CHAPTER 1 Whole Numbers Slide 2Copyright 2012, 2008, 2004, 2000 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 1.6 Rounding and Estimating; Order Slide 3Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. aRound to the nearest ten, hundred, or thousand. bEstimate sums, differences, products, and quotients by rounding. cUse for to write a true sentence in a situation like 6 10.

1.6 Rounding and Estimating; Order a Round to the nearest ten, hundred, or thousand. Slide 4Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. We round numbers in various situations when we do not need an exact answer.

EXAMPLE 1.6 Rounding and Estimating; Order a Round to the nearest ten, hundred, or thousand. 1 Slide 5Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Round 47 to the nearest ten. 47 is between 40 and 50. Since 47 is closer to 50, we round up to 50.

EXAMPLE 1.6 Rounding and Estimating; Order a Round to the nearest ten, hundred, or thousand. 2 Slide 6Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Round 42 to the nearest ten. 42 is between 40 and 50. Since 42 is closer to 40, we round down to 40.

EXAMPLE 1.6 Rounding and Estimating; Order a Round to the nearest ten, hundred, or thousand. 3 Slide 7Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Round 45 to the nearest ten. 45 is halfway between 40 and 50. We could round 45 down to 40 or up to 50. We agree to round up to 50.

Title 1.6 Rounding and Estimating; Order Slide 8Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. When a number is halfway between rounding numbers, round up.

Title 1.6 Rounding and Estimating; Order Slide 9Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. To round to a certain place: a) Locate the digit in that place. b) Consider the next digit to the right. c) If the digit to the right is 5 or higher, round up. If the digit to the right is 4 or lower, round down. d) Change all digits to the right of the rounding location to zeros.

EXAMPLE 1.6 Rounding and Estimating; Order a Round to the nearest ten, hundred, or thousand. 5 Slide 10Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Round 6485 to the nearest hundred. a) Locate the digit in the hundreds place, 4. b) Consider the next digit to the right, 8.

EXAMPLE 1.6 Rounding and Estimating; Order a Round to the nearest ten, hundred, or thousand. 5 Slide 11Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. c) Since that digit, 8, is 5 or higher, round 4 hundreds up to 5 hundreds. d) Change all digits to the right of hundreds to zeros.

EXAMPLE 1.6 Rounding and Estimating; Order a Round to the nearest ten, hundred, or thousand. 6 Slide 12Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Round 6485 to the nearest thousand. a) Locate the digit in the thousands place, 6. b) Consider the next digit to the right, 4.

EXAMPLE 1.6 Rounding and Estimating; Order a Round to the nearest ten, hundred, or thousand. 6 Slide 13Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. c) Since that digit, 4, is 4 or lower, round down, meaning that 6 thousands stays as 6 thousands. d) Change all digits to the right of thousands to zeros.

1.6 Rounding and Estimating; Order a Round to the nearest ten, hundred, or thousand. Slide 14Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Sometimes rounding involves changing more than one digit in a number.

EXAMPLE 1.6 Rounding and Estimating; Order a Round to the nearest ten, hundred, or thousand. 7 Slide 15Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Round 78,595 to the nearest ten. a) Locate the digit in the tens place, 9. b) Consider the next digit to the right, 5.

EXAMPLE c) Since that digit, 5, is 5 or higher, round 9 tens to 10 tens. To carry this out, we think of 10 tens as 1 hundred + 0 tens and increase the hundreds digit by 1, to get 6 hundreds + 0 tens. We then write 6 in the hundreds place and 0 in the tens place. d) Change the digit to the right of the tens digit to zero. Note that if we round this number to the nearest hundred, we get the same answer. 1.6 Rounding and Estimating; Order a Round to the nearest ten, hundred, or thousand. 7 Slide 16Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

1.6 Rounding and Estimating; Order b Estimate sums, differences, products, and quotients by rounding. Slide 17Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Estimating can be done in many ways. In general, an estimate made by rounding to the nearest ten is more accurate than one rounded to the nearest hundred, and an estimate rounded to the nearest hundred is more accurate than one rounded to the nearest thousand, and so on.

EXAMPLE 1.6 Rounding and Estimating; Order b Estimate sums, differences, products, and quotients by rounding. 10 Slide 18Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Estimate the following product by first rounding to the nearest ten and then to the nearest hundred:

EXAMPLE 1.6 Rounding and Estimating; Order b Estimate sums, differences, products, and quotients by rounding. 10 Slide 19Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. We see that rounding to the nearest ten gives a better estimate than rounding to the nearest hundred.

1.6 Rounding and Estimating; Order b Estimate sums, differences, products, and quotients by rounding. Slide 20Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. When we round to make an estimate, the outcome is rarely the same as the exact result. Thus we cannot use an equals sign when we round. Instead, we use the symbol This symbol means “is approximately equal to.”

EXAMPLE 1.6 Rounding and Estimating; Order b Estimate sums, differences, products, and quotients by rounding. 12Microwave Ovens. Slide 21Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Ellen manages a small apartment building and is planning to purchase a new over-the-range microwave oven for each of the 12 units in the building. One model that she is considering costs $248. Estimate, by rounding to the nearest ten, the total cost of the purchase.

EXAMPLE 1.6 Rounding and Estimating; Order b Estimate sums, differences, products, and quotients by rounding. 12Microwave Ovens. Slide 22Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

1.6 Rounding and Estimating; Order c Use for to write a true sentence in a situation like Slide 23Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

1.6 Rounding and Estimating; Order ORDER OF WHOLE NUMBERS Slide 24Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 1.6 Rounding and Estimating; Order c Use for to write a true sentence in a situation like Slide 25Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

1.6 Rounding and Estimating; Order c Use for to write a true sentence in a situation like Slide 26Copyright 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 69 is a false inequality.