CHAPTER 1 Whole Numbers Slide 2Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 1.1Standard Notation; Order 1.2Addition and Subtraction 1.3Multiplication and Division; Rounding and Estimation 1.4Solving Equations 1.5Applications and Problem Solving 1.6Exponential notation and Order of Operations 1.7Factorizations 1.8Divisibility 1.9Least Common Multiples

OBJECTIVES 1.1 Standard Notation; Order Slide 3Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. aGive the meaning of digits in standard notation. bConvert from standard notation to expanded notation. cConvert between standard notation and word names. dUse for  to write a true statement in a situation like 6  10.

1.1 Standard Notation; Order a Give the meaning of digits in standard notation. Slide 4Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. A digit is a number 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9 that names a place-value location. For large numbers, digits are separated by commas into groups of three, called periods. Each period has a name: ones, thousands, millions, billions, trillions, and so on.

1.1 Standard Notation; Order a Give the meaning of digits in standard notation. Slide 5Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 1.1 Standard Notation; Order a Give the meaning of digits in standard notation. 1 Slide 6Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. In each of the following numbers, what does the digit 8 mean?

EXAMPLE 1.1 Standard Notation; Order a Give the meaning of digits in standard notation. Slide 7Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. In each of the following numbers, what does the digit 8 mean?

EXAMPLE 1.1 Standard Notation; Order a Give the meaning of digits in standard notation. 7Hurricane Relief. Slide 8Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Private donations for relief for Hurricanes Katrina and Rita, which struck the Gulf Coast of the United States in 2005, totaled $3,378,185,879. What does each digit name?

1.1 Standard Notation; Order b Convert from standard notation to expanded notation. Slide 9Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. To answer questions such as “How many?”, “How much?”, and “How tall?”, we often use whole numbers. The set, or collection, of whole numbers is 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,11, 12, … The set 1, 2, 3, 4, 5…, without 0, is called the set of natural numbers.

1.1 Standard Notation; Order b Convert from standard notation to expanded notation. Slide 10Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Consider the data in the table below showing the Advanced Placement exams taken most frequently by the class of The number of Biology exams taken was 144,796. This number is expressed in standard notation.

1.1 Standard Notation; Order b Convert from standard notation to expanded notation. Slide 11Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. We write expanded notation for 144,796 as follows:

EXAMPLE 1.1 Standard Notation; Order b Convert from standard notation to expanded notation. 10Expanded Notation Slide 12Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Write expanded notation for 211,693, the number of Advanced Placement Calculus exams taken by the class of 2007.

1.1 Standard Notation; Order c Convert between standard notation and word names. Slide 13Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. We often use word names for numbers. When we pronounce a number, we are speaking its word name. Russia won 72 medals in the 2008 Summer Olympics in Beijing, China. A word name for 72 is “seventy-two.”

EXAMPLE 1.1 Standard Notation; Order c Convert between standard notation and word names. Word Names Slide 14Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

1.1 Standard Notation; Order c Convert between standard notation and word names. Slide 15Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. For word names for larger numbers, we begin at the left with the largest period. The number named in the period is followed by the name of the period; then a comma is written and the next number and period are named. Note that the name of the ones period is not included in the word name for a whole number.

EXAMPLE 1.1 Standard Notation; Order c Convert between standard notation and word names. 14 Slide 16Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

1.1 Standard Notation; Order c Convert between standard notation and word names. Slide 17Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. The word “and” should not appear in word names for whole numbers. For decimal notation, it is appropriate to use “and” for the decimal point. For example, is read as “three hundred seventeen and four tenths.”

EXAMPLE 1.1 Standard Notation; Order c Convert between standard notation and word names. 15 Slide 18Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Write standard notation. Five hundred six million, three hundred forty-five thousand, two hundred twelve

EXAMPLE 1.1 Standard Notation; Order c Convert between standard notation and word names. 15 Slide 19Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Write standard notation.

1.1 Standard Notation; Order d Use for  to write a true statement in a situation like 6  10. Slide 20Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. We know that 2 is not the same as 5. We express this by the sentence 2 ≠ 5. We also know that 2 is less than 5. We symbolize this by the expression 2 < 5.

1.1 Standard Notation; Order d Use for  to write a true statement in a situation like 6  10. Slide 21Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. We can see this order on the number line: 2 is to the left of 5. The number 0 is the smallest whole number.

1.1 Standard Notation; Order Order of Whole Numbers Slide 22Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 1.1 Standard Notation; Order d Use for  to write a true statement in a situation like 6  Slide 23Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

1.1 Standard Notation; Order d Use for  to write a true statement in a situation like 6  10. Slide 24Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. A sentence like = 13 is called an equation. It is a true equation. The equation = 11 is a false equation. A sentence like 7 < 11 is called an inequality. The sentence 7 < 11 is a true inequality. The sentence 23 > 69 is a false inequality.