hello everyone this video will cover the information in chapter two section five so uh in section five we are going to practice writing conversion factors and so this will be the first step in being able to identify and utilize conversion factors in multi-step word problems so it's just important for us to be able to understand how to write equalities and then also on the different ways that we can write conversion factors so if we look at 2.46 write the equality and two conversion factors for each of the following pairs of units so for a we have the centimeter and the meter so here is one of our multiplicative prefixes centi and so there are 100 centimeters in one meter right centi and so this is the equality we are saying that these two amounts are equal and if we wanted to write this as a conversion factor we could write it as 100 centimeters over 1 meter or we could write it as 1 meter over 100 centimeters right and so this is basically right one one to one um these two things are equivalent which is why we can write it and we can write it either way um because they are equal and the way that we would choose to write the conversion factor as we work out a problem whether it's 100 centimeters over 1 meter or 1 meter over 100 centimeters is going to be largely dependent upon which unit we need to cancel out as i had mentioned previously units cancel out just as numbers do when we are dividing by the same number or the same unit they will cancel out so again which way we choose to write our conversion factor is going to be is going to depend on the unit we are trying to get rid of um so just kind of keep that in your back pocket for now we'll see lots of examples um moving forward um to put this into practice so for b we have kilometers and miles so 1 kilometer is equal to 0.621 miles um certainly we could have also said that 1.61 kilometers is equal to one mile either way is correct and then we could write the conversion factors as one kilometer over 0.621 miles or 0.621 miles over one oh that's an m kilometer um so i i believe i had already mentioned this before for a lot of these conversions right uh kilometers and miles or pounds and grams or even quarts and liters um i don't necessarily expect you to memorize these when i teach general chemistry on the ground i have a reference sheet that i give to all of my students and it includes a periodic table and it also has a number of these conversion factors um and also some really helpful uh equations for this course or for that course um but which will also be helpful for this course so i'm gonna make that available and if you have the ability to print it's a good thing to to have on hand when you are working some example problems as i mentioned i do think it is a good idea to memorize the multiplicative prefixes that is not something that i tend to give my students i do expect them to just know those um again you know you all are in a bit of a different situation since you are purely online um and you can have that information in front of you but the more you can familiarize yourself with those multiplicative prefixes and get comfortable um converting between them um the the quick the more quickly you will be able to work through problems and so for c now we have pounds and grams so one pound is equal to 453.592 grams all right so we know that one pretty precisely and then just as before um we have our equality and we can write our conversion factor one pound is equal to 400 sorry trouble with my writing pad 592 grams or 453 grams over one pound and then we have uh lastly here for d quartz and liters and so one and so q t is the symbol for quart okay shorthand and that is 0.946 liters and then we can write that as 1 quart 0.946 liters or 946 liters over 1 quarts and so when we are converting or setting up these conversion factors between units that are not within the same measuring system they tend to be measured numbers whereas when we are converting within the same measuring system for example the metric system those are exact numbers so going between centimeter and meter those are exact numbers but when we're going in between kilometers and miles etc those are going to be measured numbers again we're converting between units that are in different measuring systems okay so now we'll move on to 2.48 so before we move on to 2.48 i'm looking at my notes and i think that i typed this one wrong so if you look in your uh textbook at 2.46 i think that this is supposed to be centimeters and inches i've been doing a lot a lot of typing to put these into a word document but just to clarify there are 2.54 centimeters in one inch um and certainly we could write that in the equality form or we could put one inch over 2.54 centimeters as another conversion factor so let's move on to 2.48 write the equality and two conversion factors and identify the numbers as exact or give the number of significant figures for each of the following and i do want to mention at this point that the importance of being able to identify numbers as either exact or measured is that exact numbers are thought to contain an infinite number of significant figures um and so we do not uh include them when we are counting up sig figs um and and using that to determine the total number of sig figs to use in our final answer whereas when values are measured we do have to take into the take into consideration the number of significant figures um that those conversion factors contain so so so that's um so that's why we need to be able to distinguish the two so for 2.48 a we have one liter is 1.06 quarts um we wrote it the other way up here we said one quart is equal to 0.946 liters but the equality would then be 1 liter is equal to whoops 1.5 0 6 quarts so there is our equality and i'm going to not write out those two conversion factors but they would look like this except it would be 1.06 quarts over 1 liter or 1 liter over 1.06 quarts now which of these is measured and which of these is exact well the one liter is an exact number okay so we look at this and off the bat we think one significant figure but because it is an exact number we can take that to have an infinite number of sig figs 1.000000 etc whereas the 1.06 that is a measured number that contains three significant figures okay whereas the one liter is exact for b at the store oranges are 1 1.29 or 1.29 per pound so our equality is we're going to pay 1.29 for one pound of oranges and again we could write this as a conversion factor all right 1.29 1.29 for one pound or we could write one pound over a dollar 29 and so when it comes to exact or measured the dollar 29 that is a measured quantity whereas that one pound that's exact okay for c we have one deciliter contains 100 milliliters so our equality b1 deciliter equals 100 milliliters so we have our metric system with our two multiplicative prefixes so these are both exact numbers and would not factor into our accounting of significant figures now d we have an 18 carat gold ring contains 75 percent gold by mass so this is where we want to focus so our equality is if we have so uh 75 gold by mass means that if we have 100 grams of a gold ring it's going to contain 75 grams of actual gold metal um so this one may be a little tricky we've got this 18 carat here but what we are looking for is again by by mass right so that's why we know that we're working in grams a unit of mass and the 100 grams of gold ring that's an exact number but that 75 grams of actual gold metal that's going to be a measured quantity and then we could write this as 75 grams of gold over 100 grams of gold ring or we could flip it and say for every 100 grams of a gold ring that we have over 75 grams of gold so those would be our two conversion factors okay and i think we've only got um one more in section five the last example that we'll work through in section five is two point five four right inequality and two conversion factors for each of the following uh medications so i'm going to try to do this pretty quickly we have 2.5 milligrams of coumadin per 1 tablet of coumadin and so um really quickly if we wanted to write an equality right we would just put the equal sign in there 2.5 milligrams of coumadin equals one tablet of coumadin and if we wanted to write conversion factors that's 2.5 milligrams okay over one tablet of the medication so same thing here right if we wanted to write the equality we just do that put the equal sign and so 10 milligrams of clozapin over one tablet and it would be the same down here oh this is milligrams nope 1.5 grams over one milliliter and it also would be correct um to write these conversion factors as one tablet over 2.5 milligrams right one tablet over 10 milligrams and one milliliter over 1.5 grams and again as we progress throughout this chapter hopefully you will see that the way that we choose to write that conversion factor is just dependent um on you know what is our known beginning and what is our desired end right so which units do we need to cancel out so that is going to conclude my video for section 5.