Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Chapter 3 Decimals

3-5-2 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Section 3.5 Working with Fractions and Decimals

3-5-3 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Convert a Fraction to a Decimal Rule for Converting a Fraction to a Decimal Divide the numerator by the denominator.If necessary,insert zeros in the dividend after the decimal point to allow the division to continue.Also,if necessary,insert zeros as placeholders in the quotient to get the correct number of decimal places.

3-5-4 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Terminating Decimals and Repeating Decimals Terminating Decimal A decimal whose expansion ends. Repeating Decimal A decimal that continues indefinitely with one or more repeating digits.

3-5-5 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Example Convert each fraction to a decimal. a.b.c. d.

3-5-6 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Solution Strategy a. b. c.

3-5-7 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Solution Strategy d. e.

3-5-8 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Simplify an Expression Containing Fractions and Decimals When an expression contains a mix of fractions and decimals, we can either convert the fractions to decimals, or we can convert the decimals to fractions. In general, if all of the decimals have terminating decimal expansions, then we convert the fractions to decimals or vice versa. If, on the other hand, the fractions have a repeating decimal expansion, then we prefer to convert the decimals to fractions in order to avoid rounding error.

3-5-9 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Example Simplify each expression. b. c. a.

Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Solution Strategy = = 0.98 Simplify each expression. a. c.b. = 15

Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Simplify an Expression Using the Order of Operations Often, expressions containing fractions and decimals will have more than one operation. When multiple operations are present, we must simplify the expression using order of operations. Once again, here are the rules.

Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Order of Operations

Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Example Simplify each expression. b. c. a.

Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Solution Strategy Simplify each expression. a.

Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Solution Strategy Simplify each expression. b.

Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Solution Strategy Simplify each expression. c.

Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Example Apply your knowledge At Safeway market, a customer purchased pounds of bananas at $1.19 per pound, pounds of peaches at $2.49 per pound, and pounds of cherries at $5.99 per pound.

Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Example Apply your knowledge a.What was the cost of each kind of fruit? Round answers to dollars and cents. b.What was the total cost of the purchase?

Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Solution Strategy = $4.17 a. What was the cost of each fruit? Bananas: Peaches: = $10.89

Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Solution Strategy = $7.49 a. What was the cost of each fruit? Cherries: b. What was the total cost of the purchase? = $22.55