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Significant Digit Accountability For Exponentiation, Trigonometric, And Logarithmic Operations

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2001 Annual Conference


Albuquerque, New Mexico

Publication Date

June 24, 2001

Start Date

June 24, 2001

End Date

June 27, 2001



Page Count


Page Numbers

6.875.1 - 6.875.6

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John Barrett Crittenden

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NOTE: The first page of text has been automatically extracted and included below in lieu of an abstract

Session 3553

Significant Digit Accountability for Exponentiation, Trigonometric, and Logarithmic Operations John Barrett Crittenden Virginia Polytechnic Institute and State University


Freshman engineering students are typically exposed to a number of elementary subjects during their first semester or quarter. One topic introduced to new engineering students is associated with the number of significant digits to be used for the final answer of a typical engineering problem. Elementary engineering texts often cover the topic as it relates to addition, subtraction, multiplication, and division. However, rules associated with exponentiation, trigonometric function use, and the use of logarithms are not included in these introductory texts, or in any other texts. The application of significant digit practices is proposed as it pertains to trigonometric function use as well as logarithmic and exponentiation operations.

I. Introduction

Each fall thousands of freshman engineering students are introduced to the engineering profession by taking courses that include a potpourri of topics, including the proper accountability of significant digits. Texts1,2,3,4,5 used for introductory courses often include a section on the procedures to follow for reading measuring devices and for displaying the appropriate number of significant digits in the final answer of an engineering problem. This paper does not argue the importance of reading scaling devices appropriately, but does question the necessity of teaching the rules given to account for significant digits in the elementary arithmetic operations of addition, subtraction, multiplication, and division.

The purpose of introducing students to the concept of significant digit accountability when solving an engineering problem is to ensure that they display a meaningful final answer when using a hand-held calculator or other computing device for solving a problem. Often new engineering students will write the eight or ten digit calculator or computer display when indicating the answer to an assigned problem. Instructors thus feel obligated to cover the topic of significant digit accountability.

The rules often presented to address significant digit accountability are directed toward the elementary mathematical operations of addition, subtraction, multiplication, and division. Eide states for multiplication and division:

“The product or quotient should contain the same number of significant digits as are contained in the number with the fewest significant digits.”3

For addition and subtraction, Eide also states:

Proceedings of the 2001 American Society for Engineering Education Annual Conference & Exposition Copyright  2001, American Society for Engineering Education

Crittenden, J. B. (2001, June), Significant Digit Accountability For Exponentiation, Trigonometric, And Logarithmic Operations Paper presented at 2001 Annual Conference, Albuquerque, New Mexico.

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