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

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 1.1 Standard Notation 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. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 3

1.1 Standard Notation Digit A number 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9 Give the meaning of digits in standard notation. Digit A number 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9 that names a place-value location. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 4

1.1 Standard Notation a period Give the meaning of digits in standard notation. period Digits separated into groups of three by commas Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 5

1.1 Place Value Each period has a name: Give the meaning of digits in standard notation. Each period has a name: ones, thousands, millions, billions, trillions, etc. PLACE-VALUE CHART Trillions Billions Millions Thousands Ones Hundred Ten One Hundred Ten One Hundred Ten One Hundred Ten One Hundreds Tens Ones

1.1 Place Value a PLACE-VALUE CHART 9 5 2 Give the meaning of digits in standard notation. PLACE-VALUE CHART Trillions Billions Millions Thousands Ones 9 5 2 Hundred Ten One Hundred Ten One Hundred Ten One Hundred Ten One Hundreds Tens Ones 952 ones 952 ones

1.1 Place Value a PLACE-VALUE CHART 2 4 5 8 4 2 8 1 5 4 8 , , , Give the meaning of digits in standard notation. PLACE-VALUE CHART Trillions Billions Millions Thousands Ones 2 4 5 8 4 2 8 1 5 4 8 Hundred Ten One Hundred Ten One Hundred Ten One Hundred Ten One Hundreds Tens Ones 245 s , 840 s , s , 281 ones billion million thousand 548

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 1.1 Standard Notation a Give the meaning of digits in standard notation. In each of the following numbers, what does the digit 8 mean? 8 thousands 8 hundred thousands 8 billions 8 hundreds 8 millions 8 ones Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 9

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 1.1 Standard Notation a Give the meaning of digits in standard notation. 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? 9 ones 7 tens 8 hundreds 5 thousands 8 ten thousands 1 hundred thousands 8 millions 7 ten millions 3 hundred millions 3 billions Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 10

1.1 Standard Notation b When most of us started using numbers Convert from standard notation to expanded notation. When most of us started using numbers we started with the counting numbers. What number do you start counting with? 1,2,3,4,5,6,7,… In math, these are called the natural numbers. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 11

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 1.1 Standard Notation 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. Whole numbers are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ,11, … The set goes on indefinitely. There is no largest whole number, and the smallest whole number is 0. How are whole numbers different from natural numbers? Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 12

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 1.1 Standard Notation 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 13

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 1.1 Standard Notation b Convert from standard notation to expanded notation. Standard notation is how we usually write numbers. Expanded notation for 144,796 is as follows: Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 14

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 1.1 Standard Notation b Convert from standard notation to expanded notation. 10 Expanded Notation Write expanded notation for 273,691, the number of Advanced Placement Calculus exams taken by the class of 2009. 273,691 = 2 hundred thousand + 7 ten thousand + 3 thousand + 6 hundred + 9 tens + 1 one Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 15

1.1 Standard Notation c We often use word names for numbers. 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 16

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 1.1 Standard Notation c Convert between standard notation and word names. Word Names Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 17

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 1.1 Standard Notation 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 18

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 1.1 Standard Notation c Convert between standard notation and word names. 14 Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 19

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 1.1 Standard Notation c Convert between standard notation and word names. The word “and” should not appear in word names for whole numbers. Although we commonly hear such expressions as “two hundred and one,” the use of “and” is not correct 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 20

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 1.1 Standard Notation c Convert between standard notation and word names. 15 Write standard notation. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 21