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- Solutions 34

A gas can holds 5.0 gallons of gasoline. What is this quantity in cm ^{3}?

Hey guys, in this question we're told that a gas canister has a capacity to hold 5 gallons of gasoline and we're just asked to convert those gallons in the centimeters cubed. Alright so this is going to require us to do some converting in more than one step so let me take myself out of the image, so we're starting out with 5 gallons now the connections we need to realize here is remember that 1 millimeter is equal to 1 centimeters cubed and also remember if we know milliliters that's connected to liters, 1 milli is equal to 10^-3 and then finally we have a connection between gallons and liters, remember here that 1 gallon equals 3.785 liters, alright so we need to get rid of gallons so gallons go on the bottom we're going to change that into liters so liters goes on top, 1 gallon is 3.785 liters. Gallons cancel out now we have liters now are going to convert liters to milliliters so liters on the bottom millimeters on top remember 1 goes with the metric prefix so 1 milli is 10^-3, liters cancel out now we have milliliters and remember milliliters and centimeters cubed they're the same thing so everything cancels out so we have centimeters cubed at the end, when we plug this into our calculators you'll get 18925 centimeters cubed but 5.0 gallons has 2 significant figures so our number has to have 2 significant figures, to the right of that 8 is a 9 which means that this 8 gets booted up to a 9 rounded up to a 9 so that's going to give us 1.9x10^4 centimeters cubed. So here it's important to realize always write down your units so you can see how things cancel out and also, it's important to realize how do we utilize unit conversions correctly so that all these units can cancel out so we get the final answer at the end and again significant figures are still in play so to have the absolute best answer learn the number sig figs you should have.