Dimensional Analysis: Metric Conversions
0 Comments


Welcome to Dimensional Analysis: The Metric
System. Our objective for this video is to learn how
to maneuver through a metric conversion chart so that we can easily convert between metric
units. In order to do this you first need to know
what is Dimensional Analysis, know what a Conversion Factor is, and know the Rule for
Selecting a Conversion Factor. If you don’t know these last three things,
you MAY be a little lost in this video. If that’s the case, go watch my other video
“Dimension Analysis: The Nuts and Bolts of Creating Ratios Between Units.” It goes into more depth with lots of examples. Otherwise, let’s get started! So, all metric conversion charts will supply
you with the same information. There will be a column with a written prefix,
a column with an abbreviation of that prefix, and a multiplier for that prefix given as
an exponent as well as a number. The prefix can be added to some base unit
such as grams or liters, and that prefix will give us a clue about how much of something
we’re given. For example, you may be measuring distance
which would be in the bases unit of meters. And let’s say you were measuring a part
of your yard to put in a garden. This typically won’t be a big area, so it
may only be 2 meters by 3 meters. On the other hand, let’s say you were planning
a trip to Texas, well now the distance would likely be measured not in meters but in kilometers. A mile is equal to about one and a half kilometers,
and from where we are in New England, it’s about 2600 miles to Texas or 4200 kilometers. If we were to give that measurement in meters,
we would have to say 4 million 200 thousand meters. By assigning the prefix of kilo to our base
units, we can now express larger units of measure more easily. And that’s great and all, but . . .
How do we know how to move through these prefixes and multipliers to create conversion factors
for our problems? Well, let’s start by selecting a couple
of pieces of information. Let’s take kilo and milli and move them
to a scaled down version of this chart. So here we have a simple, scaled down version
of our metric chart with our prefix, symbol and two multipliers. I’ve put in a black row between kilo and
milli, and in this row I’m going to add a base unit. The base unit is the starting point, it’s
the unit that the prefixes get added to express a different amounts. Gram has the symbol of g, and its multiplier
is one. Our kilo is now kilogram, and our milli is
now milligram. So, where gram expresses mass in units of
10s or 100s, kilograms expresses mass in units of 1000s, so that 2 kilograms would be 2000
grams. Or conversely, milligrams would be used to
express mass in 1 1000th of a gram. Let’s look at an example of how we would
use this chart to make those types of conversions. Let’s convert between gram and kilogram. What’s the relationship between these two? You may know that 1000 g equals a kilogram,
but how did you come up with that? That’s the big question here, right? So in our problem we are given 1 kilogram
and we need to give an answer in grams. Clearly we need a conversion factor, right? Of course. The units we’re given are kilograms and
we want our answer in grams. What’s the relationship between these two
units? Well, if we look at our chart, we see we have
grams and kilograms right here – I will be using the symbols in the problem so I’ve
highlighted them. And, if we move to the multipliers, we have
these two multipliers. In this example I’m using the numbers. In another example I will use the exponents. But for now we’ll be dealing with these
numbers. Now, let’s set up our equation, then I’ll
explain how we’ll use the information we’ve identified in the chart. So, let’s take our given which is 1 kilogram
and make it a fraction. Next, let’s place our symbols so that the
units we seek are on top. In this case, we want grams, so our symbol
for gram will go in the numerator, and the symbol for kilogram will go in the denominator. So far so good. But what values go in this conversion factor? The values from the multiplier section of
our chart. And this is how we figure out how to place
those values. We go to the multiplier for kilogram which
is 1000 and plug that in to our gram, so that in our numerator we have 1000 grams. And next we go to the multiplier for gram
which is 1 and plug that in to our kilogram so that we have 1 kilogram in our denominator. And with that slight of hand you’ve created
your conversion factor!. Let’s finish working this problem. We can cross out kilograms. Now we do the math – 1 times 1000 grams
over 1 times 1 is 1000 grams over 1. Our answer gets reduced further , and we have
1000 grams as our final answer. Is this true, does 1000 grams equal one kilogram? Yes. So we know
this system of using the chart works. Let’s work another problem using gram and
milligram. Our problem says convert 1 gram to milligrams. So looking at our units, we are given grams,
and what we seek are milligrams. Let’s go to the chart and identify our players
which are grams and milligrams and their multipliers 1 and 0.001. Our first step to solving our problem is to
set up the equation, so we take our given and make it a fraction. Second we begin creating our conversion factor
keeping in mind that what we seek goes on top. In this case we seek milligrams, and we are
given grams, so the start of our conversion will be milligrams over grams. Now let’s go to our chart. To get the values for our conversion factor
we look to the multipliers. For milligrams in our conversion factor, we
look to the multiplier for gram which is 1, and plug that in to the conversion factor. And for grams in the conversion factor, we
look to the multiplier for milligram which is 0.001, and plus that in to the conversion
factor. Now that we have our conversion factor, our
third set in solving our problem is to cross out units that appear in both the numerator
and denominator. This would be grams. Nothing else will cancel. So we move on to the fourth step which is
to do the math. In our numerator we have 1 times 1 milligram
and in the denominator we have 1 times 0.001. We can further reduce this fraction by dividing
the top by the bottom, that is, dividing the numerator by the denominator, and our final
answer is 1000 milligrams. And 1 gram does equal 1000 milligrams. Let’s work another problem, one where the
units aren’t right next door to each other in our chart. Let’s make a conversion between kilograms
and milligrams. Let’s convert 1 kilogram to milligrams. So, looking just at our units, we are given
kilograms and what we seek are milligrams. Now let’s go to the chart and identify our
players. We have the symbols, and we have the multipliers. Ok, everything is identified, let’s set
up our equation. We take our given which is one kilogram and
make it a fraction. Second we begin creating our conversion factor
keeping in mind the units we seek are milligrams which means our conversion factor units will
be milligrams over kilograms. Now we go to the chart for our values. The value for milligrams is going to come
from the multiplier for kilograms which is 1000, and the value for kilograms is going
to come from the multiplier for milligrams which is 0.001. When we apply the multiplier to the opposite
units, we are creating a relationship between the units. There is in fact a longer way to do this,
but this method is much faster and will save you a lot of steps and a lot of potential
headaches. OK, now we’ve created our conversion factor,
now we move to the third step in problem solving and that is to cross out the units that appear
in both the numerator and denominator, and for this problem that would be kilograms. And with that, nothing else will cancel, so
we move on to our fourth step in problem solving which is to do that math. Looking at the numerator we have 1 times 1000
milligram, and in the denominator we have 1 times 0.001, which gives us 1000 milligrams
over 0.001. We can further reduce this by dividing the
numerator by the denominator, and our final answer is 1 million milligrams. Now, in all of the previous examples I’ve
used the multiplier expressed as a number. Let’s work this same problem using the multiplier
expressed as an exponent. Let’s set up our problem, taking our given
and writing it an a fraction. Now we set up our conversion factor keeping
in mind that the units we seek are milligrams, so milligrams would go in the numerator and
kilograms would go in the denominator. And just like we did for the other conversion
factors, we are going to the chart to find our values. So, for milligrams we go to the multiplier
for kilogram which is 10 to the third and plug this in to our conversion factor in the
numerator, and next for kilograms we do the multiplier for milligram which is 10 to the
negative third and plus this in to our conversion factor in the denominator. And voila, we have our conversion factor compliments
of the chart. Our next step in problem solving is to cross
out repeating terms which would be the kilogram units. Nothing else cancels. So now we are ready for our final step in
problem solving which is to do the math. When working with exponents, as long as the
base units are the same, the only numbers that undergo manipulation are the powers. In our problem, both of our exponents have
the base unit of ten. Our powers are 3 and negative three. So what are we going to do with those? You may remember from your algebraic career,
that when dividing exponents with the same base, you simply subtract the power in the
denominator from the power in the numerator. How easy is that! And from basic math rules, subtracting a negative
is the same thing as adding a positive. So what may have looked like to you was going
to be a more complicated method is actually pretty simple and doesn’t even require that
you have a calculator! Alright so, ten to the power of three plus
three milligrams can be tidied up by adding the threes, which will give us 10 to the six
milligrams. And that is equal to one million milligrams
which is the same answer when we worked the problem using the other multiplier. Let’s bring back our metric conversion chart
and work a problem. Here we are being asked how many liters is
in 2200 milliliters. Looking at JUST the units, we are given milliliters,
and we are seeking an answer in liters. Now let’s go to our chart and identify our
players. We have only one, milli. Liters is NOT listed because it is a base
unit, it’s the starting point, remember? And the multiplier for it will be one. Alright, now that we have that out of the
way, let’s begin setting up our equation. First we start with our given, which is 2200
milliliters, and we are writing that as a fraction so we put it over one. Second we must craft our conversion factor
keeping in mind the rule that states that the units we seek go on top, so let’s start
by writing the conversion factor with just the units. The units we seek are liters, so we write
liters on the top of the line which puts it in the numerator, and the units we’re given,
which are the units we will eliminate in this process, will go in the denominator. Now we have to plug in values for our conversion
factor. To find the value to plug into our numerator
we would go to the multiplier for milliliters, which is 0.001, so we plug that in next to
our liter unit. Now we would go to the multiplier for liter
to get the value we’ll use in the denominator, and because liter is the base unit, we know
that the multiplier is one, so we can plug in ONE right next to our milliliter units,
and with that we have created our conversion factor. The third step in problem solving is to cross
out repeating terms which would be the milliliter units. Nothing else cancels. So now we are ready for our final step in
problem solving which is to do the math. Multiplying the numerators we have 2200 times
0.001 liters which is 2.200 liters, and one times one in the denominator which is one,
and bringing everything to the right of the equals sign we have 2.200 liters over one. This can be reduced giving us the final answer
of 2.200 liters. Let’s work another example. Here we are being asked how many giga hertz
are in 1.3 peta hertz? So what do we look at first? The units. The units we are given peta hertz, and the
units we are seeking for our answer are giga hertz. So, not let’s go to the chart and identify
our players. Here at the top we have peta and giga, and
their multipliers. Well, we have a lot of zeroes so I’m going
to use the exponents instead of the numbers to work this problem. I think that will be easier. The first step in problem solving is to do
what? Yes, write our given as a fraction, so we
have 1.3 peta hertz over one. Second we must create our conversion factor. keeping in mind that the units we seek are
giga hertz, so giga hertz would go in the numerator and peta hertz would go in the denominator. Now we go to the chart to find our values. So, for giga hertz we go to the multiplier
for peta hertz which is 10 to the fifteenth and
plug this in to our conversion factor in the numerator, and next for peta hertz we do the
multiplier for giga hertz which is 10 to the nineth and plus this in to our conversion
factor in the denominator. And with, we have YET AGAIN created our conversion
factor compliments of the chart. The third step in problem solving is to cross
out repeating terms which would be the peta hertz units. Nothing else cancels. So now we are ready for our final step in
problem solving which is to do the math. In our first term we simply eliminated the units,
and that leaves us with 1.3. Now, we can deal with the second term which
is ten to the fifteenth giga hertz over ten to the ninth. We can re-write that as ten to the fifteen
minus nine giga hertz, and the only math function we have to do is subtract nine from fifteen. How easy is THAT! Making our final answer 1.3 times ten to the
sixth giga hertz. So, how WOULD you use that metric chart to
create a conversion factor? Well, apply the multipliers to the units with
which you seek to form a relationship. You look at your problem noting the units
you’re given and in what units your answer needs to be given. These two pieces of information will lay the
path for how you will maneuver through the chart. Technically what we are doing when using the
chart is applying the multiplier of the units you seek to the units you want to eliminate,
and also applying the multiplier of the units you wish to eliminate to the units you seek. A bit of the old green and blue arrow switch
a roo. After you’ve done that, follow the rule
for selectin a conversion factor which is the units you seek are on top. This concludes our adventure in the world
of metric conversion charts. Thanks for watchin

Leave a Reply

Your email address will not be published. Required fields are marked *