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A bedroom has a volume of 115m^{3}. What is its volume in:

b. dm^{3}

Hey guys, on this question we're told that a room has a volume of 115 meters cubed and we have to convert those meters cubed into decimeters cubed. So we're going to start out with 115 meters cubed we want to get rid of meters so meters goes on the bottom decimeters goes on top, deci is a metric prefix and remember 1 is associated with a metric prefix so 1 deci is 10^-1 but meters and meters cubed will not cancel out completely so we have to cube this entire thing, what effect does that have? So we're going to have 115 meters cubed, now here this is really -1x3 so it's going to be 10^-3, so 10^-3 meters cubed on the bottom and then 1 decimeters cubed on the top so this cancels out with this so what we get at the end is 1.15x10^-1 decimeters cubed and I actually no it wouldn't be -1 it would be to the 5 actually. So that will be our answer 1.15x10^5 decimeters cubed.