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Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 3.1 Decimals and the Place Value System Read and write decimals Round decimals 1.2345 rounded to the nearest tenth is 1.2

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Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 3.1.1 Read and Write Decimals Our money system, based on the dollar, uses the decimal system. Moving one place from right to left increases the value ten times. Moving one place from left to right, causes the value of the digit to become ten times smaller.

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Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved How much is 0.1? It is one part of a 10- part whole. 0.1 is read “one tenth” If this chart represented a dollar, the white segment would be equal to $0.10.

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Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved The decimal point Separates the whole number part from the decimal part, as the number extends from left to right. 26.8 is read twenty six and eight tenths or 26 point 8.

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Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved Place value names The first place to the right of the decimal point is tenths. (0.1) Second place is hundredths. (0.01) Third place is thousandths. (0.001) Fourth place is ten-thousandths. (0.0001) and so on.

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Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved How to read or write a decimal 4.15 Four and fifteen hundredths 9.067Nine and sixty-seven thousandths. 5.5Five and five tenths. Read the whole number part first, saying “and” to indicate the beginning of the decimal part of the number.

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Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved Reading decimals as money amounts When reading numbers that represent money amounts, read whole numbers as dollars. Decimal amounts are read as “cents.” $46.57 is read “forty–six dollars and fifty- seven cents.”

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Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 3.1.2 Round to a Specific Decimal Place 1. Find the digit in the specified place. 2. Look at the next digit to the right. If this digit is less than 5, eliminate it and all digits to its right. If the digit is 5 or more, add 1 to the digit in the specified place, and eliminate all digits to its right.

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Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved Try these examples Round to the nearest tenth 12.456 12.5 31,343.387 31,343.4 346.2778 346.3

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Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 3.2 Operations with Decimals Add and subtract decimals Multiply decimals Divide decimals 4.685 + 6.8 = ?

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Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved Add and subtract decimals Write the numbers in a vertical column, aligning digits according to their places. Attach extra zeros to the right end of each number so each number has the same quantity of digits. Add or subtract as though the numbers are whole numbers. Place the decimal point in the sum or difference to align with the decimal point in the respective operation.

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Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved Be orderly to avoid mistakes 3.47 -.29 18

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Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved Add zeros where necessary.780 -.092 =.688

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Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved Try these examples. (Without using your calculator) 6. 485 + 1.4 + 0.8 + 11.999 = 20.684 10.008 – 7.6 = 2.408.976 -.04217 =.93383

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Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 3.2.2 Multiply Decimals Multiply the decimal numbers as though they are whole numbers. Count the digits in the decimal parts of both decimal numbers. Place the decimal point in the product so that there are as many digits in its decimal part as there are digits you counted in the previous step. If necessary, attach zeros to the left end of the product to place the decimal point accurately.

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Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved Look at this example. 3.45 x 4.082 = How many places are there to the right of the decimal point? Five; so, the answer will have five places to the right of the decimal. The answer is 14.08290 The last zero can be dropped and the answer would be 14.0829.

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Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved Try these examples (Without using your calculator) 1.7 x.08 = 0.136 4.67 x 5.004 = 23.36868.01 x 1.001= 0.01001

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Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 3.2.3 Divide Decimals Divide a decimal by a whole number: Place a decimal point for the quotient directly above the decimal point in the dividend. Divide as though the decimal points are whole numbers. 8.4 divided by 3 = ?

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Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved Try these examples (Without using your calculator) 12.4 ÷ 6 = 2.06 (repeating) 36.5 ÷ 2 = 18.25 192.45 ÷ 50 = 3.849

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Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved Try this word problem Jill wants to buy a bottle of detergent. If a 100- ounce bottle costs $6.49 and a 50-ounce bottle costs $3.99, which would be the better buy on a cost per ounce basis? What are those amounts? Answer: The 50-ounce bottle has a cost of.0798 per ounce while the 100-ounce bottle has a cost of.0649 per ounce. The bigger bottle is a better buy.

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Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved Divide by a decimal Change the divisor to a whole number by moving the decimal point to the right, counting the places as you go. Use a caret ( ^ ) to show the new position of the decimal point. Move the decimal point in the dividend to the right as many places as you moved the divisor. Place the decimal point for the quotient directly above the new decimal point for the dividend. Divide as you would divide a whole number.

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Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved Try these examples Without using your calculator) 12.3 ÷.06 = 205 15 ÷.004 = 3,750 20.765 ÷.08 = 259.5625

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Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved Try these word problems Seth Parker has an hourly rate of $12.27 and his gross weekly pay was $441.72. How many hours did he work? 36 hours Amber Sellnow has an hourly rate of $8.75 per hour and her gross weekly pay was $245.00. How many hours did she work last week? 28 hours

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Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved Convert a decimal to a fraction. Convert a fraction to a decimal. 1/2 = 50% 25% = 1/4 3.3 Decimal and Fraction Conversions

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Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved Convert a decimal to a fraction Find the denominator: write 1 followed by as many zeros as there are places to the right of the decimal point. Find the numerator: use the digits without the decimal point. Reduce to lowest terms and/or write as a whole or mixed number.

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Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved Here’s an example Write 0.8 as a fraction “8” becomes the numerator. There is one place to the right of the decimal point: 1 + 0 = 10. “10” becomes the denominator. 0.8 = 8/10 Reduce to lowest terms. 4/5

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Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved Try these examples 0.75 converted to a fraction becomes… ¾ 0.625 converted to a fraction becomes… ⅝ 0.25 converted to a fraction becomes… ¼

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Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved Convert a fraction to a decimal Write the numerator as a dividend and the denominator as the divisor. Divide the numerator by the denominator, taking the division out as many decimal places as necessary or desirable. Note: In some cases, a repeating decimal will be the quotient of the operation. You may indicate that it is a repeating decimal or round as needed.

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Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved Here’s an example Write ⅞ as a decimal. Divide 8 into 7.000. The result is 0.875 In this case the quotient is called a terminating decimal; there is no remainder.

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Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved Try these examples Convert ½ to a decimal. 0.5 Convert ⅜ to a decimal. 0.375 Convert ⅔ to a decimal. 0.6666(repeating) or 0.67

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