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Interpreting units in formulas

CCSS Math: HSN.Q.A.1

Video transcript

- [Voiceover] Consider the formula P is equal to W divided by T where P represents power, W represents work and has units of Joules and Joules can be expressed as kilograms times meters squared per seconds squared and T represents time and has units of seconds. And when you get to physics class you'll get very familiar with things like Joules which can be represented as kilograms times meters squared per seconds squared and things like power. But here we're going to learn to manipulate these units so that they make sense. So it says select an appropriate measurement unit for power. And what we've seen multiple times in our mathematical careers is that on a certain level you can manipulate units in a lot of the same ways that you would manipulate variables or numbers. So if power is equal to work divided by time we could also say that the units for power are going to be the units for work divided by the units for time. So the units for work...the units for work right over here is Joules. And so we could write it's going to be Joules per and then the unit for time is seconds. So you might want to say it's Joules per second. But we don't see Joules per second as a choice here, so we probably want to expand out Joules as being kilogram meters squared per seconds squared so lets do that. So this is going to be equal to Joules we can re-write as kilogram times meters squared over seconds squared and we are going to divide all of that by seconds. And so what's that going to be? Well we could re-write this, this is going to be kilograms (and I'm intentionally trying not to skip any steps), kilograms times meters squared per seconds squared and dividing by seconds is the same thing as multiplying by 1 over seconds. So times 1 over seconds and so if we treat these units the way that we might treat things like variables this would be equal to, in the numerator, we would have kilogram times meters squared or kilogram times square meters over the denominator you have seconds squared times seconds, you have seconds to the third power. So a unit for power, one way to express the units for power, could be kilogram meters squared per second cubed. And we see that this is this first choice kilograms meters squared per seconds cubed.