CHAPTER 1 Whole Numbers Slide 2Copyright 2011 Pearson Education, Inc. 1.1Standard Notation 1.2Addition 1.3Subtraction 1.4Multiplication 1.5Division 1.6Rounding and Estimating; Order 1.7Solving Equations 1.8Applications and Problem Solving 1.9Exponential Notation and Order of Operations

OBJECTIVES 1.9 Exponential Notation and Order of Operations Slide 3Copyright 2011 Pearson Education, Inc. aWrite exponential notation for products such as 4 ∙ 4 ∙ 4. bEvaluate exponential notation. cSimplify expressions using the rules for order of operations. dRemove parentheses within parentheses.

Exponential Notation The 5 is called an exponent. The 4 is the base. 1.9 Exponential Notation and Order of Operations a Write exponential notation for products such as 4 ∙ 4 ∙ 4. Slide 4Copyright 2011 Pearson Education, Inc.

EXAMPLE Solution Exponential notation is is the base. 6 is the exponent. 1.9 Exponential Notation and Order of Operations a Write exponential notation for products such as 4 ∙ 4 ∙ 4. A Write exponential notation for 7  7  7  7  7  7. Slide 5Copyright 2011 Pearson Education, Inc.

EXAMPLE Solution 84 = 8 ∙ 8 ∙ 8 ∙ 8 = 4, = 10 ∙ 10 ∙ 10 ∙ 10 = 10, Exponential Notation and Order of Operations b Evaluate exponential notation. BEvaluate: 8 4 and Slide 6Copyright 2011 Pearson Education, Inc.

Rules for Order of Operations 1. Do all calculations within parentheses ( ), brackets [ ], or braces { } before operations outside. 2. Evaluate all exponential expressions. 3. Do all multiplications and divisions in order from left to right. 4. Do all additions and subtractions in order from left to right. 1.9 Exponential Notation and Order of Operations c Simplify expressions using the rules for order of operations. Slide 7Copyright 2011 Pearson Education, Inc.

EXAMPLE Solution There are no parentheses or exponents, so we start with the third step. 24 ÷ 3 ∙ 4 = 8 ∙ 4 = 32 Doing all multiplications and divisions in order from left to right 1.9 Exponential Notation and Order of Operations c Simplify expressions using the rules for order of operations. CSimplify: 24 ÷ 3 ∙ 4. Slide 8Copyright 2011 Pearson Education, Inc.

EXAMPLE Solution 20 ÷ 4 ∙ 3 ÷ (10 – 7) = 20 ÷ 4 ∙ 3 ÷ 3 = 5 ∙ 3 ÷ 3 = 15 ÷ 3 = Exponential Notation and Order of Operations c Simplify expressions using the rules for order of operations. DSimplify: 20 ÷ 4 ∙ 3 ÷ (10 – 7). Slide 9Copyright 2011 Pearson Education, Inc.

EXAMPLE Simplify expressions using the rules for order of operations. Solution 1.9 Exponential Notation and Order of Operations c E Slide 10Copyright 2011 Pearson Education, Inc. Simplify:

The average of a set of numbers is the sum of the numbers divided by the number of addends. 1.9 Exponential Notation and Order of Operations Average Slide 11Copyright 2011 Pearson Education, Inc.

EXAMPLE Solution The average on Mason’s four tests is Exponential Notation and Order of Operations c Simplify expressions using the rules for order of operations. FMason has 4 math tests with scores of 76, 85, 92, and 91. Find the average of all four tests. Slide 12Copyright 2011 Pearson Education, Inc.

When parentheses occur within parentheses, we can make them different shapes, such as [ ] (also called “brackets”) and { } (also called “braces”). All of these have the same meaning. When parentheses occur within parentheses, computations in the innermost ones are to be done first. 1.9 Exponential Notation and Order of Operations d Remove parentheses within parentheses. Slide 13Copyright 2011 Pearson Education, Inc.

EXAMPLE Solution 1.9 Exponential Notation and Order of Operations d Remove parentheses within parentheses. GSimplify: Slide 14Copyright 2011 Pearson Education, Inc.