A penny has a thickness of approximately 1.0 mm. If you stacked Avogadro's number of pennies one on top of the other on Earth's surface, how far would the stack extend (in km)? [For comparison, the sun is about 150 million km from Earth and the nearest star (Proxima Centauri) is about 40 trillion km from Earth.]

Video transcript

Hello everyone today, we are being given the following problem and asked to solve for it, it says a nickel has a thickness of about 1.95 millimeters. If you stacked avocados number of nickel on top of each other on the Earth's surface, calculate the height of the stack in kilometers. So the first thing in this problem that we want to do is you want to write out are given. So we want to write out are given which is 1.95 mm and we have to get two km per the question. And so how are we going to do that? Well, what we're going to do is we're going to first Multiplied by avocados number, which is six .02, 2 Times 10 to the 23rd that says of nickel. So we're just gonna write that as our units. And this of course is going to just be over one, but we don't need to include the one and then we have to go from millimeters to kilometers. So what we're gonna do is we're gonna go from millimeters to meters and meters to kilometers. So we can use the conversion factor that one m is equal to 1000 millimeters next to go from meters to kilometers. We can see that one kilometer is equal to m. And so then We can see our units canceling out. So we have our meters canceling out, we have our mm canceling out as well. And so we're just gonna be left with our kilometers of nickel, which when we fill out and plug it into our calculator, we will get 1.17 times 10 to the 18th km as our final answer. I hope this helped until next time.