa, we’re gonna place in 1 for kPa and 0.145 for psi and that will give us the same answer, see? So it doesn’t matter what the conversion
factor is as long as when you set up your solution, your units cancel off. To
recap, when converting between units always start with a value that is given
followed by the unit and then we multiply and draw a line across at the
bottom of the line place the unit that is given so they cancel off. At the top
of the line, place the desired unit that will give us the final unit which is
what we want. Then we insert in the numbers from the conversion factor. Then you do the math and you’ll get the calculated value. You’ll always get the
conversion right using this method. We went through two examples together. Why don’t you try out one on your own? I’ll place the answer in the description box.
Thanks for watching. I’ll see you in the next video.

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