in this video we're going to look at two things we're going to learn how to convert between squared units of area so like between square feet and square in and then we're going to look at how to convert between cubic units of volume so like between cubic feet and cubic Ines this question asks how many square in are in 2.4 Square ft so we're going to be converting here between feet squared square fet and Ines squared square in and we'll be starting with 2.4 Square ft we're going to want to multiply this by a conversion factor to get rid of the square feet so to make this conversion factor we want to find a relationship between feet in inches 1 foot equals 12 in there it is here's a mistake that people often make I don't want you to make it often people take a look at this relationship and they think okay I'm going to make that into do a conversion factor 12 in over 1T I can just multiply this by the conversion factor absolutely not don't do it why not why can't you do this well it's because this unit up here is feet squared and this unit down here is just regular feet so you can't cancel them because they're different units square feet regular feet so we've got to make a relationship that we can then use to build the conversion factor and this relationship has to have square feet and square in here's how we do it okay we're going to start by rewriting 1 foot equal 12 in and now what we're going to do is we're going to square both sides of this it's fine to square something on one side of an equal sign if you square what's on the other side of the equal sign so I'm going to put both of these things in parentheses squared squared okay now we have to distribute this exponent so it's going to be 1^2 = 1 and the squar also goes to the feet so now we got feet squared there's our 1 square foot = 12 sared that's going to be 144 and then we got inches squared so now we have square Ines now I can use this relationship to make a conversion factor that has feet squared or square feet so this is saying for every 1 square foot I have I have 144 square in so since I have 2.4 Square ft here I'm going to want to multiply this by the 144 square in that I have in each of my one square ft now I have square feet up here and square feet down there so they'll cancel out that leaves me with units of square in and I'll do 2.4 * 14 4 ided 1 rounded to two significant figures equals 350 square in now let's look at units of volume what is 2,400,000 cubic cm in cubic meters the answer might surprise you so we're going from cm cubed to M cubed and we're starting with 2,400,000 cub CM the relationship between met and CM is that there are 100 cm in one meter but as we saw before don't mess up and think that you can write a conversion factor to get rid of cubic cm by putting something like this with 100 cm on the bottom no because these are regular cenm they're not cubic cenm so to get this into a relationship that will give us cubic cm we're we're going to rewrite 1 M = 100 cm and now I'm going to cube both sides of the equation this to the 3 and this the 3 distribute this now 1 the 3 just equals 1 M to 3 gives us 1 cubic meter now 100 cubed is 1 million all right 100 * 100 * 100 and now the cube distributed onto cenm gives cubic cm so the conversion factor now is going to put cubic cenm on the bottom so I'm going to have a million cubic cm and I'm going to have one square meter on the top just telling us that for every one square meter we have we have a million cubic cenm cubic centimet on the top on the bottom 2,400,000 * 1 divided by a million is going to give us 2.4 cubic M so a whole bunch of cubic cenm are not that much in cubic meters so you can use this strategy of squaring or cubing both sides of a relationship to come up with conversion factors that you can use to convert between any squared units of area or cubed units of volume so just as one last example if I wanted to convert between say square miles and square kilometers I just take this relationship and I'd Square both sides giving me 1 square mile equals 2589 Square km or I could do this exact same thing to get cubic col and cubic miles 1 cubic mile equal 6679 cubic kilm so you can then use these relationships to build conversion factors that will let you go back and forth between these two units