1. CHAPTER OUTLINE 3 Decimals Slide 1 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 3.1Decimal Notation and Rounding 3.2Addition and Subtraction of Decimals 3.3Multiplication of Decimals and Applications with Circles 3.4Division of Decimals 3.5Fractions, Decimals, and the Order of Operations

2. Section 3.4 Homework questions?

3. Section Objectives 3.4 Division of Decimals Slide 3 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1.Division of Decimals 2.Rounding a Quotient 3.Applications of Decimal Division

4. PROCEDUREDividing a Decimal by a Whole Number Slide 4 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. To divide by a whole number: Step 1 Place the decimal point in the quotient directly above the decimal point in the dividend. Step 2 Divide as you would whole numbers.

5. Example 1Dividing by a Whole Number Slide 5 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Divide and check the answer by multiplying.

6. Section 3.4 Division of Decimals 1.Division of Decimals Slide 6 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. When dividing decimals, we do not use a remainder. Instead we insert zeros to the right of the dividend and continue dividing.

7. Example 2Dividing by an Integer Slide 7 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Divide and check the answer by multiplying.

8. Example 3Dividing by an Integer Slide 8 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Divide and check the answer by multiplying.

9. Section 3.4 Division of Decimals 1.Division of Decimals Slide 9 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sometimes when dividing decimals, the quotient follows a repeated pattern. The result is called a repeating decimal.

10. Example 4Dividing Where the Quotient Is a Repeating Decimal Slide 10 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

11. Example Solution: 4Dividing Where the Quotient Is a Repeating Decimal (continued) Slide 11 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. The quotient is 0.05666....To denote the repeated pattern, we often use a bar over the first occurrence of the repeat cycle to the right of the decimal point. That is,

12. Avoiding Mistakes Slide 12 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. In Example 4, notice that the repeat bar goes over only the 6. The 5 is not being repeated.

13. Section 3.4 Division of Decimals 1.Division of Decimals Slide 13 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. The numbers and are examples of repeating decimals. A decimal that “stops” is called a terminating decimal.

14. Example 6Dividing Decimals Slide 14 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

15. PROCEDUREDividing by a Power of 10 Slide 15 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. To divide a number by a power of 10, move the decimal point to the left the same number of places as there are zeros in the power of 10.

16. Example 8Dividing by a Power of 10 Slide 16 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

17. Section 1. Divide:502.96 ÷ 8. 2. Divide: 3 ÷ 20 3. Divide:0.64 ÷ (- 0.4) 4.Divide:-70 ÷ (- 0.6) 5. Divide:0.0039 ÷ 10 3.4 Try these on your own:

18. Example 9Rounding a Repeating Decimal Slide 18 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

19. Section 3.4 Division of Decimals 2.Rounding a Quotient Slide 19 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sometimes we may want to round a quotient to a given place value. To do so, divide until you get a digit in the quotient one place value to the right of the rounding place. At this point, you can stop dividing and round the quotient.

20. Example 10Rounding a Quotient Slide 20 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Round the quotient to the tenths place.

21. Example 12Using Division to Find a Rate of Speed Slide 21 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. In a recent year, the world-record time in the men’s 400-m run was 43.2 sec. What is the speed in meters per second? Round to one decimal place. (Source: International Association of Athletics Federations)

22. Section 1. Round the quotient to the indicated place value: 42.68 ÷ 5.1; hundredths. 2. A 46.5 – ft. cable is to be cut into 6 pieces of equal length. How long is each piece? 3.4 Try these on your own: