In this section, we want to continue our conversions.
But this time, we're going to convert between units in the U.S. system and units in the metric system,
and between units in the metric system and units in the U.S. system.
The more common conversions between the two systems, I've written over here. For length, we have 1 inch is the same as 2.54 centimeters.
For volume, we have 1 gallon is the same as 3.79 liters. And then, also, for weight, 1 ounce is the same as 28.3 grams.
So, here's just three conversions between the U.S. and the metric system. Now, we're also going to do a little bit with temperature,
and you've seen this formula before: F = (9/5)C + 32. We've used that formula before when we did the section on formulas.
But let's go to the board now and see if we can't take these basic conversion factors and do some converting between the two systems.
Here's our first example: We want to convert 4 meters into feet. So, I'm going to start with meters, and I want to end up with up with feet.
And let's see, as far as my conversions go, this is what I know: 1 inch, that's a 1, by the way, 1 inch is equal to 2.54 centimeters.
So, I need to go between, I know how to go between inches and centimeters; and I'm going to start with meters.
So, I'm going to start with 4 meters. And then, I want to multiply by something that's going to allow meters to divide out,
and maybe give me centimeters. That way, I can go from meters to centimeters; then, I'll go from centimeters to inches;
then, I'll go from inches to feet. So, let's see: there's 100 centimeters in every 1 meter. So, that will take care of my meters.
Now, let's convert between the two systems. I'll get centimeters to divide out, and I'll be left with inches, if I have 1 and 2.54.
Now, the centimeters have divided out. I keep an eye on what I'm trying to go towards, which is feet.
So, I'm going to multiply by something that will allow inches to divide out and leave me with feet, and that will be 12 inches in 1 foot.
So, those will divide out. So, I end up, then, with 4(100)(1)(1) ÷ (1)(2.54)(12)
2.54(12); and everything has divided out except for feet. Now, if I do this arithmetic right here,
4(100) ÷ 2.54(12), let's see, I've already done that to the nearest hundredth, that comes out 13.12 feet.
So, you see, if I have just this one conversion factor that goes between inches and centimeters, that will allow me to convert any units of length
even if I don't start with centimeters; in this case, for instance, I started with meters; I can go from meters to centimeters;
then, go between the two systems from centimeters into inches; I end up with inches;
and from inches, I can go to any unit of length in the U.S. system. In this case, I went to feet by multiplying by this conversion factor.
So, here's the one that goes between the two systems. And then, I had to put another couple of them in
that I know from the previous work in this chapter to get me to go from meters all the way to feet. Let's look at another problem:
this time, I want to go from 2 liters to quarts. So, I want to convert 2 liters into quarts. And this is the conversion factor I have:
1 gallon is equal to 3.79 liters; so, 1 gallon is 3.79 liters. I want to go from liters to quarts. So, I'm going to start here with 2 liters;
I'm going to multiply by a conversion factor that will allow liters to divide out, and I'll go directly to gallons.
So, I'll get my conversion between the two systems right away: 1 and 379, in order that this is the number 1. My liters divide out;
I'm left with gallons. I keep an eye on what I'm going towards, which is quarts.
So, I want to multiply by a conversion factor that will allow gallons to divide out and leave me with quarts.
Well, I know that there's 4 quarts in every 1 gallon. So, those divide out. And now, I'm left with 2(1)(4) = 8 ÷ 3.79;
and my units are quarts. Now, I've done that arithmetic, and let's see, that comes out to be 2.11 to the nearest one hundredth,
I'll round to the nearest one-hundredth quart. So, when I do that arithmetic on a calculator, 8 ÷ 3.79 comes out 2.11 quarts.
So, in this case, I start with liters; I want to end up with quarts. Here's the conversion factor I have that goes between the two systems,
between gallons and liters: gallons in the U.S. system; liters in the metric system. I start with liters, and I go right to gallons.
Then, once I've got gallons, I want to go to quarts; I multiply by this conversion factor. I end up with 2.11 for the number of quarts in 2 liters.
Let's look at our next problem. We have 1 pound, and we want to convert that to grams. So, I want to convert pounds to grams;
and this is what I know: 1 ounce is equal to 28.3 grams. So, I'm going to start with pounds
and end up with grams. So, I start with 1 pound,
and then, I want to multiply by a conversion factor that's going to allow pounds to divide out. Let's see, if I go from pounds to ounces,
then I can go from ounces to grams with this relationship, right here. So, let's go from pounds to ounces.
And what I know is that there's 16 ounces in every 1 pound. So, now my pounds have divided out, and I'm left with ounces.
From ounces, I want to go to grams. So, I'm going to multiply so that ounces divide out. I'll put it in the denominator here
because it's in the numerator here, and I want to be left with grams. So, 28.3 grams and 1 ounce, so that this is the number 1.
This tells me there's 28.3 grams in every 1 ounce. My ounces divide out, and I'm left with 16(28.3) grams.
And now, that comes out to be 452.8 grams, when I round to the nearest tenth; so, to the nearest tenth, that's 452.8 grams.
So, I start with pounds; I go from pounds to ounces; and then, from ounces to grams.
Now, let's take a look at our next problem that involves temperature. We want to convert 20 degrees Celsius into degrees Fahrenheit.
Now, I write the formula up here, again, degrees Fahrenheit are always equal to 9/5C + 32.
So, I'm simply going to take this 20 and substitute it in here. So, this F = 9/5(20) + 32. So, I divide 5 into 20; it goes 4 times;
4(9) = 36, + 32; and 36 + 32 comes out to be 68. And now, I'll put my units in degrees F.
So, 20 degrees on the Celsius scale is exactly the same as 68 degrees on the Fahrenheit scale. And I simply used this formula.
So, it's a little different kind of problem; I'm not actually using my conversion factors. I'm really going back to just a formula
that I substitute one value in, into, and then, I get out the second value.
In any case, there's a look at converting between the U.S. system and the metric system and a brief look at temperature.