M1410P02

# M1410P02 - (Preliminaries Basic Algebra P.13 PRELIMINARY...

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(Preliminaries: Basic Algebra) P.13 PRELIMINARY TOPIC: BASIC ALGEBRA ( APPENDIX A ) Why bother? Calculus students often make many algebra errors! Review Appendix A as necessary. I will cover a selection of topics. TOPIC 1: ROUNDING Example The “ ” symbol means “is approximately equal to” or “is about.” For example, the number π 3.14159 . π rounded off to the nearest … … integer is: 3 … tenth (i.e., to one decimal place) is: 3.1 … hundredth (i.e., to two decimal places) is: 3.14 … thousandth (i.e., to three decimal places) is: 3.142 Note: Remember that π 3.14159 . We say that the “1” in the third decimal place of π has been rounded up to “2.” This is because the digit in the next decimal place is 5 or higher. Outside the U.S., there may be different rules if that digit is a “5.”

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(Preliminaries: Basic Algebra) P.14 To count decimal places, count all digits to the right of the decimal point, “.” To count significant digits (or figures), locate the leftmost nonzero digit, and count it and all digits to the right of it. Example 70.1230 This is written out to four decimal places. We count the four digits after the decimal point. This is written out to six significant digits. We include the two digits to the left of the decimal point. The “0” at the end indicates that we claim accuracy to four decimal places. Writing “70.123” would not have had that effect. We call 70 the integer part of this decimal. Example 0.001020, or .001020 Whenever 0 is the integer part, it is optional to write it. These are written out to six decimal places. We count all six digits after the decimal point, including the “leading zeros” after the decimal point and before the “1,” the leftmost nonzero digit. These are written out to four significant digits. We do not include the leading zeros, but we include the “1” and all digits after the “1.”
(Preliminaries: Basic Algebra) P.15 Example 70.001 This is written out to three decimal places. This is written out to five significant digits. Because the integer part is not 0, we count all digits, including any zeros to the left of the decimal point. We will never write something like 070.001, for example. Word Problems Depending on the nature of a word problem, decimal answers may need to be rounded down, rounded up, or rounded off. Remember to write down any appropriate units such as feet, pounds, etc. as part of your answer. Exact vs. Approximate Answers Unless other instructions are given, your math instructors will typically expect you to give exact answers to problems, with the exception of some word problems. For example, if the answer to a problem is π , you should write π and not some decimal approximation such as 3.14. Other expressions such as ln5 and sin37 , which we will study later, should be handled similarly.

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