2. CHAPTER 3 Decimal Notation Slide 2Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 3.1Decimal Notation, Order, and Rounding 3.2Addition and Subtraction 3.3Multiplication 3.4Division 3.5Converting from Fraction Notation to Decimal Notation 3.6Estimating 3.7Applications and Problem Solving

3. OBJECTIVES 3.1 Decimal Notation, Order, and Rounding Slide 3Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. aGiven decimal notation, write a word name. bConvert between decimal notation and fraction notation. cGiven a pair of numbers in decimal notation, tell which is larger. dRound decimal notation to the nearest thousandth, hundredth, tenth, one, ten, hundred, or thousand.

4. 3.1 Decimal Notation, Order, and Rounding a Given decimal notation, write a word name. Slide 4Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

5. 3.1 Decimal Notation, Order, and Rounding Slide 5Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. thousandths

6. EXAMPLE 3.1 Decimal Notation, Order, and Rounding a Given decimal notation, write a word name. 1 Slide 6Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. a. Write a word name for 1788.045. Answer: One thousand, seven hundred eighty-eight and forty-five thousandths b. The life expectancy at birth in the U.S. is projected to be 79.2 years in 2015. Write the word name for 79.2 Answer: Seventy-nine and two tenths

7. 3.1 Decimal Notation, Order, and Rounding Slide 7Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

8. EXAMPLE 3.1 Decimal Notation, Order, and Rounding b Convert between decimal notation and fraction notation. 2 Slide 8Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. a. Write fraction notation for 0.876. Do not simplify. For a number like 0.876, we generally write a 0 before the decimal point to draw attention to the presence of the decimal point.

9. 3.1 Decimal Notation, Order, and Rounding Convert between decimal notation and fraction notation. Slide 9Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. b. Write fraction notation for 23.78. Do not simplify. c. Write fraction notation for 5.6789. Do not simplify.

10. 3.1 Decimal Notation, Order, and Rounding Slide 10Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. To convert from fraction notation to decimal notation when the denominator is 10, 100, 1000, and so on, a) count the number of zeros, and b) move the decimal point that number of places to the left. Leave off the denominator.

11. 3.1 Decimal Notation, Order, and Rounding Slide 11Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

12. EXAMPLE 3.1 Decimal Notation, Order, and Rounding b Convert between decimal notation and fraction notation. 3 Slide 12Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

13. 3.1 Decimal Notation, Order, and Rounding To convert from fraction notation to decimal notation when the denominator is 10, 100, 1000, and so on, Slide 13Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Write decimal notation Answer: 7.43 a.b. Answer: 6.7089 c. Answer: 0.0830

14. 3.1 Decimal Notation, Order, and Rounding b Convert between decimal notation and fraction notation. Slide 14Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. If a mixed numeral has a fractional part with a denominator that is a power of ten, such as 10, 100, or 1000, and so on, we first write the mixed numeral as a sum of a whole number and a fraction. Then we convert to decimal notation.

15. EXAMPLE 3.1 Decimal Notation, Order, and Rounding b Convert between decimal notation and fraction notation. 4 Slide 15Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

16. 3.1 Decimal Notation, Order, and Rounding Slide 16Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. To compare two numbers in decimal notation, start at the left and compare corresponding digits moving from left to right. If two digits differ, the number with the larger digit is the larger of the two numbers. To ease the comparison, extra zeros can be written to the right of the last decimal place.

17. EXAMPLE 3.1 Decimal Notation, Order, and Rounding c Given a pair of numbers in decimal notation, tell which is larger. 5 Slide 17Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

18. EXAMPLE 3.1 Decimal Notation, Order, and Rounding c Given a pair of numbers in decimal notation, tell which is larger. 6 Slide 18Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. a. Which of 2.04 and 2.039 is larger? Answer: 4>3, thus, 2.04 is larger than 2.039 b. Which of 21.006 and 21.05 is larger? Answer: 5>0, thus, 21.05 is larger than 21.006

19. 3.1 Decimal Notation, Order, and Rounding Slide 19Copyright 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.

20. EXAMPLE 3.1 Decimal Notation, Order, and Rounding d Round decimal notation to the nearest thousandth, hundredth, tenth, one, ten, hundred, or thousand. 7 Slide 20Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Round 3872.2459 to the nearest thousandth, hundredth, tenth, one, ten, hundred, and thousand.