there's just some extra practice problems for you again i have these for every chapter we're going to cover this does not negate you guys practicing stuff on chem 101 or in your textbook or anywhere else so please find other resources to practice but here's just some more examples kind of worked out they're worked out at the end of your student notes the the powerpoint slides from here on are at the end of the powerpoints i give you so you have access to it there as well and you can see the worked out examples either through the video or if you want to check and or if you don't want to watch the video just check quickly these are again posted at the end of the student notes so please check that out the whole point of these videos is just to walk through these examples with you slowly so that sometimes just hearing someone explain it makes a little more sense on why we do a certain conversion or why we perform a certain operation than just looking at someone else's work i hope this helps so chapter one focusing on measure matter measurements and problem solving lots of significant figures lots of dimensional analysis lots of conversions so that's what this is going to focus on so the first examples we have here these are examples one through five in your notes and so i forgot to put the numbers in here i apologize one two three four and five so we're going to work them in this order the first example we've got 4.932 multiplying by 39.47 and then that quantity is we're subtracting 3.21 from that quantity so when you're looking at this example you need to realize orders of operation so back to i don't remember what math class we learned these then but whenever you learned orders of operation um pemdas if you remember that that's how i was taught at least if you plug this directly into your calculator as written it will follow the order's operation because your calculator is going to do multiplication first then subtraction but if you don't plug things into your calculators properly calculators don't care about orders of operation they're going to just you kind of do what they want in this case though we can plug this directly in because the hierarchy is that this is going to happen first then this quantity we're going to subtract 3.21 from that quantity if you're confused what i mean with orders operation please come see me in office hours okay so 4.932 has four sig figs 39.47 also has four sig figs when i multiply these two together i get a calculated answer of 194.6604 and i know i want four sig figs i'm not going to round yet i'm not going to round until the end because i don't want to create round off error my measurements i am however going to mark where that sig fig should sit it should be in this case four sig figs would be my tens place from this quantity i'm going to subtract 3.21 and this calculated answer will be 191.45604 now remember multiplication and division we look at the number of sig figs but for addition subtraction we look at the decimal place so now we need to look at our decimal places here i'm at the tens place here i'm at the hundredths place we need to limit our sig figs to the least precise measurement which will be the tens place so we need to round our number to here so our final number here will be rounded to 191.5 if you have five or higher for the number you're getting rid of the first number to the right of the number you're gonna end up keeping you're going to round up so we round this up to 191.5 okay the next example 5.982 times 0.00201 this has four sig figs this has three sig figs remember leading zeros not significant captive zeros zero stuck between two other digits are significant when i multiply this together i get the value zero point zero one two zero two three eight two for multiplication division we need to keep the least number of sig figs so i'm gonna count one two three those leading zeros are not significant but this zero i underlined is in fact significant the final answer here will be 0.0120 that answer does have 3 sig figs that 0 is after a decimal place after an integer the other way to check yourself is you can always put this into scientific notation and that number is still in fact significant about this example 4.953 plus 9.20 divided by 11.315 by orders of operation if i plug this into my calculator it's going to give me the wrong answer orders of operation because i'm using the division sign like this it acts as a parenthesis it's really telling me to do this math the numerators math before i do the division from the denominator so i'm going to take 4.953 and add that to 9.20 that's going to give me a calculated answer of 14.153 remember for addition subtraction we're looking at the least precise value so here we go to the third sig third decimal place here the second so our final answer will be accurate here to the second decimal place but i'm not going to round yet i don't want to create round off here so i'm going to take this whole value and divide it by 11.315 but you need to recognize here that this has four sig figs well this has five which means my final answer can only have four sig figs so when i put this in my calculator i get 1.250817499 again calculators don't care about sig figs you need to count to the fourth sig fig one two three four i need to cut my number right here now up here forgot to specify when i cut it here there was a 2 after so i just wrote it down which is why i kept the 0. here i need to round up because i'm getting rid of an 8. this equals 1.251 so first calculation second calculation you can do either one of these answers here for the same answer third calculation we do have some more examples like this throughout because bottom line students just struggle with these um examples and that's completely fine but you need to have these down because we're doing it applied to chemistry it just gets a little bit more difficult um you obtained 5.68 grams of a compound for an experiment a few minutes later you obtained an additional 8.32 grams of the same compound what is the total mass of the substance well let's see we've got 5.68 grams a little bit later we get another 8.32 grams which means i'm gonna add these two values together you can either write these on top of each other so it's really easy to see where your decimal places are or you can realize that each value has two decimal places so our final answer needs to have two decimal places if i put this into my calculator it's going to give me an answer of 14. although that's not correct it's not precise either i need to say 14.00 and i need to put the unit on there if you get a number with the unit you need to include the unit there's very few times in chemistry that we do not include units there's some very specific cases and we will make that very clear to you when units are not included often 95 97 of the time you must have your units included or the value the answer is not correct okay number five 8.672 times ten to the sixth divided by one point three seven six times ten to the fourth because i'm doing division here i need to look at the number of sig figs so i have four sig figs in my numerator and four sig figs in my denominator that makes the math easy i don't have to do much i don't think about it much i should keep four sig figs in my final answer when i calculate this out i'm going to get 6.302325 five eight and that is times ten to the negative ten it's a pretty small number but i'm dividing a small number by a fairly big number so i expected pretty small i want to keep to four decimal places one two three four so i'm going to cut it right here i need to cut between that two and three because it's a three i'm going to round down and i'm going to say 6.302 times 10 to the minus 10. don't forget this at the end students will forget that because it never seems so long and they forget it's up yet don't forget that this is not 6.302 it is 6.302 times 10 negative 10. very different numbers if you're gonna tell me that you're going to give me you know six point three zero two dollars yeah you can try six dollars that's cool whatever you know i can get something solved you're gonna tell me you're gonna give me six point three zero two times ten to get ten dollars i don't know how small you're cutting that penny but it's pretty dang small okay so we're on to six seven eight and nine example six we have five point seven four centimeters plus point zero point eight two three centimeters plus two point six five one centimeters now you are more than welcome to write these out vertically to each other what i mean by that is you are more than welcome to rearrange this and say 5.4 centimeters 0.823 centimeters and 2.651 centimeters so that you guys can quickly figure out where to draw the line and then add it up from there i'm completely fine with that i don't like taking the time to do that i am much faster so whenever one's faster if you do it i am much faster at just counting my decimal places and saying okay two decimals three decimals three decimals and that's how i do the math i want you to pick what's most comfortable for you when i add this up though i get a calculated answer of 9.214 i know that my least precise value is 5.74 it is to the second decimal place meaning i need to keep this the second decimal so i'm going to write 9.21 but i'm not done because i have these units they're all in centimeters which means i can add them up but i need to make sure to write some of these here number seven 4.8 liters plus 3.965 liters when i add this up i'm going to get 8.765 liters i have one decimal place i have three decimal places i'm going to keep my answer to one decimal place i'm going to round this to 8.8 liters number eight now i'm doing multiplication 5.02 nanometers times 89 665 nanometers times 0.1 nanometer these are all length units a nanometer is a unit of length but if you recognize this we're going to get nanometers cubed here which can correlate to eventually we could do a conversion we're not going to in this example we could do conversion back to centimeters cubed and then to volume so um one centimeter cubed equals one milliliter this is how we find volume it's your length times your width times your height so back to geometry um that's what this is looking at is actually calculating a volume of something you need to be aware of that you have to pay attention to what you're doing with units here so let's go back a little bit let's look at our sig figs here when we look at sig figs we've got three sig figs here five sig figs here and two sig figs here remember leading zeroes are not significant but trailing zeroes zeros after a decimal after an integer are in fact significant so our final answer here needs to have two sig figs when i plug this in my calculator i'm going to get five thousand eleven point eight three i need to keep this to two sig figs though so i'm gonna round to here i'm gonna say forty five thousand but i've got a nanometer times a nanometer times a nanometer that is the same as nanometers cubed so nanometer times nanometer times nanometer gives me nanometers cubed number nine 5.892 divided by 6.10 and i've got grams and milliliters here first let's do the math i've got four sig figs here and three sig figs here again trailing zeros are significant they make we're going to keep them they're going to be happy if we keep them around so our final answer must have three sig figs calculate this out and you're gonna get zero point i need to keep this to three sig figs so i'm going to round to here i'm going to cut the value here because the 9 is the first number i'm going to get rid of i'm going to have to round up so my final answer here is going to be 0.966 but i'm not done i need to put my units in i've got grams per ml those are in fact my units i am taking grams divided by milliliters it's completely valid units too that's actually the units we use to represent density okay number 10 11 12 and 13. so let's look at 10 first we've got 2.526 divided by 3.1 plus 0.470 divided by 0.623 plus 80.705 divided by 0.4326 by orders of operation we're going to do each individual division piece first and then we're going to add all the numbers together so here i've got four sig figs here i've got two when i do this math the two point five two six or two point five two six divided by three point one my answer is zero point eight one four eight three eight seven zero nine seven it's pretty long do you really need to write all that no you're not gonna create round off here that far i'm gonna keep a few numbers after but i'm gonna run it to about here because my significance is only to second second decimal there only two sig figs i'm keeping three numbers past that i am not creating round off error at that point four seven zero three sig figs zero point six two three three sig figs so my final answer here needs to have three sig figs when i do this division i get zero point seven five four four one four and at three sig figs i would round to this four if i was going to rob right now 80.705 has five sig figs and 43.26 has four sig figs when i divide 80.705 by 0.4326 i get 188.1273 i need to keep four sig figs so i'm going to go to the value here the number one now i'm on to addition so now i need to look at how precise is my measurements and i need to round to the least precise measurement this is the one hundreds place this is the thousands place this is the tenths i'm gonna round my final answer to the tenths ah i apologize i wrote the wrong number right here i wrote the number for the overall summation here um this should be one point eight six five five eight zero it is still to the um tense point tens place here i just wrote the word number and i apologize for that when you add this all together you should get the answer 188.12727 but i know i need to keep this to my tens place because this is the least precise which means my final answer here will be a 188 6.404 times 2.91 divided by 18.7 minus 17.1 the division sign here acts as a parenthesis so i'm going to take 6.404 multiply that by 2.91 first i do that and i get a value of six 18.63564 that's a calculated answer here i actually have four sig figs here i have three sig figs so if i was gonna round this is my final answer i would round to the third sig fig here i'm going to divide this value however i'm not going to stop yet i'm going to divide this value by the quantity found from a 18.7 minus 17.1 the answer here is 1.6 note this has one decimal this has one decimal this has one decimal that answer is correct 1.6 is correct there there's no rounding error there that's just literally the only answer after that i would put zeros so that is the actual answer here if i needed more significance i would write a zero after that six but i don't now i'm going to divide 18.63564 by 1.6 i get a calculated answer of 11.647275 i need to round this based on sig figs so i've already identified where my sig figs are here this has three sig figs this has two sig figs i need my final answer to round to two sig figs so i'm going to cut my answer here i need to round that answer up to a value of twelve so i can keep just two sig figs number twelve have 9.5 centimeters plus 4.1 centimeters plus 2.8 centimeters plus 3.175 centimeters divided by 4. this is doing an average i've got four measurements here and i'm doing some kind of average when i look here since i'm doing the division line here again acts as a parenthesis i need to do the addition first i have one decimal place one decimal place one decimal place and three decimal places when i do the addition i need to keep my final answer to one decimal place so when i add up 9.5 plus 4.1 plus 2.8 plus 3.175 i get a calculated answer of 19.575 if i'm to look at how many decimal places i need again i'm going to keep it to one for the decimal place here but this is going to be divided by four now the four here you could argue either way you could argue that this answer is an exact number or a measurement i'm going to tell you it's an exact number i'm going to tell you that you made four measurements and therefore what that means is that 4 does not limit your final sig figs for the answer instead it's just a value but it's like how 100 centimeters equals one meter it doesn't limit our final answer if i take 19.575 divide that by four i get a calculated answer of 4.89375 and now i need to round this this does not limit sig figs this has three sig figs i need to round my final answer to 4.89 which contains just three sig figs okay ninety um nine point eight seven five times ten to the day ten to the second minus nine point nine five times 10 to the second divided by 9.875 times 10 to the second kilograms um i forgot to fix this in here i apologize this does say percentage in your notes this is how we find a percent error we take a known value and subtract out some other value what we normally do is an absolute value here just so we can have a positive number because we don't really sometimes we care which way the error means if it's a positive or negative error in that right now it doesn't matter because um the bigger number comes first but you'll see that when you take lab second semester anyway let's um when let's go ahead and look at this example 9.875 times 10 to the second kilograms minus 9.975 times 10 to the second kilograms we are doing subtraction and we're doing this with scientific notation so when i calculate that out it's going to give me an answer of 8.0 so my numerator's gonna be eight point zero kilograms and that's going to be um sorry eight i apologize for that the eight point zero is what's important in a sec and then divided by the nine point eight seven five times 10 to the second kilograms but we have to look at our significance our precision in our measurements because we're doing subtraction remember the shortcut for doing scientific notation you want to see basically what value are you at this is 10 to the second which means 10 to the first 10 to the 0 10 to the negative 1 or the first decimal place 10 to the second first 0 and negative 1 or first decimal place which is why this answer would actually be 8.0 not just 8. so make sure you guys are paying attention to that when you're doing scientific notation so there is two sig figs here and there's four sig figs down here now for our division step so we will be limiting our final answer to just two sig figs we do this calculation here and then we multiply this by 100 percent the 100 is an exact measurement it's we're just taking something from a fractional form into a percentage so it does not limit our sig figs overall you should find your answer here with correct sig figs to be 0.81 and do not forget to write that percent symbol because percent is your unit in this case okay numbers 14 15 and 16. convert 1.76 picometers to centimeters remember when you're doing dimensional analysis to first write down what do you want to know we want to know centimeters so i'm going to say number of centimeters second thing you're going to write down is what measurement you're given you're told 1.76 picometers pico is lower case p if you know the conversions between the individual units so pico de semi senti that's fine i always teach my students to do it through the base unit so we're always going to convert through meters or liters or grams in when i'm doing an example again if you want to do it the other way that's just one direct shot that's fine but if it goes awry and you get it wrong i'm sorry so i'm going to convert three meters first i'm going to convert to meters and i know it takes 10 to the ninth picometers to equal one meter at this step i've canceled out my picometers and i have meters now i'm going to use my conversion to go from meters to centimeters i know there are 100 centimeters in one meter that cancel out my meters and i have centimeters which is what i want when you calculate this out you're going to find the answer to be 1.76 times 10 to the negative seven centimeters now you can do these conversions as long as you've got them written correctly i do not mind so i use one meter to ten to the ninth pico meters you can also write 10 to the negative 9 meters to one pico meter those are both correct i said 100 centimeters to 1 meter you could say 10 to the second centimeters to one meter you could say one centimeter to 10 to the negative second meters all of those are correct they're all going to give you the same answer if you're unsure about that or uncomfortable with that pause this video and work them all out using a different conversion you will get the same answer every time i don't care which one you use i flip around whatever my brain picks out of the ether at that moment in time so more often than not i'll do whole numbers like this because i like bigger numbers um but whatever works better for your brain is what i want you guys to use i'm not insistent upon using one conversion over the other as long as you're doing your conversions correctly okay convert 43 degrees c to kelvin remember kelvin is equal to degree c plus 273.15 you need to have that memorized there's no if stands or thoughts about it we're using calvin for the entire school year so you need to be comfortable with calvin so this is equal to 43 degrees c plus 273.15 equals 316.15 k if i look at this now i'm doing addition this is to the 10 to the zero space or the ones place meaning no decimal places so i'm going to round this to 316 kelvin and the boiling point of liquid nitrogen is negative 196 degrees c what is the temperature on the kelvin scale again kelvin equal to degree c plus 273.15 so i have negative 196 degrees c plus 273.15 and when you add this up you're going to find that your value is 77k so we've gotta round to the first place here you're going to have to round up when you do this calculation you should get a 76.85 you're going to round up to 77 because we need to keep it with no decimal places because our least precise measurement is negative 196. okay number 17 a european car is advertised as having a gas mileage of 15 kilometers per liter convert this rating to miles per gallon we have some conversions that we're provided with here we've got one meter lowercase m means meter means a few other things too but it means meter equals 1.094 yards 1760 yards equals one mile we use m i to abbreviate miles 1.06 quartz is equal to one liter and four quarts equals one gallon so first write down what do you want to know well you want to know miles per gallon next write down what you're told you're told 15 kilometers per liter then use conversions to get to where you want to go so i see i have a conversion for a meter to a yard now you can convert the numerator first or the denominator i don't care if you do distance first or um volume first i tend to convert whatever's in the numerator first and then work on the denominator do what's comfortable to you okay so we're going to work on converting kilometers over two miles and then i'm going to work on converting liters to gallons so 15 kilometers i do have a conversion that has one meter equal to 1.094 yards i know a conversion between meters and kilometers so i'm going to do the conversion i know to convert to meters then i'm going to use the conversion that's provided to convert to yards so i know there's 1000 meters in one kilometer if i was to stop right here my kilometers have cancelled out and i'm in meters now i can use this conversion so times 1.094 yards per 1 meter how do i know what goes in the numerator what goes in the denominator because i'm trying to cancel things out so i'm trying to cancel out my meters and the only way to cancel my meters is to put in the denominator plus i'm eventually going to need my distance in the numerator so it makes sense that way too but if you think about what's cancelling sometimes that can help get you on the right track now i am in yards what can i do now well i have a conversion for yards going to miles and overall i want to get to miles so that's the perfect conversion to use i know one mile is equal to 1760 yards how do i know it's one mile because it says 1 760 yard equals mile that implies one mile that cancels out my yards and leaves me with miles so now i've got my numerator set now i just need to work on my denominator so let's work on our denominator we've got liters we want gallons well i have a conversion here showing me a quart to a liter so i'm going to go ahead and use that conversion i'm going to say 1 liter in my numerator and 1.06 port in my denominator why am i doing it that direction because i need to cancel out my leaders and my leaders are currently in my denominator now i'm in miles per quart i want miles per gallon though and i've got a conversion for quartz to gallons times four quart to one gallon and if i stop here that cancels out my quartz and leaves me with gallons now i've got all of my units correct when i calculate this out i'm going to have it in miles per gallon which is exactly what i want when you calculate this through the calculator you're going to get an answer of 35.1 and again i know i've mentioned this in class but it does not matter you can do all the numerator then all the denominator you can mix it up i don't care what i mean by that in your calculator you can say 15 times 1000 times 1.094 times 4 divided by 1760 divided by 10 1.06 you could say 15 times 1000 times 1.094 divided by 1760 divided by 1.06 times 4. those will give you the same answer that's because multiplication division have equal weight in order of operation do what you're comfortable with but when you calculate this out you are going to get an answer of 35.184 we have to think about our sig figs really quick this is an exact measurement which means it does not limit our sig figs this has three sig figs this has three sig figs this has four sig figs this is exact how do i know that if you are in the metric system they're exact so this is within the metric system it's exact um for one quart to four gallons i just know that one there'll be times that i will tell you guys if they're exact and if i'm giving you the sound like a quiz or something i would say exact next to it all i would say is the word exact next to the conversion you need to know what exactly means but i don't always expect you to know that the one only one that i can think of on top of my head that i know you have to know is 2.54 centimeters equals one inch that's exact you need to know that one but back to it we've got two sig figs here our final answer needs to be limited to two sig figs so i need to round this to two sig figs i'm going to say 35 miles per gallon so 15 kilometers per liter 35 miles per gallon pretty good gas mileage okay number 18 the density of pure silver is 10.5 grams per centimeter cubed at 20 degrees degrees c if 5.25 grams of pure silver pellets are added to a graduated cylinder that contains 11.2 milliliters of water to what volume level will the water in the cylinder rise so this is called a displacement method and it's often used in laboratories to figure out the volume of an irregularly shaped item or species so you've got graduated cylinder here and you've got some volume in it and graduated cylinders are just that they're graduate they have lines on them telling us different volumes let's say our volume is actually down here so it's easier to draw where i'm at we're going to go and we're going to put into here 5.25 grams of silver pellets so because i don't have a color silver on here let's say i put the 5.25 grams in here they're down here and now my volume is here so my volume's here now uh this is the volume this difference here is due to those pellets the amount of volume increase here is due to the fact that those pellets were put into that system so what volume is this water going to be at it's going to be the final volume is going to be 11.2 milliliters plus the volume of silver well how do i figure out the volume silver i have its mass and i have its density i'm going to rearrange that to solve for its volume so density is equal to mass over volume in this case our density is equal to 10.5 grams per 1 centimeter cubed i'm going to rearrange this and use the mass of the actual substance we have the amount of pellets we have to figure out the volume of pellets i have if i want to find volume i can rearrange this to solve if i take your mass and divide it by density it's going to give me volume so i've got 5.25 grams divided by 10.5 grams divided by centimeter cubed this gives me 0.500 centimeters cubed now i know some students are not comfortable doing it that way so let me show you the slightly longer way this is the same as saying 5.25 times one centimeter cubed divided by 10.5 grams you're saying the same thing here okay it's just a conversion whichever way you're comfortable writing out it's gonna give you the same answer but i know that one centimeter cubed is equal to one milliliter so i know that 0.500 centimeter cubed i can write that as times one mil divided by one centimeter cubed this equals zero point five zero zero milliliters now i can add this volume to this and i can figure out the volume total volume of the graduate cylinder once the silver pods have been added one more thing why did i keep this 2.500 why did i add two zeros here i added two zeros because i apologize there's three sig figs here and there's three sig figs here so i need to keep three sig figs my answer so i've got 11.2 milliliters of water plus 0.500 mils for the space added from the silver pellets this will give me a calculated value of 11.700 mils now i'm doing addition so i need to think about how many decimal places one decimal three decimals i'm going to round this and say my final volume is 11.7 milliliters number 19 a roll of aluminum foil is made out of a long aluminum sheet that is 304 millimeters wide and 0.016 millimeters thick what maximum length of aluminum foil can be made if we have a 1.10 kilogram sample of the aluminum so how we're going to go about solving this well we're given some values from equations here cube sphere and cylinder and thinking about this one if i've got my width and i've got my thickness i'm going to use cubes i'm going to figure out how long can i make this piece of aluminum foil and compare that back to um so i'm looking at for length here but i've got my kilograms i know my width and my thickness i can use all this information to figure out what length of aluminum foil i can find so first thing i'm going to do is i'm going to use density to relate mass and volume if i look up the density of aluminum foil i find it to be 2.7 grams per nut which also means grams per centimeter cubed note there is two sig figs in this measurement you can find density more accurate when i looked it up on google that's just the first thing that came up so i'm going to limit all of our answers to two sig figs not really that big of a deal since we have two sig figs here anyway and it would have been limited to two sig figs when you're doing calculations in the per say real world if you're doing a calculation and your value you look up such as density is what's limiting your values you should probably find it a little more accurately to a few more sig figs than you have because we want your measurement to really limit your final answer not just whatever hap whatever constant we happen to look up because densities are valid to many more decimal places than just one so let's get back to it i want to know eventually what length of little foil i can get so i want to know number of millimeters cubed i know i have a 1.10 kilogram sample well oh by the way why do i want millimeters because i'm going to have to use this equation here and this is in millimeters and this is in millimeters so since i'm going to need them in millimeters anyway i figure why not find millimeter style i know i'm using a 1.10 kilogram sample of aluminum i know that there is 1 000 grams of aluminum per one kilogram of aluminum that's just my metric measurements i know based on density there is one centimeter cubed of aluminum per every 2.7 grams of aluminum that means if i have exactly one milliliter or one centimeter cubed of aluminum it will weigh exactly 2.7 grams so i know i have more grams than that but it's going to tell me exactly the volume i have in that case instead i do want this in millimeters instead of centimeters so that i'm going to do one last conversion to get this into millimeters and i know that it's 10 millimeters in every one centimeter now be careful when you stop here this is one millimeter over one centimeter one centimeter cannot cancel out a centimeter cubed you need to cube this whole quantity now check it and make sure that all of your things are canceling that should be kilograms of aluminum kilograms of aluminum cancel grams of aluminum canceling with grams of aluminum centimeters cubed centimeters cubed everything's cancelling we're going to get millimeters be careful when you enter this of your calculator as well this is the same as 1.10 times 1000 divided by 2.7 times 10 raised to the third grade dude you don't have to you can do mix up the order of these things i don't care about that but make sure that however you put in your calculator this is equivalent to 10 to the third most calculators use this little carrot sign to say raise two when you calculate out your number of millimeters cubed you should find this value to be four zero seven four zero seven point four zero seven four and this is millimeters cubed it's a pretty big number definitely repeating itself um we don't need to keep all of those digits right now but i'm going to keep them just for the next calculation because i'm going to round up the edge i don't want to deal with grounding air so now that i know my millimeters cubed that means i know my volume i know the volume of aluminum foil the aluminum foil um i can make from 1.10 kilograms now i want to go ahead and figure out okay if i know that what is the length of the aluminum foil i can use or i can produce from this so i'm gonna i've got four zero seven four zero seven point four zero seven four millimeters cubed this is equal to length times width times height length which is what i'm trying to solve with is 304 millimeters and height or thickness is 0.016 millimeters rearrange that equation and solve for length so length equal to four zero seven four zero seven point four zero seven four millimeters cubed divided by 304 millimeters times 0.016 millimeters note here that this millimeter this millimeter cancels out with two of them up there and this gives me a final calculated answer of eight three seven five nine point seven millimeters it's a pretty big number i'm going to actually convert that to meters so and i'm going to round to two sig figs so first that equals 84 000 millimeters which i'm going to convert you can write out the conversion if you need to that's totally fine but you need to get comfortable seeing that that would be equal to 84 meters so if i have a sample of little foil that is 3.04 millimeters wide and 0.016 millimeters thick the maximum length of aluminum foil that we made if i have 1.10 kilograms of aluminum foil would be 84 millimeters or sorry 84 meters many milli millimeters but 84 meters long okay an iceberg has a volume of 7655 cubic feet what is the mass of the ice in kilograms composing the iceberg hence the density of ice is 0.917 grams per ml at 0 degrees c so i want to find the number of kilograms i told i have a volume of 7 655 feet so write down what i want to know number of kilograms and write down what i'm given seven six five five feet cubed because it's cubic feet i'm going to go ahead and convert this um because i'm trying to get to kilograms and i'm gonna have to use density here i know 0.917 grams per 1 ml is the same as 0.917 grams per 1 centimeter cubed but that means i need to get this value into centimeters the only conversion i know between the american system and the um metric system for is 2.54 centimeters equals one inch you may know another conversion that's fine that's just the one that i chose to have memorized so i'm going to go ahead and get my value to inches so i'm going to multiply this by 12 inches to one foot make sure to cube that i need to cancel out those cubes and i know there's 2.54 centimeters for every one inch again cube this quantity if i see that my feet cubed have canceled and my inches cubed have canceled and i am now in centimeters cubed now that i'm in centimeters cubed i can go ahead and use my density so times 0.917 grams per one centimeter cubed now i'm in grams and i can easily convert to kilograms one kilogram is equal to one thousand grams again you could also write that as one kilogram is equal to ten to the third grams ten to the minus third kilograms equal to one gram whatever conversion you know that is correct is completely fine to use i just tend to use non-scientific notation ones if i can so check to make sure this cancels my centimeters cubed this cancels my grams it leaves me with kilograms make sure when you plug this in your calculator you're careful you've got 7655 times 12 to the third times 2.54 to the third times 0.917 divided by 1000 make sure you're remembering to raise these to the third power which again is usually that little carrot symbol or triangle without the bottom on your calculator when you calculate this out you should get a calculated answer 198773.9 now you have to look back at sig figs this has four sig figs this is exact which means it does not limit sig figs this is exact which means it does not limit sig figs this has three sig figs so i'm gonna go ahead and round this answer to three sig figs so this will equal you can either write this as one nine nine zero zero zero kilograms or you'll more often see this as one point nine nine times ten the fifth kilograms we'll often put into scientific notation when it gets that big just because it's easy for people to lose zeros when they're looking at them if we put it in scientific notation we're not losing those zeros okay lead metal can be extracted from a mini mineral called galena which contains 86.6 percent led by max a particular ore contains 68.5 percent glean of imaps if lead can be extracted with 92.5 efficiency what massive or is required to make a lead sphere with a 5 centimeter radius lots of things going on here lots of conversions you're probably reading this question and thinking what it's kind of overwhelming that's okay we're going to work our way through it first what we need to think about is how are these just some background information how do we often get these materials we extract them out of ores out of rocks out of species in the ground a lot of the elements the natural occurring naturally occurring elements we have we've been able to extract from other sources lead is extracted from this mineral this mineral is contained within a particular ore so it's an extraction upon an extraction and so we can look at these things and we actually can get conversion factors from it so we know lead metal can be extracted from the mineral which is 86.6 led by max so that's like over here we say sterling silver has a silver alloy containing 92.5 silver by mass we have 92.5 grams of silver per one grams alloy here we have 86.6 grams of lead per 100 grams of the galena a particular ore contains 68.5 percent related by max that means i have 68.5 grams of glenna per 100 grams of ore it's another conversion factor lastly it tells me that lead can be extracted with 92.5 efficiency that means for every i've that what that means i get 92.5 grams elena sorry 94 2.5 grams um of ore extracted per 100 grams of ore used so if i have a 100 gram sample of the ore i'm successfully able to extract 92.5 percent of that so 92 so 92.5 grams that other 7.5 grams is just kind of wasted or lost so how can i go about this well let's see i want to know how to make a lead sphere i wanted let's here at the center with a radius of five centimeters so i know the equation for a sphere volume equals four thirds pi r squared or sorry pi r cubed so i know four thirds pi r cubed and i want to figure out how much volume do i need what do i actually how much do i need to extract to be able to make this sphere so i'm going to figure out what's the volume of the let i actually need if i can figure out the volume i can use density to convert back to grams i can use grams to convert back to how much order do i actually need the mass of the ore of the mass of the or that i need in the first place so again lots of conversions it's a very complex problem so let's look at volume of lead needed we've got four thirds pi r is five centimeters that told us that's what our radius was cubed calculate this out and you're going to get 523.599 centimeters cubed we cube this entire thing which means we cube the five and the centimeters we have three sig figs there so technically our sig fig stuff here at 523 i'm just not going to round quite yet now that i have my volume i'm going to use the density of lead to figure out my grams sometimes you'd have to look these up outside again on the exam i would give you the density but density of lead is equal to 11.29 grams per centimeter cubed it's pretty heavy a lot of metals have higher densities so grams of lead needed we've got 523.599 marking my sig figs centimeter cubed times 11.29 grams per 1 centimeter cubed this gives me a value of 5911.43 grams of lead so i need about 5 900 grams of lead to make this 5 centimeter radius sphere let's figure out how much ore that equates to how much ore do i actually need in the first place to be able to extract to be able to pull out that mineral to be able to pull out the lead so if i need five nine one one my sig figs are under that first one just to keep them marked for you guys so we have three sig figs here and four safeties here five nine one one point four three grams of lead i know that i can get i have 100 grams of glena per the 86.6 grams of lead i can actually pull out i know that for every 100 grams of ore extracted i have 68.5 grams of the galena and i know that for every 100 grams of ore 92.5 grams of ore is actually extracted calculate all this out and your answer is one zero seven seven three and this is grams of ore sig figs are still here at three everything either has everything their calculations have three sig figs and so i'm going to round this and i'm going to say 1.1 sorry 1 0 1.0 8 times ten to the fourth grams or you could also again write one zero eight zero zero grams either one is fine of or required if you want to convert that to kilograms you can we don't often report things in kilograms but you could go ahead and write 10.8 kilograms as well so i'd have to start with 10.8 kilograms of ore to make that five centimeter radius lead sphere the mass of a feel of the jet must be calculated before each flight to ensure that the jet is not too heavy to fly a 747 is filled with 1 730 231 liters of jet fuel if the density of the fuel is 0.768 grams per centimeter cubed what is the mass of the fuel in kilograms so i've got this many liters i've got your density here i wanted what's the mass specifically in kilograms so number of kilograms of fuel starting out with 173 231 liters i know there's a thousand milliliters per one liter why am i converting to milliliters because i know that one mill equals one centimeter cubed so one centimeter cubed to one milliliter now i can go ahead and use density to convert to grams 0.768 grams per 1 centimeter cubed and i know one kilogram contains one thousand grams calculate this out you get one three three zero four one as your calculated answer we need three sig figs in our final answer which is limited by our density so our final answer will be one point three one point three three times ten to the fifth kilograms i have one point three three times ten to the fifth kilograms of fuel and again if you feel more comfortable you should always check make sure units are cancelling liters to liters mils to mills centimeter cubes centimeter cubed and grams to grams leaving me kilograms i recommend making sure units cancel until you guys are very comfortable and even then sometimes it's good to check because sometimes you'll just put things on the wrong side of the equation you'll put in the numerator to the denominator etc and it can kind of throw off your entire calculations you should always check that your units have cancelled okay 23 convert 5.12 times 10 to the negative third grams into micrograms so i want to know number of micrograms i'm starting with 5.12 times 10 to the negative third grams i know micrograms are smaller so i'm expecting this number to look bigger than it does now i know there are 10 to the sixth micrograms this is one of the conversions you need to have memorized per one gram this gives me five one two zero micrograms or you can write this as five one five point um one two times ten to the third micrograms do not leave the zero here if you put in the scientific notation the way i have this written this has three sig figs if i had written five one two zero with a decimal at the end that has four sig figs our final answer needs three sig figs convert 435 centimeters to kilometers so number of kilometers is equal 435 centimeters again some of you may know the conversion straight to kilometers that's totally fine i always convert through base units because it's the only conversions i personally have memorized so my base unit is meter i know one meter contains 100 centimeters now that i have meters i can convert to kilometers i know one kilometer has 1000 meters this gives me an answer of 4.35 times 10 to the negative third kilometers does that answer make sense to me yep seven meters are much smaller than kilometers so if i'm converting two kilometers i expect the number to look smaller and lastly convert 32.145 times 10 to the 12th nanoliters to a deciliter i know nanoliters are pretty small this is a pretty big number here so i expect the number to get smaller than a deciliter deciliter is times 10 to the negative one nanoliter is times 10 negative 9 compared to a meter so i want to know number of deciliters i've got 32 0.145 times 10 to the 12 nanoliters again i'm going to convert through my base unit first so 1 liter has 10 to the ninth nanoliters now that i'm in liters i can convert to deciliters i know there is 10 deciliters for every 1 liter my final answer 3.2145 times 10 to the fifth deciliters okay determine the volume of an object that has a mass of 455.6 grams and a density of 19.3 grams per centimeter these calculations should seem pretty straightforward to you at least once we're past the first chapter we're going to use density a lot throughout this entire school year to be able to use as conversion to convert between different between volume and mass units so you need to be very comfortable with this concept of density if i want volume i've got mass and i've got density i can just i can um reorganize this equation density equals mass over volume if i want to solve for volume that just means mass over density so volume is equal to 455 455.6 grams divided by 19.3 grams per centimeter cubed this gives me let's see where's my answer 23.6 centimeters cubed the other way you can do this if you don't like this look here because you can't figure out the units is you can say 455.6 grams times 1 centimeter cubed divided by 19.3 grams it's doing the exact same thing it just kind of throws students off the denominator of your denominator becomes a numerator but that's that is hard for students to see sometimes so if you need to put out unto a conversion factor that's totally fine number 27 the density of lead is 11.3 grams per centimeter cubed what is the mass of lead required to make a one centimeter cubed fishing sinker well again density mass number volume i want to know mass so mass is going to equal density times volume 11.3 grams per one centimeter cubed volume is one centimeter cubed so the mass will just be 11.3 grams so if i want to make a one centimeter cubed fishing sinker i need 11.3 grams of lead and number 28 can you find the mistakes i want you to look at numbers one two and three here under number 28 and see where do you think the mistakes are go ahead and pause the video and see what you think now looking back at this we've got centigrams and we're trying to convert we're trying to find the number of centigrams from the number of micrograms we have 3700 micrograms i don't care if you guys don't write this divided by one here um some students prefer it it's up to you it means the same thing whether you put it there or not thirty seven hundred micrograms and i'm converting this to grams i know there is ten to the sixth micrograms for every one gram so this conversion is correct it's one million micrograms to one gram then i've got times one thousand centigrams per one gram this is not correct this should be 100 centigrams per one gram so that's where the mistake is in the first one what about the second one got 2500 or 25 seconds and again i don't care about these um divided by one thing here 25 seconds and i'm converting this to nanoseconds i've got one times ten to the negative nine nanoseconds per one second but a nanosecond is 10 to the negative ninth right it is except the nano is a lot smaller so it is either 10 to the ninth nanoseconds to every one second or one nanosecond to ten to the negative nine seconds so make sure you're paying attention if it's positive if it is a really big number a really small number that you're multiplying or dividing by and the last example i want number of kilometers per second and i'm starting with kilometers per hour i've got 115 kilometers per one hour okay and i'm going to convert that to seconds i've got times 1 hour divided by 60 seconds not correct this is where students will mix this up if you want to do a direct conversion like this you have to make sure you've got the correct number of seconds there if i was to do this equation i would say 115 kilometers per one hour times one hour per 60 minutes times one minute per 60 seconds now this ends up being 3 600 seconds if you want to do it as one fell swoop that's fine i write them out because students often mess up this conversion okay so look back