Now we're going to talk about the prefix of the metric system, the symbols that correspond to it, and the multiplier. So first, we're going to start with deca. The symbol for deca is da. The multiplier is 10 to the 1, or just 10. Hecto has a symbol, lowercase h. The multiplier is 10 squared, or 100. Kilo Kilo is lowercase k and it's 10 to the third or a thousand so what this means is that one kilogram is 1000 grams or 1 times 10 to the third grams Next up we have Mega.
Now, it's not going to be a lowercase, but this is a capital case, capital M. And this is 10 to the 6th. Mega is basically a million. So a megawatt.
A megawatt. power plant produces 1 times 10 to the 6 watts or a million watts. Next up we have Giga represented by the symbol capital G. Giga is 10 to the 9 which is equivalent to a billion. So a gigajoule is 1 times 10 to the 9 joules.
So what I have here are called conversion factors. Notice how I'm writing all of my conversion factors. This is going to be important when we're solving problems. So what you always want to do is you always want to attach a 1 to the prefix.
And then the multiplier goes with the base unit, whether it's joules for energy, watts for power, grams for mass. So you always attach the multiplier to the base unit. And it makes it easy to write the conversion factors. Once you have the conversion factors down, then it's going to be easy to convert from one unit to another. After giga, what we have next...
is Tera capital T. Tera is 10 to the 12th which is equivalent to a trillion so one terawatt is 1 times 10 to the 12 watts. After Tera the next one in the list is Peta In most cases, if you're studying for an exam, typically you need to know up to Terra.
So going past 10 to 12, you usually don't need to know these unless your professor gives you these notes. But usually up to 12 is the limit. But there are some other ones beyond 12, and I'm going to give it to you. Beta is 10 to 15. So remember Mega is a million, Giga is a billion, Tera is a trillion, Peta represents a quadrillion.
Exa, capital E, that's 10 to the 18, which is a quintillion. After Exa, you have Zeta. And that's not a lowercase z, but this is a capital Z, but I am running out of space.
Zeta is 10 to the 21st, or 10 to the 21. And that is a sextillion. After that, we have Yoda. Represented by the symbol capital Y.
And that's 10 to the 24th, which is a septillion. So if you know up to 10 to the 12th, You should be okay for your exam. Now let's go over the multipliers that have a negative exponent. This is the other half. So let's start with the prefix deci, represented by the symbol lowercase d.
Deci is 10 to the minus 1. Next we have centi, lowercase c, that's 10 to the negative 2. And then milli, lowercase m, is 10 to the minus 3. The only time you have a capital symbol is mega and above, like mega, giga, tera, and anything above that. Everything else, the symbol is 10 to the minus 1. The symbols are lowercase. So think about what this means.
Think about how we can write a conversion factor with this information. 1 centimeter, always put a prefix in front of, put a 1 in front of the prefix. 1 centimeter is 1 times 10 to the minus 2 meters. So always attach the multiplier to the base unit.
1 milliliter. 1 times 10 to the minus 3 liters. Now once you write this conversion factor, what you can do is you can alter it. If we multiply both sides by 100, we get that 100 centimeters is equal to 1 meter. 10 to the negative 2 times 100 is simply 1. If we multiply this by 1,000, we get this common conversion factor.
1,000 milliliters is equal to 1 liter. So if you can write the standard conversion factors, you can get the common ones as well, simply by adjusting the equation. Now after milli, the next one is micro. Micro is 10 to the minus 6. So 1 micrometer is 1 times 10 to the negative 6 meters. After micro.
we have a nano lowercase n nano is 10 to the minus 9. So think of 10 to the 9 which was giga that represents 1 billion. Nano 10 to the negative 9 is a billionth. Mega 10 to the 6 was a million. Micro 10 to the minus 6 is a millionth with a th at the end. So 1 nanometer is 1 times 10 to the negative 9 meters.
After nano, it's pico, lowercase p, 10 to the negative 12. 1 picometer is 1 times 10 to the negative 12. meters now there's some other ones below this so I'm going to run through the list quickly next we have femto the lowercase F that's 10 to negative 15 after femto is at oh with the symbol lowercase a, and this is 10 to negative 18. After ato, it's zepto, lowercase z, 10 to negative 21. And after zepto, it is yakto, lowercase y, 10 to negative 24. But for the smaller units, typically you need to know up to pico. So you need to know from pico, 10 to negative 12, to tera, 10 to the positive 12. Those are the common prefixes that... going to encounter in class.
The other ones, they're optional. Typically, they're not commonly used. Now let's talk about how we can convert from one unit to another. So for instance, let's say if we have 478 meters and we wish to convert it to kilometers. How can we do that?
Well, this is a one-step conversion problem. So we just need to know the conversion factor between kilometers and meters. We know that kilo represents 10 to the third, or 1,000. So we can write the conversion factor. One kilometer, always put a one in front of the prefix, 1 kilometer is 1 times 10 to the 3rd meters.
So step 1, write a 1. Write the prefix with the base unit. Write the multiplier. And then the base unit without the prefix.
And that's how you can write your conversion factor. Now to convert it, start with what you're given. We're given 478 meters. We'll put it over 1. In the next fraction, we're going to put our conversion factor.
Notice that we have the unit meters on top. So, to cancel meters, we need to put this part of the equation in the bottom. This is going to be 1 times 10 to the 3 meters, and then the other part is going to go on top. So we need to set the fractions in such a way that the unit we want to convert from disappears and the unit that we want to get to remains. So this becomes 478 divided by 1000, and that gives us the answer 0.478 kilometers.
So that's how you can do a one-step. conversion problem. Let's try another one. Let's say we have 400, actually, let's say 0.236 liters, and we want to convert that to milliliters.
Feel free to pause the video and try that example. So first, let's write the conversion factor. 1 mL is equal to, remember mL is 10 to the minus 3, so it's going to be 1, and then we're going to put the multiplier, 10 to the negative 3, and then the base unit liters.
So that's our conversion factor. Now let's start with what we're given. We're given 0.236 liters. We'll put that over 1. Now we got to find out what goes on the top and the bottom of the next fraction. Since we have liters on top of the first fraction, we want liters to be on the bottom of the second, which means milliliters have to go on top.
So this number attached to liters has to go on the bottom. So we'll put 1 times 10 to the minus 3 liters on the bottom, and then this will, by default, go on top. So this tells us that we need to divide by 1,000 to convert liters into milliliters. Actually, not by 1,000. We need to divide by 10 to the minus 3, which is 0.001.
That has the equivalent effect of multiplying by 1,000. So it's 0.236. You can divide it by 0.01.
Or if you multiply it by 1,000, you're going to get 236 milliliters. By the way, when dividing this, put this in parentheses, because your calculator may divide by 1 and then multiply it by 10 to negative 3. Now let's try a two-step conversion problem. Let's say we have...
496 micrometers. We want to convert that to... actually let's say this is in picometers.
496 picometers. And we want to convert that to micrometers. Try that problem. Now, even though there are shortcut methods available that you can use, what I'm going to do is I'm going to do this one step at a time.
I'm going to convert picometers into the base unit meters, and then meters to micrometers. So let's write the conversion factor from pico to meters. Pico is 10 to the minus 12, so one picometer is 1 times 10 to the negative 12 meters.
We'll use that in the first step. For the second step, we'll convert meters to micrometers. One micrometer, we know it's, micro is 10 to the minus 6, so it's 1 times 10 to the negative 6, and then the base unit meters.
So let's start with what we're given, 496 picometers over 1. Let's use the first conversion factor to go from picometers to meters. So because we have the unit picometers on the top left, we're going to put it on the bottom right of the second fraction. Meters is going to go on top.
So we have 1 picometer is equal to 10 to negative 12 meters. So now the unit picometers will cancel. And now let's use the second conversion factor to go from meters to micrometers. Since we have meters here, we're going to put meters on the bottom, micrometers on top.
So it's 1 micrometer, and the number that's attached to meters is 10 to negative 6. So now we can cross out the unit meters. So when we do the math, we're going to get the answer. So you can plug this in your calculator, or you can do it mentally.
Let's talk about how we can do this mentally. So we have 496. We can ignore the 1. What's important here is the 10 to negative 12. Now notice that we have a 10 to negative 6 on the bottom. What we can do is take this and move it to the top. If you have, let's say...
x to the negative 3, this is 1 over x cubed. If you move it from the top to the bottom, the exponent changes sign. It goes from negative 3 to positive 3. Likewise, if you have a negative exponent on the bottom, and you decide to move it to the top, it'll go from negative to positive.
So if you flip it, or if you move it from one side to the other side of the fraction, it's going to change sign. So it's 10 to negative 6 on the bottom, but when we move it to the top, it's going to be 10 to the positive 6. Now when multiplying common bases, we can add the exponents. Negative 12 plus 6, that's going to be negative 6. So we have 496 times 10 to negative 6, and the unit is the unit that's left over, micrometers. Now we need to move the decimal two units to the left.
496 is the same as 4.96 times 10 to the second power. 10 squared is 100, so 4.96 times 100 is 496. And then we still have 10 to negative 6 as well. So adding these two will give us negative 4. The final answer is going to be 4.96 times 10 to the negative 4 micrometers.
So that's how you can do a problem like that without the use of a calculator. We typically leave our answer in scientific notation. So you want the decimal point to be between the first two non-zero numbers.
Now let's try another example. Let's say We have 3.54 times 10 to the negative... Actually, let's say positive. 10 to the positive 7 nanometers.
And let's convert that to... kilometers. Go ahead and try that problem.
By the way, for those of you who want harder problems to work on, go to the YouTube search bar, type in unit conversion organic chemistry tutor and a video that I've created, it's a very long video, will show up and you'll get more harder problems that involve unit conversion. Now for this problem, what I'm going to do is I'm going to convert nanometers to meters, and then meters to kilometers. So because it's a two-step problem, I need two conversion factors.
The first one, 1 nanometer, is 1 times 10 to the negative 9 meters. The second one, 1 kilometer, kilometer is 10 to the 3, so it's 1 times 10 to the 3 meters. So those are our two conversion factors that we're going to use.
Now, let's start with what we're given, 3.54 times 10 to the 7 nanometers. Now, I want nanometers on the bottom. and meters on top, so that these will cancel. And then I want meters on the bottom, and my final unit kilometers on top, so that these will cancel.
So now I've just got to fill it in. So we have a 1 in front of the nanometer, we'll put that here, and then it's 10 to negative 9 meters. So this will go here. For the second one, we have a 1 in front of kilometers, and 10 to the 3 in front of meters.
So now let's do the math. It's 3.54 times 10 to the 7, and then we have 10 to negative 9. And we're going to move this to the top. That's going to be 10 to the minus 3. So now let's add.
7 plus negative 9 is negative 2. Negative 2 plus negative 3 is negative 5. So the final answer is going to be 3.54 times 10 to the negative 5 kilometers. So that's how you can do a two-step conversion problem when dealing with units in the metric system. Thanks for watching.