Today’s topics:
• The names of some important sets of numbers (more on this later)
• Properties of exponents (review from previous math courses)
• Defining 0 exponent and negative exponent
• Simplifying expressions involving exponents, using those properties and definitions
In the textbook, we discussed Examples 1-4 of section 4.1
We begin by defining some important sets of numbers (some you may have seen before):
the Natural numbers
the Whole numbers (which include the Natural numbers)
the Integers (which include the Whole numbers)
the Rational numbers (which include the Integers)
If we think of “number” as a directed distance from 0 on the number line, then the points on the number line correspond to these numbers we have defined so far. But it turns out that there are ponts (distances) which cannot be represented as a ratio of integers. We call these numbers Irrational numbers.
My notes on the properties of exponents are linked on the Documents page here. (So far we have only discussed the first two pages of this.) It’s important to make sure that you familiarize yourself with these properties and that you use them correctly. Have these notes at hand when you work the problems.
Homework:
• Find and deal with your City Tech email: you must use this email address in WeBWorK!
Do not try log in to WeBWorK or Piazza yet – it is not set up. I will put up a separate post when they are ready for you to log in.
Note: there are some students whose city tech email addresses I do not have: listed below. Please, these students, send me an email from your city tech email address as soon as possible so I can set up WeBWorK. You may send it to either of the email addresses listed on the course information sheet I handed out in class.
Students whose city tech email I do not have:
Elie,DorothyOK
Lopez, FrankOK
Metovic, Edin
Smith-davila, JacquelineOK
• Review the names of the important sets of numbers. You must be able to use these words correctly and understand them when they are used.
• Review the definitions and properties of exponents.
• Review the examples we discussed in class. Make sure that you see how the properties of exponents are being used at each step. Pay attention to parentheses and what they are telling you about the order of operations.
• Do the assigned problems from the Course Outline from p.321 up to #47 only. (the first set of exercises, from section 4.1) Please note: if a problem has no work to show and the answer is in the back of the textbook, it may not be put on the board, unless you disagree with the answer. In general, only problems that have work that you can show may be put on the board.
