Mad Slide Ruling Know your A, B, Cs and DsTeaching Students about Approximations

©2013 Ferrick Gray

http://theferrickfiles.com

Pickett

PPT4

Introduction

> Irrespective of what type of calculating device is being used, it is always desirable to be able to make some sort of estimation or approximation as to the magnitude of the answer.

> Not only is this good practice, but it also allows us to verify the correctness of our results.

Accepting Approximations

> Many people are reluctant to accept the approximations inherent in much scientific work.

> Much scientific work and applied mathematics involve measurement of some kind.

> Measurement involves error not necessarily because of carelessness, but because of the limitations of the measuring device.

> No matter how precise or accurate, we must accept small errors.

> When working with the slide rule, we are interested in the accuracy of our results.

> This corresponds to the number of significant figures (digits) we have or are working with.

> Our results can only be as accurate as the least accurate piece of information.

Significant Figures

> The location of the decimal point has nothing to do with the determination of the number of significant figures.

> Zeros that merely indicate the magnitude of a number are not significant figures.

Example:

> The numbers 0.00406, 0.0406, 0.406, 4.06, 40.6 and 406 all have three significant figures.

> The zeros before the first non-zero digit are not significant as they only indicate the magnitude of the number.

> Zeros between non-zero digits are significant.

Example:

> In general, the trailing zeros are not significant.

> The number 4060 may or may not have four significant figures. Unless there is a reason for counting the last zero as significant, we would normally disregard it.

> If our measurements are only accurate to three significant figures, any digits after this are not significant.

Example Calculation:

> Depending on our measuring device, we may be able to read to 0.5 mm, such variations may occur as above.

> Since our initial data (in red) has only two significant figures, our result has only two significant figures. The slide rule will give the appropriate result quickly.