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 3.5 Homework questions?

3. Section Objectives 3.5 Fractions, Decimals, and the Order of Operations Slide 3 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1.Writing Fractions as Decimals 2.Writing Decimals as Fractions 3.Decimals and the Number Line 4.Order of Operations Involving Decimals and Fractions 5.Applications of Decimals and Fractions

4. Section 3.5 Fractions, Decimals, and the Order of Operations 1.Writing Fractions as Decimals Slide 4 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sometimes it is possible to convert a fraction to its equivalent decimal form by rewriting the fraction as a decimal fraction. That is, try to multiply the numerator and denominator by a number that will make the denominator a power of 10.

5. Section 3.5 Fractions, Decimals, and the Order of Operations 1.Writing Fractions as Decimals Slide 5 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. However, some fractions cannot be converted to a fraction with a denominator that is a power of 10. For this reason, we recommend dividing the numerator by the denominator,

6. Example 1Writing Fractions as Decimals Slide 6 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

7. Example 2Converting Fractions to Repeating Decimals Slide 7 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

8. Section 3.5 Fractions, Decimals, and the Order of Operations 1.Writing Fractions as Decimals Slide 8 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Several fractions are used quite often. Their decimal forms are worth memorizing.

9. Example 3Converting Fractions to Decimals with Rounding Slide 9 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Convert the fraction to a decimal rounded to the indicated place value.

10. Section 1. Write each fraction or mixed number as a decimal. a. b.c. 2. Convert the fraction to a decimal rounded to the indicated place value: ; hundredths 3.5 Try these on your own:

11. Section 3.5 Fractions, Decimals, and the Order of Operations 2.Writing Decimals as Fractions (continued) Slide 11 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Convert terminating decimals to fractions by writing the decimal as a decimal fraction and then reducing the fraction to lowest terms. We do not yet have the tools to convert a repeating decimal to its equivalent fraction form. However, we can make use of our knowledge of the common fractions and their repeating decimal forms from the following table.

12. Section 3.5 Fractions, Decimals, and the Order of Operations 2.Writing Decimals as Fractions Slide 12 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

13. Example 4Writing Decimals as Fractions Slide 13 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

14. Section 1. Write the decimals as fractions in simplest form. a. 0.875b. -1.55 3.5 Try these on your own:

15. Section 3.5 Fractions, Decimals, and the Order of Operations 3.Decimals and the Number Line Slide 15 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. A rational number is a fraction whose numerator is an integer and whose denominator is a nonzero integer. Rational numbers consist of all numbers that can be expressed as terminating decimals or as repeating decimals.

16. Section 3.5 Fractions, Decimals, and the Order of Operations 3.Decimals and the Number Line Slide 16 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. A number that cannot be expressed as a repeating or terminating decimal is not a rational number. These are called irrational numbers. The rational numbers and the irrational numbers together make up the set of real numbers. Furthermore, every real number corresponds to a point on the number line.

17. Example 5Ordering Decimals and Fractions Slide 17 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Rank the numbers from least to greatest. Then approximate the position of the points on the number line.

18. Example Solution: 5Ordering Decimals and Fractions Slide 18 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. The position of these numbers can be seen on the number line. Note that we have expanded the segment of the number line between 0.4 and 0.5 to see more place values to the right of the decimal point.

19. Section 1. Rank the numbers from least to greatest. Then approximate the position of the points on the number line. 0.161,, 0.16 3.5 Try these on your own:

20. PROCEDUREApplying the Order of Operations Slide 20 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Step 1 First perform all operations inside parentheses or other grouping symbols. Step 2 Simplify expressions containing exponents, square roots, or absolute values. Step 3 Perform multiplication or division in the order that they appear from left to right. Step 4 Perform addition or subtraction in the order that they appear from left to right.

21. Example 6Applying the Order of Operations Slide 21 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

22. Example 7Applying the Order of Operations Slide 22 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Simplify.

23. Section 1. Simplify: 1. (5.8 – 4.3) 2 – 2 2. 3.5 Try these on your own:

24. Example Joanne filled the gas tank in her car and noted that the odometer read 22,341.9 mi. Ten days later she filled the tank again with 11 gal of gas. Her odometer reading at that time was 22,622.5 mi. a. How many miles had she driven between fill-ups? b. How many miles per gallon did she get? 10Using Decimals and Fractions in a Consumer Application Slide 24 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

25. Section 1. The odometer on a car read 46,125.9 miles. After a 13.5- hour trip, the odometer read 46,947.4 miles. Find the total distance traveled on the trip and the average speed in miles per hour. 3.5 Try these on your own: