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OBJECTIVES R.3 Decimal Notation Slide 2Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. aConvert from decimal notation to fraction notation. bAdd, subtract, multiply, and divide using decimal notation. cRound numbers to a specified decimal place.

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The decimal notation 42.3245 means 4 tens + 2 ones + 3 tenths + 2 hundredths + 4 thousandths + 5 ten-thousandths R.3 Decimal Notation a Convert from decimal notation to fraction notation. Slide 3Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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The decimal notation 42.3245 means We read this number as “Forty-two and three thousand two hundred forty-five ten-thousandths.” The decimal point is read as “and”. R.3 Decimal Notation a Convert from decimal notation to fraction notation. Slide 4Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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4.98 2 zeros 2 places Move 2 places. a) Count the number of decimal places. b) Move the decimal point that many places to the right. c) Write the result over a denominator with that number of zeros. R.3 Decimal Notation To Convert from Decimal to Fraction Notation Slide 5Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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EXAMPLE 3 places 3 zeros 0.924. Solution R.3 Decimal Notation a Convert from decimal notation to fraction notation. AWrite fraction notation for 0.924. Do not simplify. Slide 6Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. What do we do?

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EXAMPLE Solution To write as a fraction: 2 zeros 2 places 17.77. R.3 Decimal Notation a Convert from decimal notation to fraction notation. BWrite 17.77 as a fraction and as a mixed numeral. Slide 7Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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EXAMPLE Solution To write as a mixed numeral, we rewrite the whole number part and express the rest in fraction form: R.3 Decimal Notation a Convert from decimal notation to fraction notation. BWrite 17.77 as a fraction and as a mixed numeral. Slide 8Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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8.679. Move 3 places. 3 zeros a) Count the number of zeros. b) Move the decimal point that number of places to the left. Leave off the denominator. R.3 Decimal Notation Converting to Decimal Notation when the Denominator is a Power of Ten Slide 9Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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EXAMPLE 1 place 1 zero Solution R.3 Decimal Notation a Convert from decimal notation to fraction notation. CWrite decimal notation for Slide 10Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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Adding with decimal notation is similar to adding whole numbers. First we line up the decimal points so that we can add corresponding place-value digits. R.3 Decimal Notation b Add, subtract, multiply, and divide using decimal notation. Slide 11Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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Add the digits from the right. If necessary, we can write extra zeros to the far right of the decimal point so that the number of places is the same. R.3 Decimal Notation b Add, subtract, multiply, and divide using decimal notation. Slide 12Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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EXAMPLE Solution Line up the decimal points and write extra zeros. R.3 Decimal Notation b Add, subtract, multiply, and divide using decimal notation. DAdd: 4.31 + 0.146 + 14.2 Slide 13Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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EXAMPLE Solution Line up decimal points and subtract, borrowing if necessary. 3 4. 0 7 0 0 – 4. 0 0 5 2 84600. 3 69 1 R.3 Decimal Notation b Add, subtract, multiply, and divide using decimal notation. ESubtract: 34.07 – 4.0052 Slide 14Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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EXAMPLE 57170. 5 99103 Solution 5 7 4. 0 0 0 – 3. 8 2 5 R.3 Decimal Notation b Add, subtract, multiply, and divide using decimal notation. FSubtract 574 – 3.825 Slide 15Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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a) Ignore the decimal points, and multiply as whole numbers. b) Place the decimal point in the result of step (a) by adding the number of decimal places in the original factors. R.3 Decimal Notation Multiplication with Decimal Notation Slide 16Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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EXAMPLE Solution: Ignore the decimal points and multiply as if both factors are integers then place the decimal point. 8 5. 1 × 7. 3 2 5 5 3 5 9 5 7 0 6 2 1 2 3 1 3 1 decimal place 2 decimal places. R.3 Decimal Notation b Add, subtract, multiply, and divide using decimal notation. GMultiply 7.3 ∙ 85.1. Slide 17Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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a) Place the decimal point in the quotient directly above the decimal point in the dividend. b) Divide as whole numbers. R.3 Decimal Notation Dividing When the Divisor Is a Whole Number Slide 18Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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EXAMPLE place the decimal point Solution R.3 Decimal Notation b Add, subtract, multiply, and divide using decimal notation. HDivide 91.26 ÷ 26. Slide 19Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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a) Move the decimal point in the divisor as many places to the right as it takes to make it a whole number. Move the decimal point in the dividend the same number of places to the right and place the decimal point in the quotient. b) Divide as whole numbers, inserting zeros if necessary. R.3 Decimal Notation Dividing When the Divisor Is not a Whole Number Slide 20Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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EXAMPLE Solution 7.872 ÷ (9.6) = 0.82. Multiply the divisor by 10 (move the decimal point 1 place). Multiply the same way in the dividend (move the decimal point 1 place). R.3 Decimal Notation b Add, subtract, multiply, and divide using decimal notation. IDivide: 7.872 ÷ 9.6. Slide 21Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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EXAMPLE Solution R.3 Decimal Notation b Add, subtract, multiply, and divide using decimal notation. JFind decimal notation for Slide 22Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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EXAMPLE Solution Divide 1 ÷ 12 R.3 Decimal Notation b Add, subtract, multiply, and divide using decimal notation. KFind decimal notation for (continued) Slide 23Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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EXAMPLE Since 4 keeps reappearing as a remainder, the digits repeat and will continue to do so; therefore, The dots indicate an endless sequence of digits in the quotient. The dots are often replaced by a bar to indicate the repeating part. R.3 Decimal Notation b Add, subtract, multiply, and divide using decimal notation. KFind decimal notation for Slide 24Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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EXAMPLE Solution 5 ÷ 11 Since 6 and 5 keep reappearing as remainders, the sequence of digits “45” repeats in the quotient, and R.3 Decimal Notation b Add, subtract, multiply, and divide using decimal notation. LFind decimal notation for Slide 25Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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To round to a certain place: a) Locate the digit in that place. b) Consider the digit to its right. c) If the digit to the right is 5 or higher, round up, if the digit to the right is less than 5, round down. R.3 Decimal Notation Rounding Decimal Notation Slide 26Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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EXAMPLE Solution a. Locate the digit in the tenths place. 0.072 b. Consider the next digit to the right. c. Since that digit, 7 is greater than 5, round up to 0.1 R.3 Decimal Notation c Round numbers to a specified decimal place. MRound 0.072 to the nearest tenth. Slide 27Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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EXAMPLE Solution a. Locate the digit in the hundredths place. 34.7824 b. Consider the next digit to the right. c. Since that digit, 2 is less than 5, we round down to 34.78 R.3 Decimal Notation c Round numbers to a specified decimal place. NRound 34.7824 to the nearest hundredth. Slide 28Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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EXAMPLE R.3 Decimal Notation c Round numbers to a specified decimal place. ORound 478.3469 to the nearest thousandth, hundredth, tenth, one, ten, hundred, and thousand. (continued) Slide 29Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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EXAMPLE 478.3469 thousandth478.347 hundredth478.35 tenth478.3 one478. ten480. hundred500. thousand0. Solution R.3 Decimal Notation c Round numbers to a specified decimal place. ORound 478.3469 Slide 30Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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