Problem

Convert the following quantities into SI units with the correct number of significant figures. (d) 65 mi/h

Relevant Solution
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Hello everyone in this video, I'm gonna go ahead and convert the feet per second unit into kilometers per minute. Sam Let's go ahead and write out what we're given, which is that 0.680 ft per second. So there's actually an invisible one that we usually do not right because we know that any value divided by one is just itself. So there's no real reason to really put that one. But just for the sake of math, I kind of want to write that because I think it just flow a little bit better in dimensional analysis. So going from the feet per second unit, I want to go ahead and convert that into kilometers per minute so we can see here that we're not only going to be converting our distance unit but also our time unit and we don't have a direct conversion from These into this. So I'll go ahead and do it in baby steps. We know the direct conversion for seconds to minutes, but for feet two km maybe you do know but I do not know that direct conversion so I can take it into baby steps. But first of course these Starting off the dimensional analysis is just by running out the only piece of information that we're given in our case it is just this part right here in blue. Just go ahead and rewrite that and let's see here. So we have that 0.680 ft For that 1/2. Alright, so I'm gonna go ahead and tackle down that distance unit first you can use Or tackle down the time unit doesn't really matter because multiplication is cumulative. But I just want to go ahead and decide to kind of tackle down the harder 1 1st. So I'm gonna go ahead and go from feet to yards, yards, two m and finally meter two kilometer. That's just a way that I want to go ahead and do it because I know those direct conversions. So first going from feet to yard, I know that for every one yard it's equal to three ft And then everyone yard is equal to 0. 1 4, 4 m. And then from meters to kilometers, We know that everyone meter is equal to 0. km. So we have that kilometer unit that we want on top. Let's go ahead and check out down that time unit here. So that direct conversion from seconds to minutes is Every one minute, there's going to be 60 seconds. And as you can see further units, we can cancel feet with feet, Yard with yard, meter with meter and we have a kilometer on top and of course that second with that second, leaving us with minutes as a denominator. All right, so as for the unit sake, I know that I'm an answer will have a unit of kilometers Per minute and further numerical value. Just plugging all my math from the dimensional analysis. I get a value of 0.0124. But I want to go ahead and write this actually in scientific notation for uh, the purpose of Sig Figs significant figures. So that's going to be equal to 1.24 times 10 to the negative. Two power and same thing. Units is kilometers per minutes. Alright, and that is going to be my final answer for this problem. Thank you so much for watching.