2. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. 4.3 Multiplying Decimals and Circumference of a Circle

3. 22 © 2012 Pearson Prentice Hall. All rights reserved 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.

4. 33 © 2012 Pearson Prentice Hall. All rights reserved Multiplying Decimals StepExample 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. Decimal placed at two decimal places.

5. 44 © 2012 Pearson Prentice Hall. All rights reserved 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).

6. 55 © 2012 Pearson Prentice Hall. All rights reserved 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.

7. 66 © 2012 Pearson Prentice Hall. All rights reserved Estimating when Multiplying Decimals We can estimate when multiplying decimals to check for reasonableness. Example: ExactEstimate Since 22.26 is close to our estimate of 20, it is a reasonable answer.

8. 77 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Multiply 32.3  1.9. Estimating when Multiplying Decimals Exact Estimate rounds to This is a reasonable answer.

9. 88 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. 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.

10. 99 © 2012 Pearson Prentice Hall. All rights reserved Multiplying by Powers of 10 TypeExample 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.

11. 10 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. 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 = 343.053.4305 = Multiplying Decimals by Powers of 10

12. 11 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. 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. Decimal point moved 2 places to the right. Decimal point moved 5 places to the right. 2 zeros 5 zeros 1 zero The decimal point is moved the same number of places as there are zeros in the power of 10. Multiplying Decimals by Powers of 10

13. 12 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. 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 x 0.01 Since there are two decimal places in 0.01, move the decimal place two places to the left. 8.57 x 0.01 =0.0857. Notice that zeros had to be inserted. 008.57 = Multiplying Decimals by Powers of 10

14. 13 © 2012 Pearson Prentice Hall. All rights reserved Example Multiply. a.58.1 × 0.01 = 0.581 Move the decimal point 2 places to the left. b.85,624 × 0.1 = 8562.4 Move the decimal point 1 place to the left. c. 24.106 ×100 = 2410.6 Move the decimal point 2 places to the right.

15. 14 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. 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. The Circumference of a Circle

16. 15 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. r d Circumference = 2·   ·radius or Circumference =   ·diameter C = 2  r or C =  d The Circumference of a Circle

17. 16 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. The symbol  is the Greek letter pi, pronounced “pie.” It is a constant between 3 and 4. A decimal approximation for  is 3.14. A fraction approximation for  is.  22 7

18. 17 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Find the circumference of a circle whose radius is 4 inches. 4 inches C = 2  r = 2  ·4 = 8  inches 8  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 circumference of the circle. 25.12 inches is the approximate circumference of the circle. The Circumference of a Circle

19. 18 © 2012 Pearson Prentice Hall. All rights reserved Example Find the circumference of the following circle. Circumference = 9.1 yards

20. 19 © 2012 Pearson Prentice Hall. All rights reserved Solving Problems by Multiplying Decimals 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. Jose Severos’ pay before taxes for last week is $555.20.