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 5.3 Multiplication of Decimals Slide 3Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. aMultiply using decimal notation. bConvert from notation like 45.7 million to standard notation and convert between dollars and cents. cEvaluate algebraic expressions using decimal notation.

5.3 Multiplication of Decimals a Multiply using decimal notation. Slide 4Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Note that the number of decimal places in the product is the sum of the numbers of decimal places in the factors. To develop an understanding of decimal multiplication, consider

Title 5.3 Multiplication of Decimals Slide 5Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. To multiply using decimal notation: a) Ignore the decimal points, for the moment, and multiply as though both factors were integers. b) Place the decimal point in the result. The number of decimal places in the product is the sum of the numbers of places in the factors. Count the number of decimal places by starting at the far right and moving the decimal point to the left.

Title 5.3 Multiplication of Decimals Slide 6Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 5.3 Multiplication of Decimals a Multiply using decimal notation. 3 Slide 7Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Since the product of a negative number and a positive number is negative, the answer is –

5.3 Multiplication of Decimals a Multiply using decimal notation. Slide 8Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. We may need to write extra zeros when locating the decimal point.

EXAMPLE 5.3 Multiplication of Decimals a Multiply using decimal notation. 4 Slide 9Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

Suppose that a product involves multiplying by a tenth, hundredth, thousandth, or ten-thousandth. We can see a pattern in the following products. Note in each case that the product is smaller than That is, the decimal point in each product is farther to the left than it is in Note also that each product can be obtained from 45.6 by moving the decimal point. 5.3 Multiplication of Decimals a Multiply using decimal notation. Slide 10Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

Title 5.3 Multiplication of Decimals Slide 11Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. To multiply any number by 0.1, 0.01, 0.001, and so on: a) count the number of decimal places in the tenth, hundredth, thousandth, and so on, and b) move the decimal point in the other number that many places to the left. Use zeros as placeholders when necessary.

Title 5.3 Multiplication of Decimals Slide 12Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 5.3 Multiplication of Decimals a Multiply using decimal notation. Slide 13Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Multiply.

5.3 Multiplication of Decimals a Multiply using decimal notation. Slide 14Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Next we consider multiplying by 10, 100, 1000, and so on. We see a pattern in the following.

5.3 Multiplication of Decimals a Multiply using decimal notation. Slide 15Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Note in each case that the product is larger than That is, the decimal point in each product is farther to the right than the decimal point in Also, each product can be obtained from by moving the decimal point.

Title 5.3 Multiplication of Decimals Slide 16Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. To multiply any number by 10, 100, 1000, and so on: a) count the number of zeros and b) move the decimal point in the other number that many places to the right. Use zeros as placeholders when necessary.

Title 5.3 Multiplication of Decimals Slide 17Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 5.3 Multiplication of Decimals a Multiply using decimal notation. Slide 18Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Multiply.

5.3 Multiplication of Decimals NAMING LARGE NUMBERS Slide 19Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

5.3 Multiplication of Decimals NAMING LARGE NUMBERS Slide 20Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 5.3 Multiplication of Decimals b Convert from notation like 45.7 million to standard notation and convert between dollars and cents. 13 Slide 21Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. U.S. movie theaters sold 1.42 billion tickets in Convert 1.42 billion to standard notation. Source: Nash Information Services

5.3 Multiplication of Decimals b Convert from notation like 45.7 million to standard notation and convert between dollars and cents. Slide 22Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Converting from dollars to cents is like multiplying by 100. To see why, consider $19.43.

Title 5.3 Multiplication of Decimals Slide 23Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. To convert from dollars to cents, move the decimal point two places to the right and change the $ sign in front to a ¢ sign at the end.

EXAMPLE 5.3 Multiplication of Decimals b Convert from notation like 45.7 million to standard notation and convert between dollars and cents. Slide 24Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Convert from dollars to cents

5.3 Multiplication of Decimals b Convert from notation like 45.7 million to standard notation and convert between dollars and cents. Slide 25Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Converting from cents to dollars is like multiplying by To see why, consider 65.

Title 5.3 Multiplication of Decimals Slide 26Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. To convert from cents to dollars, move the decimal point two places to the left and change the ¢ sign at the end to a $ sign in front.

EXAMPLE 5.3 Multiplication of Decimals b Convert from notation like 45.7 million to standard notation and convert between dollars and cents. Slide 27Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Convert from cents to dollars.

5.3 Multiplication of Decimals c Evaluate algebraic expressions using decimal notation. Slide 28Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Algebraic expressions are often evaluated using numbers written in decimal notation.

EXAMPLE 5.3 Multiplication of Decimals c Evaluate algebraic expressions using decimal notation. 19 Slide 29Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Find the perimeter of a stamp that is 3.25 cm long and 2.5 cm wide. Recall that the perimeter, P, of a rectangle of length l and width w is given by the formula

EXAMPLE 5.3 Multiplication of Decimals c Evaluate algebraic expressions using decimal notation. 19 Slide 30Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.