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$\cdot$ Express each of the following approximations of $\pi$ to six significant figures: (a) $22 / 7,($ b) 35$/ 113 .$ (c) Are these approximations accurate to that precision?

(a) The number is:$\frac{22}{7}=3.14285714286$six significant figures: 3.14286(b) The number is:$\frac{355}{113}=3.14159292035$six significant figures: 3.14159(c) The exact number of $\pi$ is:$\quad 3.14159265359$approximating it to six significant figures:3.14159So we can see that the approximation $\frac{355}{113}$ is more accurate, while $\frac{22}{7}$ is less accurate in comparison to the exact value of $\pi$

Physics 101 Mechanics

Chapter 1

Models, Measurements, and Vectors

Physics Basics

Jenieveb G.

February 23, 2021

How many kernels of corn does it take to fill a 4-L soft drink bottle?

University of Washington

Hope College

University of Sheffield

McMaster University

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This is Chapter one problem. 17. It requests that we express to approximations of pi to six significant figures. So we're given the approximations 22 7th and 3 55 over one thirteen 13. So expressing to six significant figures means we encounter significant figures with the first non zero decimal three and then one for 286 That's six figures. So this is far as we go for all our approximations, and all you've to do is put the fraction of your calculator and desolate mode, and that will tell you the answers that are up on the screen right now. For part. See, it wants to know if he's approximations for accurate to that precision and what it means to be accurate to that precision. It means all the digits here. All six of them are equal to those 1st 6 significant digits of pi. So you can see here that the approximation of part B 3 55 141 13 is equal, but the 22 over seven these 1st 3 digits are equal, and then these last two years, just or not, so the first approximation is not accurate to six foot six significant figures. But the second approximation is accurate to six significant figures Now, when it's appropriate to use this approximations, it's just a question of how much priss priss precision you need. Often in a problem. You won't have six significant figures of precision. And so if you want to use an approximation for pie, for some reason, the 22 over seven will be perfectly serviceable. But that's very feast dependent.

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