- Concept Videos
- Solutions 34

A house has an area of 195m ^{2}. What is its area in:

a. km^{2}

Hey guys, in this question we're told that a house has an area that is 195 meters squared and we have to convert meters squared to kilometers squared. Alright so what we're going to do here first is we're going to have 195 meters squared we need to get rid of meters squared so we put meters on the bottom and there's a direct connection between this base unit and the metric prefix kilo so kilometers goes on top, remember 1 is associated with the metric prefix 1 kilo is 10^3, but here we have a problem meters will not completely cancel with meters squared so what do we do? We square this whole thing, what does that do? That becomes 195 meters squared times now when we're squaring a power really means that they're multiplying so this is really 3x2 so that's 10^6 meters squared and then 1 kilometers squared, that's because 1 squared is still equal to 1 so meters squared cancel out and what we get at the end is 1.95x10^-4 kilometers squared so that would be our final answer. So just realize that this involves metric prefix conversions but because it's squared we have to square in those conversions in order to get to the correct answer.