Formatting of Answers to Homework/Quizzes/Tests

The following describes the standards for providing written numerical answers to questions in this class.

Exact vs. Approximate answers.

In mathematics, all answers may be exact or approximate. In science, social science and engineering all measurements others than counts (eg. 1, 2, 3, ...) are approximate.

Exact Answers

In this class, you should assume that if in the statement of a problem you do not see a decimal point, there is no mention of rounding, all arguments to trig functions can be expressed exactly and the problem does not clearly involve measurement, then you are expected to provide an exact answer. For example:

(15+5)/6 = ?

This problem has no decimal points. Please execute all operators (do all addition, subtraction, multiplication, roots) but keep the answer exact. With non-integer results, fractions are preferred. Improper fractions are preferred over mixed numbers. So as an answer to this problem from worst to best:

(15+5)/6 = 3.33 !Wrong

(15+5)/6 = 2 1/3 Correct but please avoid mixed numbers.

(15+5)/6 = 20/6 Correct but could be reduced more.

(15+5)/6 = 10/3 Correct and in the best form!

Example 2:

4/16 =

4/16 = .25 Correct but for an exact answer, a fraction is preferred.

4/16 = 2/8 Correct but could be reduced more.

4/16 = 1/4 Correct and in best form!

Note all symbolic numbers such as π should be left as a symbolic number. Likewise irrational roots such as the square root of 2 should be left symbolically. Combining and reducing radicals when possible is preferred. I don't care if you leave a radical in the denominator of a fraction or not, although you should know that some teachers may prefer you do not do this.

Note: all of the correct answers above will be accepted with full credit.

Approximate answers

For any problem in this class in which one or more of the values that you use to find the answer are listed with a decimal point, then an approximate answer written as an integer, a decimal number or a number in scientific notation will be accepted. If there are special instructions such as "Round to 2 decimal places", please follow these instructions. If no instructions are provided, you are encouraged to use common sense and the rules of significant figures. These rules are well described in this Wikipedia article

Significant Figures

and I suggest you read it over. This treatment of numbers is important in science, the social sciences and in engineering. I will be tolerant of these kinds of errors, but I may point them out to you when I see them. If you correctly show an answer using a bar over the last significant figure, I will be impressed, although it won't affect your grade.

Example 3:

4.5/7.0 = ?

4.5/7.0 = 9/14 Correct but there is no reason to be exact here by leaving the number as a fraction

4.5/7.0 = .64285 Correct but too many significant figures

4.5/7.0 = 0.64 or .64 or 6.4E-1 or 6.4 x 10