CHAPTER 5 Decimal Notation Slide 2Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 5.1Decimal Notation, Order, and Rounding 5.2Addition and Subtraction of Decimals 5.3Multiplication of Decimals 5.4Division of Decimals 5.5Using Fraction Notation with Decimal Notation 5.6Estimating 5.7Solving Equations 5.8Applications and Problem Solving

OBJECTIVES 5.5 Using Fraction Notation with Decimal Notation Slide 3Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. aUse division to convert fraction notation to decimal notation. bRound numbers named by repeating decimals. cConvert certain fractions to decimal notation by using equivalent fractions. dSimplify expressions that contain both fraction and decimal notation.

5.5 Using Fraction Notation with Decimal Notation a Use division to convert fraction notation to decimal notation. Slide 4Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Now that we know how to divide using decimal notation, we can express any fraction as a decimal. This means that any rational number (ratio of integers) can be written as a decimal.

5.5 Using Fraction Notation with Decimal Notation a Use division to convert fraction notation to decimal notation. Slide 5Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 5.5 Using Fraction Notation with Decimal Notation a Use division to convert fraction notation to decimal notation. 1 Slide 6Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 5.5 Using Fraction Notation with Decimal Notation a Use division to convert fraction notation to decimal notation. 1 Slide 7Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

5.5 Using Fraction Notation with Decimal Notation a Use division to convert fraction notation to decimal notation. Slide 8Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. When division with decimals ends, or terminates,the result is called a terminating decimal. If the division does not terminate, the result will be a repeating decimal.

EXAMPLE 5.5 Using Fraction Notation with Decimal Notation a Use division to convert fraction notation to decimal notation. 3 Slide 9Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 5.5 Using Fraction Notation with Decimal Notation a Use division to convert fraction notation to decimal notation. 3 Slide 10Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Since 2 keeps reappearing as a remainder, the digits repeat and will continue to do so; therefore, When there is a repeating pattern, the dots are often replaced by a bar to indicate the repeating part, in this case, only the 3.

Title 5.5 Using Fraction Notation with Decimal Notation Slide 11Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. For a fraction in simplified form, if the denominator has a prime factor other than 2 or 5, the decimal notation repeats. if the denominator has no prime factor other than 2 or 5, the decimal notation terminates.

EXAMPLE 5.5 Using Fraction Notation with Decimal Notation a Use division to convert fraction notation to decimal notation. 5 Slide 12Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Because 7 is not a product of 2’s and/or 5’s, we expect a repeating decimal.

EXAMPLE 5.5 Using Fraction Notation with Decimal Notation a Use division to convert fraction notation to decimal notation. 5 Slide 13Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

5.5 Using Fraction Notation with Decimal Notation b Round numbers named by repeating decimals. Slide 14Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. In applied problems, repeating decimals are rounded to get approximate answers. To round a repeating decimal, we can extend the decimal notation at least one place past the rounding digit and then round as before.

EXAMPLE 5.5 Using Fraction Notation with Decimal Notation b Round numbers named by repeating decimals. Slide 15Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Round each to the nearest tenth, hundredth, and thousandth.

EXAMPLE 5.5 Using Fraction Notation with Decimal Notation b Round numbers named by repeating decimals. 9Gas Mileage. Slide 16Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. A car travels 457 mi on 16.4 gal of gasoline. The ratio of number of miles driven to amount of gasoline used is gas mileage. Find the gas mileage and convert the ratio to decimal notation rounded to the nearest tenth.

5.5 Using Fraction Notation with Decimal Notation c Convert certain fractions to decimal notation by using equivalent fractions. Slide 17Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. When a denominator is a factor of 10, 100, and so on, we can convert to decimal notation by finding (perhaps mentally) an equivalent fraction in which the denominator is a power of 10.

EXAMPLE 5.5 Using Fraction Notation with Decimal Notation c Convert certain fractions to decimal notation by using equivalent fractions. 10 Slide 18Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 5.5 Using Fraction Notation with Decimal Notation c Convert certain fractions to decimal notation by using equivalent fractions. 12 Slide 19Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

5.5 Using Fraction Notation with Decimal Notation d Simplify expressions that contain both fraction and decimal notation. Slide 20Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. In certain kinds of calculations, fraction and decimal notation might occur together. In such cases, there are at least three ways in which we can proceed.

EXAMPLE 5.5 Using Fraction Notation with Decimal Notation d Simplify expressions that contain both fraction and decimal notation. 13 Slide 21Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Perhaps the quickest method is to treat as

EXAMPLE 5.5 Using Fraction Notation with Decimal Notation d Simplify expressions that contain both fraction and decimal notation. 13 Slide 22Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. A second way to do this calculation is to convert the fraction notation to decimal notation so that both numbers are in decimal notation.

EXAMPLE 5.5 Using Fraction Notation with Decimal Notation d Simplify expressions that contain both fraction and decimal notation. 13 Slide 23Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. A third method is to convert the decimal notation to fraction notation so that both numbers are in fraction notation.

EXAMPLE 5.5 Using Fraction Notation with Decimal Notation d Simplify expressions that contain both fraction and decimal notation. 13 Slide 24Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 5.5 Using Fraction Notation with Decimal Notation d Simplify expressions that contain both fraction and decimal notation. 14Boating. Slide 25Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. A triangular sail from a single-sail day cruiser is 3.4 m wide and 4.2 m tall. Find the area of the sail.

EXAMPLE 5.5 Using Fraction Notation with Decimal Notation d Simplify expressions that contain both fraction and decimal notation. 14Boating. Slide 26Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 1. Familiarize. We make a drawing and recall that the formula for the area, A, of a triangle with base b and height h is

EXAMPLE 5.5 Using Fraction Notation with Decimal Notation d Simplify expressions that contain both fraction and decimal notation. 14Boating. Slide 27Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 2. Translate.3. Solve.

EXAMPLE 5.5 Using Fraction Notation with Decimal Notation d Simplify expressions that contain both fraction and decimal notation. 14Boating. Slide 28Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 4. Check. To check, we repeat the calculations using the commutative law. 5. State. The area of the sail is 7.14 m 2 (square meters). Our answer checks.