- Solutions 16

Carry out the following conversion: (f) 8.75 lb/ft^{3 }to g/mL

Alright guys, so in this question we're trying to convert 8.75 pounds per cubic feet into grams per milliliters. So first we're going to convert pounds to grams and then we're going to convert cubic feet to milliliters,lets begin. So we know that 1 pound equals 453.6 grams and then now we can convert from feet to milliliters. Now we put pounds on the bottom here so we're able to cancel out the units, so we're left with grams on the top. We're going to use the same approach to convert feet to milliliters, so we put feet on the top because we want to be able to cancel it out and the conversion is going to be that for every one feet we have 12 inches. But before we are able to cancel out the unit notice that feet here is cubed, so that means you have to cube the entire parentheses here, which means in reality this is going to give us cubic feet over 12 cubed is going to be 1728 inches cubed. So now that everything is cubed lets continue, we can cancel out cubic feet with cubic feet and then we're going to continue. So we know that for every 1 inche we have 2.54 centimeters, once again we're going to cube this so we're able to cancel out the inches and then we have cubic centimeters. So in reality this is going to turn into cubic inch over 16.387 centimeters cubed.

All I did was cubed the number to 2.54 and then cube the units as well because it gets distributed. So I am going to rewrite the other two this one just stays the same. So we're able to cancel out pounds with pounds and we're left with grams so we're going to cancel out feet with feet cubic inches with cubic inches and now we're centimeters cubed. So the conversion is that for every centimeters cubed you have 1 milliliters and that's how you connect your feet to milliliters. So now we can cancel out cubic centimeters with cubic centimeters and we're left with milliliters which is what we want. So on the top we're going to have grams and on the bottom we have milliliters multiply everything on the top and divide by everything on the bottom, your answer should be 0.140 grams per milliliters. See you guys soon.