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 d a 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 lower case k and it's 10 to the third or a thousand so what this means is that one kilogram is a thousand grams or one times ten to the third grams next up we have mega now it's not going to be a lower case but this is a capital case capital m and this is 10 to the sixth mega is basically a million so a megawatt a megawatt power plant produces one times 10 to the six watts or a million watts next up we have giga represented by the symbol capital g giga is 10 to 9 which is equivalent to a billion so a giga joule 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 gonna be easy to convert from one unit to another after giga what we have next is terra capital t terra is 10 to 12 which is equivalent to a trillion so one terawatt is 1 times 10 to the 12. watts after tara the next one in the list is peda in most cases if you're studying for an exam typically you need to know up to tara so going past 10 to 12 you usually don't need to know these unless your professor gives you you know these notes but usually up to 12 is you know the limit but there's some other ones beyond 12 and i'm going to give it to you beta is 10 to the 15. so remember mega is a million giga is a billion tera is a trillion beta represents a quadrillion exa capital e that's 10 to the 18 which is a quench quintillion after exa you have zeta and that's not a lower kc 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 12 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 one next we have centi lowercase c that's ten to negative two and then milli lowercase m is ten to the minus three the only time you have a capital symbol is mega and above like mega giga terra and anything above that everything else dissembles our lower case so think about what this means think about how we can write a conversion factor with this information one centimeter always put a prefix in front of put a one in front of the prefix one centimeter is one times ten to the minus two meters so always attach the multiplier to the base unit one milliliter is one times ten to the minus three liters now once you write this conversion factor what you can do is you can alter it if we multiply both sides by a hundred we get that a hundred centimeters is equal to one meter ten to negative two times a hundred is simply one if we multiply this by a thousand we get this common conversion factor a thousand milliliters is equal to one 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 melee the next one is micro micro is ten to the minus six so one micrometer is one times ten to negative six meters after micro we have a nano lower case n nano is 10 to the minus nine so think of ten to nine which was giga that represents one billion nano ten to negative nine is the billionth omega 10 to the six was a million micro ten to the minus six is a millionth with a th at the end so one nanometer is one times ten to the negative nine meters after nano its pico lower case p ten to negative twelve one picometer is one times ten to negative twelve 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 the negative 15. after femto is ato 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 is yakdo 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 tara 10 to the positive 12. and those are the common prefixes that you're 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 a thousand so we can write the conversion factor one kilometer always put a one in front in front of the prefix one kilometer is one times ten to the third meters so step one write a one 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 one 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 a thousand 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 one milliliter is equal to remember milli is 10 to the minus three so it's going to be one and then we're going to put the multiplier 10 to negative three and then the base unit liters so that's our conversion factor now let's start with what we're given we're given .236 liters we'll put that over one 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 a thousand to convert liters into milliliters actually not by a thousand we need to divide by ten to the minus three which is point zero zero one that has the equivalent effect of multiplying by a thousand so it's 0.236 you can divide it by .01 or if you multiply by a thousand you're going to get 236 milliliters by the way when dividing this put this in parentheses because your calculator may divide by one and then multiply by ten to negative three now let's try a two-step conversion problem let's say we have hmm 496 micrometers and 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 ten to the minus twelve so one picometer is one times ten to negative twelve 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 ten to the minus six so it's one times ten to negative six and then the base unit meters so let's start with what we're given 496 picometers over one 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 one 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 one micrometer and the number that's attached to meters is 10 to negative six 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 one what's important here is the 10 to negative 12. now notice that we have a tens of negative six 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 three this is one over x cubed if you move it from the bot from the top to the bottom the exponent changes sign it goes from negative three to positive three 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 side 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 6 i mean negative 12 plus 6 that's going to be negative 6. so we have 496 times ten to negative six 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 one nanometer is one times ten to the negative nine meters the second one one kilometer kilometer is ten to the three so it's one times ten to the three 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 just got to fill it in so we have a one 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 three point five four times ten to the seven and then we have ten to negative nine and we're going to move this to the top that's gonna be ten to the minus three 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 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