The distance from Earth to the Moon is approximately 240,000 mi. (a) What is this distance in meters?

Video transcript

Hello, everyone in this video, we're going to go ahead and do some dimensional analysis. We're basically going to be converting kilometers into yards. So first I want to go ahead and take this piece of information, I kind of break that down a little bit into something that we can actually use for dimensional analysis. So we're given the 152. million kilometers. So more of math notation. So we know that first of all, one million ran out is going to expand it out. Will be six Zeros and 1 1 And putting that into scientific notation, that's 10 to the six. Right? So if you want to go ahead and expand out this now, we go ahead and write 1:52.1 Times to the six kilometers and this is definitely going to be so much easier to put into our dimension analysis and use as conversions into the yards that we desire. So we're going from again now, kilometers and two yards artist y deep. Okay, so first I'm going to be using this part of the information given to go ahead and do these conversions. So I don't know the conversion directly from kilometers two yards. So I'm gonna go ahead and kind of break it up into units that I am familiar with. So again, starting off, I have the 152.1 times 10 to the six kilometers and I'm going to first convert my kilometers into meters. So for every one km There's going to be 1000 m then continuing on, I'm going to convert my meters into centimeters. So everyone 70 m There's going to be 0. m. Then I'm going to convert my centimeters into inches. So for every one We have 2.54 centimeters and just checking up on my units, we can see the kilometers cancel, meters will cancel, centimeters will cancel. Alright, perfect. I'm going to go ahead and scroll down a little bit and continue my conversions a goal to the next line below because I don't think everything will fit. So now that we have our units in inches, I want to go ahead and convert that into feet. So for every one third We have and then we're gonna finally go from feet into yards. So every three ft his one yard and just checking to see if we have canceled everything appropriately, we see here that the inches and inches cancel and then the feet and feet will cancel leaving us with just the yard As we have desired. So putting everything into my calculator, I will get a value of 1.66, 3 times 10 to the 11 power yards. And that is going to be my final answer for this problem