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CHAPTER 5 Decimal Notation Slide 2Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 5.1Decimal Notation, Order, and Rounding 5.2Addition and Subtraction of Decimals 5.3Multiplication of Decimals 5.4Division of Decimals 5.5Using Fraction Notation with Decimal Notation 5.6Estimating 5.7Solving Equations 5.8Applications and Problem Solving

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OBJECTIVES 5.1 Decimal Notation, Order, and Rounding Slide 3Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. aGiven decimal notation, write a word name. bConvert between decimal notation and fraction notation. cGiven a pair of numbers in decimal notation, tell which is larger. dRound decimal notation to the nearest thousandth, hundredth, tenth, one, ten, hundred, or thousand.

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5.1 Decimal Notation, Order, and Rounding a Given decimal notation, write a word name. Slide 4Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. The set of rational numbers consists of the integers and fractions like,

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5.1 Decimal Notation, Order, and Rounding a Given decimal notation, write a word name. Slide 5Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. A number written in decimal notation is often simply referred to as a decimal. The word decimal comes from the Latin word decima, meaning a tenth part. Since our usual counting system is based on tens, decimal notation is a natural extension of an already familiar system. The dot in $249.98 is called a decimal point.

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5.1 Decimal Notation, Order, and Rounding a Given decimal notation, write a word name. Slide 6Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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5.1 Decimal Notation, Order, and Rounding a Given decimal notation, write a word name. Slide 7Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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5.1 Decimal Notation, Order, and Rounding a Given decimal notation, write a word name. Slide 8Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. We read the decimal point as “and.” Note that the place values to the right of the decimal point always end in th. We can also read 26.2922 as “Two six point two nine two two” or “Twenty-six point two nine two two.”

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Title 5.1 Decimal Notation, Order, and Rounding Slide 9Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. To write a word name from decimal notation, a) write a word name for the whole number (the number named to the left of the decimal point), b) write the word “and” for the decimal point, and

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Title 5.1 Decimal Notation, Order, and Rounding Slide 10Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. c) write a word name for the number named to the right of the decimal point, followed by the place value of the last digit.

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EXAMPLE 5.1 Decimal Notation, Order, and Rounding a Given decimal notation, write a word name. 1Birth Rate. Slide 11Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. There were 14.3 births per 1000 Americans in a recent year. Write a word name for 14.3. Source: U.S. Centers for Disease Control and Prevention Fourteen and three tenths

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EXAMPLE 5.1 Decimal Notation, Order, and Rounding a Given decimal notation, write a word name. 4 Slide 12Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Write a word name for the number in this sentence: The current one-mile land speed record of 763.035 mph is held by Andy Green. Source: www.castrol.comwww.castrol.com Seven hundred sixty-three and thirty-five thousandths

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5.1 Decimal Notation, Order, and Rounding a Given decimal notation, write a word name. Slide 13Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Decimal notation is also used with money. It is common on a check to write “and ninety-five cents” as “and dollars.”

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EXAMPLE 5.1 Decimal Notation, Order, and Rounding a Given decimal notation, write a word name. 5 Slide 14Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Write $5876.95 in words, as on a check.

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5.1 Decimal Notation, Order, and Rounding b Convert between decimal notation and fraction notation. Slide 15Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Since 9.875 means nine and eight hundred seventy- five thousandths, we can write

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Title 5.1 Decimal Notation, Order, and Rounding Slide 16Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. To convert from decimal to fraction notation, a) count the number of decimal places, b) move the decimal point that many places to the right, and c) write the answer over a denominator of 1 followed by that number of zeros.

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5.1 Decimal Notation, Order, and Rounding b Convert between decimal notation and fraction notation. Slide 17Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. For a number like 0.876, we write a 0 to call attention to the presence of the decimal point.

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EXAMPLE 5.1 Decimal Notation, Order, and Rounding b Convert between decimal notation and fraction notation. 6 Slide 18Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Write fraction notation for 0.876. Do not simplify.

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5.1 Decimal Notation, Order, and Rounding b Convert between decimal notation and fraction notation. Slide 19Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Decimals greater than 1 or less than –1 can be written either as fractions or as mixed numerals.

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EXAMPLE 5.1 Decimal Notation, Order, and Rounding b Convert between decimal notation and fraction notation. 7 Slide 20Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Write 56.23 as a fraction and as a mixed numeral.

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5.1 Decimal Notation, Order, and Rounding b Convert between decimal notation and fraction notation. Slide 21Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. To write as a decimal, we can first divide to find an equivalent mixed numeral.

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Title 5.1 Decimal Notation, Order, and Rounding Slide 22Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. To convert from fraction notation to decimal notation when the denominator is 10, 100, 1000, and so on, a) count the number of zeros and b) move the decimal point that number of places to the left. Leave off the denominator.

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EXAMPLE 5.1 Decimal Notation, Order, and Rounding b Convert between decimal notation and fraction notation. 10 Slide 23Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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5.1 Decimal Notation, Order, and Rounding b Convert between decimal notation and fraction notation. Slide 24Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. To move the decimal point to the left, we may need to write extra 0’s.

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EXAMPLE 5.1 Decimal Notation, Order, and Rounding b Convert between decimal notation and fraction notation. 11 Slide 25Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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5.1 Decimal Notation, Order, and Rounding b Convert between decimal notation and fraction notation. Slide 26Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. For denominators other than 10, 100, and so on, we will usually perform long division. We convert such fractions to decimal notation in Section 5.5. If a mixed numeral has a fraction part with a denominator that is a power of ten, such as 10, 100, or 1000, and so on, we first write the mixed numeral as a sum of a whole number and a fraction. Then we convert to decimal notation.

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EXAMPLE 5.1 Decimal Notation, Order, and Rounding b Convert between decimal notation and fraction notation. 12 Slide 27Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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5.1 Decimal Notation, Order, and Rounding b Convert between decimal notation and fraction notation. Slide 28Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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Title 5.1 Decimal Notation, Order, and Rounding Slide 29Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. To compare two positive numbers in decimal notation, start at the left and compare corresponding digits, moving from left to right. When two digits differ, the number with the larger digit is the larger of the two numbers. Extra zeros can be written to the right of the last decimal place.

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EXAMPLE 5.1 Decimal Notation, Order, and Rounding c Given a pair of numbers in decimal notation, tell which is larger. 13 Slide 30Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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Title 5.1 Decimal Notation, Order, and Rounding Slide 31Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. To compare two negative numbers in decimal notation, start at the left and compare corresponding digits, moving from left to right. When two digits differ, the number with the smaller digit is the larger of the two numbers.

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EXAMPLE 5.1 Decimal Notation, Order, and Rounding c Given a pair of numbers in decimal notation, tell which is larger. 15 Slide 32Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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5.1 Decimal Notation, Order, and Rounding d Round decimal notation to the nearest thousandth, hundredth, tenth, one, ten, hundred, or thousand. Slide 33Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. We round decimals in much the same way that we round whole numbers.

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Title 5.1 Decimal Notation, Order, and Rounding Slide 34Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. To round to a certain place: a) Locate the digit in that place. b) Consider the next digit to the right. c) If the digit to the right is 5 or greater, add one to the original digit. If the digit to the right is 4 or less, the original digit does not change. In either case, drop all numbers to the right of the original digit.

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EXAMPLE 5.1 Decimal Notation, Order, and Rounding d Round decimal notation to the nearest thousandth, hundredth, tenth, one, ten, hundred, or thousand. 17 Slide 35Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Round 72.3846 to the nearest hundredth.

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EXAMPLE 5.1 Decimal Notation, Order, and Rounding d Round decimal notation to the nearest thousandth, hundredth, tenth, one, ten, hundred, or thousand. 18 Slide 36Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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