1. CHAPTER 3 – Decimals Instructor: Dr.Gehan Shanmuganathan

2. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved Learning Outcomes Read and write decimals. Round decimals. 3-1

3. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 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 number to become ten times smaller. Read and write decimals Decimal and Place-Value System 3-1-1 Section 3-1

4. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved It is one part of a 10-part whole. –0.1 is read “one tenth.” HOW TO: How much is.01? Decimal and Place-Value SystemSection 3-1 If this chart represented a dollar, the white segment would be equal to $0.10 (ten cents)

5. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved It 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. The decimal point Decimal and Place-Value SystemSection 3-1 HOW TO:

6. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 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 Place value names Decimal and Place-Value SystemSection 3-1 HOW TO: …and so on

7. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved Read the whole number part first, saying “and” to indicate the beginning of the decimal part of the number. Read or write a decimal Decimal and Place-Value SystemSection 3-1 HOW TO: 4.15— Four and fifteen hundredths 9.067—Nine and sixty-seven thousandths. 5.5—Five and five tenths.

8. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved When reading numbers that represent money amounts, read whole numbers as dollars. –Decimal amounts are read as “cents.” Reading decimals as money amounts Decimal and Place-Value SystemSection 3-1 HOW TO: $46.57 is read “forty-six dollars and fifty-seven cents.” Because 1 cent is one hundredth of a dollar, the words cent and hundredth have the same meaning. TIP:

9. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved Read and write decimals Find the digit in the specified place, and look at the next digit to the right. –If this digit is less than 5, eliminate it, and all digits to its right. –If this digit is 5 or more, add 1 to the digit in the specified place, and eliminate all digits to its right. Decimal and Place-Value SystemSection 3-1 HOW TO:

10. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved Round to the nearest tenth Examples… 12.456 31,343.387 346.2778 12.5 31,343.4 346.3 Decimal and Place-Value SystemSection 3-1

11. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

12. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved Learning Outcomes Add and subtract decimals. Multiply decimals. Divide decimals. 3-2

13. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved Add and subtract decimals 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. Operations with Decimals 3-2-1 Section 3-2

14. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved Add and subtract decimals Operations with Decimals 3-2-1 Section 3-2 3.47 -.29 18.780 -.092 =.688 Attach extra zeros to the right end of each number so each number has the same quantity of digits.

15. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved Add & Subtract Examples… 6. 485 + 1.4 + 0.8 + 11.999 = 10.008 – 7.6 = 0.976 – 0.04217 = 20.684 Operations with DecimalsSection 3-2 2.408 0.93383

16. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 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. Multiply decimals Operations with Decimals 3-2-2 Section 3-2

17. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved Example… Operations with DecimalsSection 3-2 HOW TO: 3.45 x 4.082 = How many places are there to the right of the decimal point? Five—so the product will have five places to the right of the decimal. 3.45 x 4.082 = 14.08290 The last zero can be dropped and the answer would be 14.0829.

18. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved Multiplication Examples… 1.7 x 0.08 = 4.67 x 5.004 = 0.01 x 1.001= 0.136 Operations with DecimalsSection 3-2 23.36868 0.01001

19. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved Place a decimal point for the quotient directly above the decimal point in the dividend. –Divide as though the decimal points are whole numbers. Divide decimals Operations with Decimals 3-2-3 Section 3-2

20. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved Division Examples… 12.4 ÷ 6 = 36.5 ÷ 2 = 192.45 ÷ 50 = 2.0666 (repeating) Operations with DecimalsSection 3-2 18.25 3.849

21. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved The 50-ounce bottle costs of 0.0798 per ounce while the 100-ounce bottle has a cost of 0.0649 per ounce. The bigger bottle is a better buy. 6.49 ÷ 100 = 0.0649 3.99 ÷ 50 = 0.0798 Word problem… Operations with DecimalsSection 3-2 Jill wants to buy a bottle of detergent. 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?

22. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved Change the divisor to a whole number by moving the decimal point to the right, counting the places as you go. Divide by a decimal Operations with DecimalsSection 3-2 HOW TO: 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. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved More Division Examples… 12.3 ÷ 0.06 = 15 ÷ 0.004 = 20.765 ÷ 0.08 = 205 Operations with DecimalsSection 3-2 3750 259.5625

24. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 36 hours Word problem… Operations with DecimalsSection 3-2 Seth Parker has an hourly rate of $12.27 and his gross weekly pay was $441.72. How many hours did he work? 28 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? 441.72 ÷ 12.27 = 245.00 ÷ 8.75 =

25. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

26. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved Learning Outcomes Convert a decimal to a fraction. Convert a fraction to a decimal. 3-3

27. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 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. Convert a decimal to a fraction Decimal and Fraction Conversions 3-3-1 Section 3-3

28. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved Write 0.8 as a fraction. Example… Decimal and Fraction ConversionsSection 3-3 “8” becomes the numerator. There is one place to the right of the decimal point: Write 1 with a single zero: 10. “10” becomes the denominator. Reduce to lowest terms: =

29. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved Conversions Examples… 0.75 converted to a fraction becomes… 0.625 converted to a fraction becomes… 0.25 converted to a fraction becomes… Operations with DecimalsSection 3-3

30. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved Write the numerator as the 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. Convert a fraction to a decimal Decimal and Fraction Conversions 3-3-2 Section 3-3 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. NOTE:

31. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved An Example… Decimal and Fraction ConversionsSection 3-3 Divide 8 into 7.000. The result is 0.875 In this case the quotient is called a terminating decimal. There is no remainder. Write as a decimal.

32. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved More Conversions Examples… Operations with DecimalsSection 3-3 Convert to a decimal… Convert to a decimal… 205 3750 259.5625

33. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

34. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved EXERCISES SET A

35. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved EXERCISES SET A

36. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved EXERCISES SET A

37. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved EXERCISES SET A

38. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved EXERCISES SET A

39. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved EXERCISES SET A

40. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved EXERCISES SET A

41. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved EXERCISES SET A

42. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved EXERCISES SET A

43. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved EXERCISES SET A

44. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

45. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved PRACTICE TEST

46. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved PRACTICE TEST

47. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved PRACTICE TEST

48. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved PRACTICE TEST

49. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved PRACTICE TEST

50. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved PRACTICE TEST

51. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved