Whole Numbers CHAPTER 1 1.1 Standard Notation; Order 1.2 Addition and Subtraction 1.3 Multiplication and Division; Rounding and Estimation 1.4 Solving Equations 1.5 Applications and Problem Solving 1.6 Exponential notation and Order of Operations 1.7 Factorizations 1.8 Divisibility

1.9 Least Common Multiples Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 2 1.1 Standard Notation; Order OBJECTIVES a Give the meaning of digits in standard notation. b Convert from standard notation to expanded notation. c Convert between standard notation and word names.

d Use < or > for to write a true statement in a situation like 6 10. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 3 1.1 Standard Notation; Order a Give the meaning of digits in standard notation. 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. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 4 1.1 Standard Notation; Order a Give the meaning of digits in standard notation.

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 5 1.1 Standard Notation; Order a Give the meaning of digits in standard notation. EXAMPLE 1 In each of the following numbers, what does the digit 8 mean?

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

Slide 7 1.1 Standard Notation; Order a Give the meaning of digits in standard notation. EXAMPLE 7 Hurricane Relief. 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? Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 8 1.1 Standard Notation; Order b Convert from standard notation to expanded notation. 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. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 9 1.1 Standard Notation; Order b Convert from standard notation to expanded notation.

Consider the data in the table below showing the Advanced Placement exams taken most frequently by the class of 2007. The number of Biology exams taken was 144,796. This number is expressed in standard notation. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 10 1.1 Standard Notation; Order

b Convert from standard notation to expanded notation. We write expanded notation for 144,796 as follows: Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 11 1.1 Standard Notation; Order b Convert from standard notation to expanded notation. EXAMPLE 10 Expanded Notation Write expanded notation for 211,693, the number of

Advanced Placement Calculus exams taken by the class of 2007. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 12 1.1 Standard Notation; Order c Convert between standard notation and word names. 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. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 13 1.1 Standard Notation; Order c Convert between standard notation and word names. EXAMPLE

Word Names Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 14 1.1 Standard Notation; Order c Convert between standard notation and word names. 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. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 15 1.1 Standard Notation; Order c Convert between standard notation and word names.

EXAMPLE 14 Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 16 1.1 Standard Notation; Order c Convert between standard notation and word names. 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, 317.4 is read as three hundred seventeen and four tenths. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 17 1.1 Standard Notation; Order c Convert between standard notation and word names. EXAMPLE 15 Write standard notation. Five hundred six million, three hundred forty-five

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

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 19 1.1 d Standard Notation; Order Use < or > for to write a true statement in a situation like 6 10. 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. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 20 1.1 d Standard Notation; Order Use < or > for to write a true statement in a situation like 6 10.

We can see this order on the number line: 2 is to the left of 5. The number 0 is the smallest whole number. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 21 1.1 Standard Notation; Order Order of Whole Numbers d

Use < or > for to write a true statement in a situation like 6 10. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 22 1.1 d Standard Notation; Order Use < or > for to write a true statement in a situation like 6

10. EXAMPLE 17 Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 23 1.1 d Standard Notation; Order Use < or > for to write a true statement in a situation like 6

10. A sentence like 8 + 5 = 13 is called an equation. It is a true equation. The equation 4 + 8 = 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. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 24