2.1 The real #s and absolute value Objective: Compare real numbers. Standards Addressed: 2.1.8.C: Distinguish between and order rational and irrational numbers. 2.1.8.F: Use the number line model to demonstrate integers and their applications.

The real numbers: Natural numbers (N) 1, 2, 3, …. Whole numbers (W) 0, 1, 2, 3, …. Integers (Z) …, -3, -2, -1, 0, 1, 2, 3, … Rational numbers (Q) p/q, where p and q are integers and q ≠ 0. Terminating (2.77) & repeating (1/3) Irrational numbers (I) #s whose decimal part doesn’t terminate or repeat (i.e. ∏ ) Real numbers (R) all rational & irrational #s

Ex.1 a. 0 b. ½ c. -8 d. 8 e. R, Q, Z, W R, Q R, Q, Z R, Q, Z, W, N R, I

Ex.2 Use division to write each rational # as a decimal & indicate whether the # is a terminating decimal or a repeating decimal. a. 4/5 Terminating b. 4/11 Repeating c. 5/8 Terminating d. 7/9 Repeating e. 5/12 Repeating f. ¾ Terminating

The Symbols Used to compare 2 Real #s are stated & Explained Below: < is less than or equal to > is greater than or equal to

Ex. 3

Opposites On the # line, 2 #s that lie on opposite sides of 0, and are the same distance from 0 are opposites. The opposite of a negative # is always a positive #. The opposite of zero is zero itself.

Ex. 4 EvaLUATE EACH EXPRESSION.

Ex. 5 ABSOLUTE VALUE 14.2 7 13