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The density of iron is 7.86 g/cm^{3}. What is its density in pounds per cubic inch (lb/in^{3})?

Hey guys, in this question they give to us 7.86 grams per centimeters cubed and we're asked to convert that into pounds over cubic inches or inches cubed so if we're going to work this out let's first start by writing up the number again 7.86 grams per 1 centimeters cubed. Alright so let's do the hard part first we want to get rid of centimeters cubed so we'll put centimeters here on top so it can cancel out with these centimeters here on the bottom and inches on the bottom here, 1 inch is equal to 2.54 centimeters cubed...Or centimeters I mean but remember this is centimeters cubed and this is centimeters they're not the same thing so what does that mean? That means I have to cube this entire thing, so we're going to do 2.54 cubed so they cancel out finally, now as a result of this inches on the bottom also gets cubed so we'll have inches finally. Next thing I'm going to do now is we're going to say here we want to get rid of grams so grams go here on the bottom, we want pounds so pounds go on the top remember 1 pound is equal to 453.592 grams, grams cancel out and what I'll have left at the end is pounds over inches cubed. Now what is this effect of cubing this thing going to have? So, 7.86 grams over 1 centimeters cubed 2.54 cubed gives me 16.3871 over 1 inch cubed, OK? So, centimeters cubed cancel out then we put grams here on the bottom, pounds here on top so grams cancel out so what we'll have left at the end is pounds over inches cubed so here at the end our answer will be they give to us originally 7.86 which has 3 sig figs so our answer at the end has to have 3 sig figs so 0.284 pounds over inches cubed so here changing the units gives us this as our final answer.