Approximating diameter and circumference

0:00- [Instructor] Which diameter and circumference values are reasonable approximations for circles? Pause this video and have a go at that. All right, so what we need to realize is that the ratio between the circumference and the diameter of a circle is, if it's a perfect circle, it's going to be equal to 3.14159, so on and so forth.

0:23And we call that special number pi. You might have learned that already. So it's going to be roughly whatever the diameter is, you multiply it by 3 point something something, that should be a reasonable approximation for a circle. So not all of these might be perfect circles, and these are measurements, so there might be some imperfections.

0:40But let's see. If we take 0.7, and if we were to multiply it by 3 point something something, what would we get? Well, if we multiplied this by 3, we would get, we would get 20... If we multiply by 3, we would get 2.1, 3 point something something, maybe 2.2. This looks awfully far away. Another way to think about it, 3.8 divided by 0.7 is going to be over 5.

1:08So actually I'm definitely going to rule this one out. Let's see here. If I took 5 divided by 1.6, that actually does look kind of like 3 point something something. So times 3., and a bunch of stuff right over there. So this one's looking pretty good. Diameter 0.8, circumference 2.5.

1:29This one also looks like, if I multiply 0.8 times 3, I get to 2.4. So a little bit more than 3. Yeah, this one looks reasonable as well. Okay, 1.2 to 2.9. See if I multiply this by 3, I'd get all the way to 3.6. And if 3 point something something would be higher than 3.6, so I'll rule this one out as well.

1:52So I'm liking these two choices. If I multiply 1.6 times 3, I would get 4.8. This is a little bit more than 4.8, so I like that one. And I made the same argument for choice C here as well.