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1 Business Math Chapter 3: Decimals. Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights.

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Presentation on theme: "1 Business Math Chapter 3: Decimals. Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights."— Presentation transcript:

1 1 Business Math Chapter 3: Decimals

2 Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved Decimals and the Place Value System Read and write decimals Round decimals rounded to the nearest tenth is 1.2

3 Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved 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.

4 Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved 4 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.

5 Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved 5 The decimal point Separates the whole number part from the decimal part, as the number extends from left to right is read thirty four and seven tenths or 34 point 7.

6 Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved 6 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.

7 Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved 7 How to read or write a decimal 3.12 Three and twelve hundredths 9.067Nine and sixty-seven thousandths. 4.5Four and five tenths. Read the whole number part first, saying and to indicate the beginning of the decimal part of the number.

8 Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved 8 Reading decimals as money amounts When reading numbers that represent money amounts, read whole numbers as dollars. Decimal amounts are read as cents. $35.98 is read thirty–five dollars and 98 cents.

9 Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved 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.

10 Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved 10 Try these examples Round to the nearest tenth , ,

11 Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved Operations with decimals Add and subtract decimals Multiply decimals Divide decimals = ?

12 Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved 12 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.

13 Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved 13 Be orderly to avoid mistakes

14 Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved 14 Add zeros where necessary =.688

15 Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved 15 Try these examples. (Without using your calculator) = – 7.6 = =.93383

16 Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved 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.

17 Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved 17 Look at this example x = 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 The last zero can be dropped and the answer would be

18 Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved 18 Try these examples (Without using your calculator) 2.4 x.06 = x = x 1.001=

19 Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved 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. 3.4 divided by 3 = ?

20 Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved 20 Try these examples (Without using your calculator) 12.4 ÷ 6 = 2.06 (repeating) 36.5 ÷ 2 = ÷ 50 = 3.849

21 Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved 21 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 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.

22 Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved 22 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.

23 Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved 23 Try these examples. Without using your calculator) 12.3 ÷.06 = ÷.004 = 3, ÷.08 =

24 Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved 24 Try these word problems. Bill Sullivan has an hourly rate of $14.32 and his gross weekly pay was $ How many hours did he work? 40 hours Jan Stevens has an hourly rate of $7.75 per hour and her gross weekly pay was $ How many hours did she work last week? 25 hours

25 Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved 25 Convert a decimal to a fraction. Convert a fraction to a decimal. 1/2 = 50% 25% = 1/4 3.3 Decimal and Fraction Conversions

26 Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved 26 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.

27 Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved 27 Heres an example. Write 0.8 as a fraction 8 becomes the numerator. There is one place to the right of the decimal point: = becomes the denominator. 0.8 = 8/10 Reduce to lowest terms. 4/5

28 Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved 28 Try these examples converted to a fraction becomes… ¾ converted to a fraction becomes… 0.25 converted to a fraction becomes… ¼

29 Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved 29 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.

30 Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved 30 Heres an example. Write as a decimal. Divide 8 into The result is In this case the quotient is called a terminating decimal; there is no remainder.

31 Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved 31 Try these examples. Convert ½ to a decimal. 0.5 Convert to a decimal Convert to a decimal (repeating) or 0.67


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