 All right, ladies and gentlemen, welcome to Tutor Terrific. Here's my final video for unit one of my physics course on measurements, units, estimating and problem solving. Today, we're gonna look at estimation one more time. We're gonna practice everything and we are going to maybe scratch our heads a little bit. You guys might be wondering, oh my gosh, is physics all about math? Well, not necessarily, but mostly. So that's what you guys signed up for. Physics is mostly math. It's mathematical language is used to describe it. So if you're scratching your head a little bit, don't worry. You'll get used to it. So I wanna talk a little bit more about estimation, do a little more practice with estimation. We did one problem in my previous lesson, but today I wanna talk about just the existence of more open-ended estimation problems. Sometimes you're not given any information to start with any approximations, anything to get going, and you might have to estimate every measurement that's involved. For example, estimate the volume of water that falls in San Francisco each year. Oh my gosh, you'd have to estimate everything. You'd have to estimate the surface area of San Francisco, how much rain falls in a certain square meter and during the year, what's the annual rainfall? You'd have to estimate all of that. So we're not gonna do this problem. We're gonna do another problem though that I really enjoy because it reminds me of my physics textbook. When I used to teach physics in the classroom, we would use this one, the sixth addiction, Jean Coley's physics book. This is the book that I based my entire course off of and I really enjoy it. So in honor of that book, I'd like for us to estimate the thickness of a page of that textbook, a single page you would think, oh, it's not thick at all. Well, no, it's not, but it does have some finite thickness. So I'm not giving you anything to start with, although any thick book that you could find, any textbook of your own, you could find and sort of play along with this. So we have to estimate something related first, specifically for this situation, maybe a couple of things. First of all, what you would do if you had this book in front of you is I would have given you a ruler and had you measure the thickness of all the pages together, not including, of course, the cover and back. So when I had my students do this, and you can do this yourself, if you have a textbook like this, is you can get that measurement and then you would need to count them a, count them a, count and estimate the number of pages. Why would you need to estimate this? Well, because there's all those Roman numeral pages at the beginning and maybe some special page numbers at the end, and you don't have all day, so you wouldn't wanna count each individual page that's numbered plus Roman numeral pages. So you'd have to estimate that. Then, as you might have guessed, you would take the total number of pages and use that and divide the total thickness of the book by the number of pages in the book to get the thickness of each page, thickness per page. So let's try it. Now, recall from my last lesson that we are only gonna use one sig fig in all of our estimates and our final result. And the proper power of 10 is what really matters here, not the digits themselves. And we are gonna make sure that all our measurements are in SI units as well. So this is a good example of a book that's about the same thickness as the textbook. And so I had my students measure this and we've got about three centimeters, approximately three centimeters. We converted that to meters, the SI unit for length, and that's three times 10 to the minus two meters. Okay, so that's the thickness we're working with. Now, what about the number of pages? Well, we counted somewhere around 900 or so numerical Arabic numeral pages, and then about 100 or so pages plus the beginning and the end of Roman numerals to come up with about 1,000 pages. Now, some students wanted to be more accurate than that. Maybe you do too. Well, I could find out exactly how many. That's not the point here. The point is not to figure out exactly how many pages to be perfect. We're just estimating. We're doing this quickly. We don't have a ton of time. We're just doing an estimation. And so that's about one times 10 to the three pages if I put that in scientific notation. So like I said, the thickness of each page will be the total thickness divided by the number of pages. So we take that three times 10 to the minus two meters and divide that by 1,000. Basically, one times 10 to the three pages. We would get three times 10 to the minus five meters per page. Now, 10 to the minus six, that's a micrometer. So we have two, we have a power of 10 larger than that. So that'd be 30 micrometers per page. Wow, that's really small. So you get an idea of the size of a thousandth of a millimeter, the micrometer, by looking at the thickness of an individual page. You can even see it. So that's an example of estimating without any estimations or approximations or parts of that process given to you at the beginning. Let's do another one like that. Estimate the number of heartbeats in a typical human's lifetime. Wow, okay. Okay, typical human. That's definitely letting us know that estimation is on the table. Nothing's given to you in the beginning. So let's begin. We will need to obviously get a beat frequency how often does the heart beat for a typical human and a lifespan to make this happen. Then we're gonna need to really think about average heartbeat frequency for a human, maybe an adult, because adults live, the adults are a larger majority of a lifespan than children, which have a higher heartbeat frequency. Then the average lifespan needs to be estimated as well, and that's obviously changed over time. And then we would convert all the units to the same unit as far as time is concerned, and we can always use SI units. They're always a good choice. I'm always gonna push it in my class, and that would be the seconds. So typical lifespan would have to be converted into seconds. Okay, and then we'd multiply our total frequency by the total lifespan. That would be beats per second times seconds, which would get rid of the seconds unit, and we'd just have beats left. So that's the plan. Let's execute it. So if you were to take your own pulse, as a healthy human, you'd get about one beat per second, okay? And you could measure this in a minute, and I had my students do this, take a watch and stopwatch and go for a minute, and most of them got around 60 or 70. And so we rounded to 60 beats per minute. Now, if you were to look at an average lifespan, typically online, we just looked it up. It's about 75 years right now. And some students found a older figure that had shorter lifespans, historical figures. So we rounded, decided to round down to 70 worldwide. 70, single sig fig numbers and measurements right now. Okay, so we need to convert this frequency, beats per minute into SI units, which would be beats per second. And BPS is what that's called. 60 beats per minute, we would divide that by 60 to turn that into beats per second, conversion. So we have one beat per second, and that's what we found when we took our pulses. In addition to that, we need to convert the age to SI units. This is gonna be a challenge. It's gonna be many steps because we have 70 years and I wanna convert that to seconds. So I start with converting the years to days. Then I convert the days to hours, and then I convert the hours to seconds. We're gonna be multiplying a lot. And I got two times 10 to the nine. Again, I probably could get a little bit more accurate measurement than that, but not with seven zero. One sig fig is my initial measurement. Two times 10 to the nine seconds. Now as I said in the previous slide, we're gonna multiply the frequency by this average lifespan, so that seconds cancel. One beat per second times two times 10 to the nine seconds. Those S's cancel, you get two times 10 to the nine beats. Two billion beats. Your heart is an amazing organ. It beats two billion times in the average lifetime. And if you live longer than 70 years, you live up to 100 years, you can get three billion beats. So that's giga beats right there, giga beats. Your heart is an amazing organ. And that's the power of estimation, guys. Continue to use it, and we will see it's usefulness throughout this course. But for now, guys, thanks for watching this video. You have finished my first unit. Look forward to my second unit very soon. This is Falconator, signing out.