# Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Chapter 3 Decimals.

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Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Chapter 3 Decimals

Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Converting Fractions to Decimals and the Order of Operations 3.6

Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Equivalent Fractions and Decimals A number can be expressed in two equivalent forms: as a fraction and as a decimal. Fraction three and one-fourth Decimal three and twenty-five hundredths Same quantity, difference appearance

Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Converting a Fraction to a Decimal Converting a Fraction to an Equivalent Decimal Divide the denominator into the numerator until a)the remainder becomes zero, or b)the remainder repeats itself, or c)the desired number of decimal places is achieved. Common equivalent fractions and decimals

Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Terminating and Repeating Decimals Terminating decimals (The remainder is zero when converting the fraction into a decimal.) Repeating decimals (When converting, the remainder is a digit or group of digits that repeats.) repeating digitrepeating group of digits

Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Converting a Fraction to a Decimal Example: Write as an equivalent decimal. repeating remainders 0.277.0 0 0 3 6 140 126 140

Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Ordering Fractions and Decimals Example: Fill in the blank with one of the symbols. Change the fraction into a decimal for easier comparison. >

Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Order of Operations 1.Perform operations inside any parentheses. 2.Simplify any expressions with exponents. 3.Multiply or divide from left to right. 4.Add or subtract from left to right. Do first Do last Example: Evaluate 9.6 + 3.6 – (0.4) 2. Exponents Addition = 9.6 + 3.6 – 0.16 = 13.2 – 0.16 = 13.04Subtraction

Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Order of Operations Example: Evaluate (2.4) 2 + 3.6 ÷ (1.2 – 0.7). Parentheses Exponents = (2.4) 2 + 3.6 ÷ 0.5 = 5.76 + 3.6 ÷ 0.5 = 5.76 + 7.2Division = 12.96Addition (2.4) 2 + 3.6 ÷ (1.2 – 0.7)