4 Chapter Chapter 2 Decimals

Multiplying Decimals and Circumference of a Circle Section 4.3 Multiplying Decimals and Circumference of a Circle

Objective A Multiply Decimals.

Multiplying Decimals Multiplying decimals is similar to whole numbers. The only difference is that we place a decimal point in the product. Multiplying Decimals Step 1: Multiply the decimals as though they are whole numbers. Step 2: The decimal point in the product is placed so that the number of decimal places in the product is equal to the sum of the number of decimal place in the factors. Objective A

Multiplying Decimals Step Example Step 1: Multiply the decimals as though they are whole numbers. Multiply: Step 2: The decimal point in the product is placed so that number of decimal places in the product is equal to the sum of the number of decimal places in the factors. Total of 2 decimal places. Objective A Decimal placed at two decimal places. 5

Example Multiply: 15.9 × 0.62 1 decimal place 2 decimal places Insert the decimal point in the product so that there are 3 decimal places (1 + 2 = 3). Objective A 6

Example Multiply: 0.648 × 0.5 3 decimal places 1 decimal place Insert the decimal point in the product so that there are 4 decimal places. Objective A 7

Estimate when Multiplying Decimals. Objective B Estimate when Multiplying Decimals.

Estimating when Multiplying Decimals We can estimate when multiplying decimals to check for reasonableness. Example: Multiply 5.3 and 4.2 Exact Estimate Objective A Since 22.26 is close to our estimate of 20, it is a reasonable answer. 9

Chapter 1 / Whole Numbers and Introduction to Algebra Example Multiply 32.3  1.9. Exact Estimate rounds to rounds to This is a reasonable answer.

Multiply Decimals by Powers of 10. Objective C Multiply Decimals by Powers of 10.

Multiplying Decimals by Powers of 10 Chapter 1 / Whole Numbers and Introduction to Algebra Multiplying Decimals by Powers of 10 There are some patterns that occur when we multiply a number by a power of ten, such as 10, 100, 1000, 10,000, and so on.

Multiplying by Powers of 10 Type Example Multiplying Decimals by Powers of 10 such as 10, 100, 1000 . . .: Move the decimal point to the right the same number of places as there are zeros in the power of 10. Multiplying Decimals by Powers of 10 such as .1, .01, .001 . . .: Move the decimal point to the left the same number of places as there are decimal places in the power of 10. Objective A 13

Chapter 1 / Whole Numbers and Introduction to Algebra Multiplying Decimals by Powers of 10 Move the decimal point to the right the same number of places as there are zeros in the power of 10. Multiply: 3.4305  100 Since there are two zeros in 100, move the decimal place two places to the right. 3.4305  100 = 3.4305 = 343.05

Chapter 1 / Whole Numbers and Introduction to Algebra Examples 76.543  10 = 765.43 76.543  100 = 7654.3 76.543  100,000 = 7,654,300 Decimal point moved 1 place to the right. 1 zero Decimal point moved 2 places to the right. 2 zeros Decimal point moved 5 places to the right. 5 zeros The decimal point is moved the same number of places as there are zeros in the power of 10.

Multiplying by Powers of 10 Chapter 1 / Whole Numbers and Introduction to Algebra Multiplying by Powers of 10 Move the decimal point to the left the same number of places as there are decimal places in the power of 10. Multiply: 8.57 × 0.01 Since there are two decimal places in 0.01, move the decimal place two places to the left. 8.57 × 0.01 = 008.57 = 0.0857 Notice that zeros had to be inserted.

Examples Multiply. 58.1 × 0.01 Move the decimal point 2 places to the left. b. 85,624 × 0.1 Move the decimal point 1 place to the left. c. 24.106 ×100 Move the decimal point 2 places to the right. = 0.581 = 8562.4 Objective A = 2410.6 17

Evaluate Expressions with Decimal Replacement Values. Objective D Evaluate Expressions with Decimal Replacement Values.

Example Evaluate 7y for y = –0.028. Substitute –0.028 for y. 7y = 7(–0.028) = –0.196

Find the Circumference of Circles. Objective E Find the Circumference of Circles.

Chapter 1 / Whole Numbers and Introduction to Algebra The Circumference of a Circle The distance around a polygon is called its perimeter. The distance around a circle is called the circumference. This distance depends on the radius or the diameter of the circle.

Chapter 1 / Whole Numbers and Introduction to Algebra Circumference of a Circle r d Circumference = 2·p ·radius or Circumference = p ·diameter C = 2 p r or C = p d

p The symbol p is the Greek letter pi, pronounced “pie.” It is a constant between 3 and 4. A decimal approximation for p is 3.14. A fraction approximation for p is . 22 7

Chapter 1 / Whole Numbers and Introduction to Algebra The Circumference of a Circle Find the circumference of a circle whose radius is 4 inches. 4 inches C = 2pr = 2p ·4 = 8p inches 8p inches is the exact circumference of this circle. If we replace  with the approximation 3.14, C = 8  8(3.14) = 25.12 inches. 25.12 inches is the approximate circumference of the circle.

Example Find the circumference of the following circle. 9.1 yards Objective A 25

Solve Problems by Multiplying Decimals. Objective F Solve Problems by Multiplying Decimals.

Example Jose Severos, an electrician for Central Power and Light, worked 40 hours last week. Calculate his pay before taxes for last week if his hourly wage is $13.88. Objective A Jose Severos’ pay before taxes for last week is $555.20. 27