1. Basic Math Conversions Math for Water Technology MTH 082 Fall 08 Chapters 1, 2, 4, and 7 Lecture 1 Math for Water Technology MTH 082 Fall 08 Chapters 1, 2, 4, and 7 Lecture 1

2. Why are you here? 1.Laid off/retraining 2.Military 3.Just entering college 4.Decided to go back to school to complete college/degree 1.Laid off/retraining 2.Military 3.Just entering college 4.Decided to go back to school to complete college/degree

3. What is your education level? 1.High School or GED 2.Associates Degree 3.BS or BA/College Degree 4.Graduate Level 1.High School or GED 2.Associates Degree 3.BS or BA/College Degree 4.Graduate Level

4. How much math have you taken? 1.High School Math 2.College Math (MTH10- MTH50) 3.College Algebra I (MTH 060) 4.Intermediate Algebra II (MTH 065) 5.Calculus or higher (MTH 251+) 1.High School Math 2.College Math (MTH10- MTH50) 3.College Algebra I (MTH 060) 4.Intermediate Algebra II (MTH 065) 5.Calculus or higher (MTH 251+)

5. Have you taken the Math Placement Exam for incoming students in the testing center? 1.Yes 2.No 1.Yes 2.No

6. I have had MTH 065 (Intermediate College Algebra II) and thus completed the prerequisite for this course? 1.True 2.False 1.True 2.False

7. Although I have not completed the prerequisite for this course, I am willing to work _________% harder than my teammates? 1.100% 2.50% 3.25% 4.0% 1.100% 2.50% 3.25% 4.0%

8. Objectives Review and demonstrate proficiency in math problems that include: 1. manipulation of fractions and decimals 2. percent and unit conversions Review and demonstrate proficiency in math problems that include: 1. manipulation of fractions and decimals 2. percent and unit conversions

9. RULES TO SOLVING MATH PROBLEMS 1.READ THE PROBLEM FIRST (AND PUT IT INTO YOUR OWN WORDS) 2.LAY OUT THE PROBLEM=DRAW A DIAGRAM 3.DETERMINE WHAT YOU HAVE AND WHAT YOU NEED (YOU MAY HAVE EXTRA) 4.PERFORM CONVERSIONS 5.ARTICULATE THE REASON FOR USING AN EQUATION 6.DO DIMENSIONAL ANALYSIS FIRST 7.APPLY THE EQUATION---DO NOT PLUG AND CHUG 8.SOLVE THE PROBLEM 9.CHECK YOUR WORK 1.READ THE PROBLEM FIRST (AND PUT IT INTO YOUR OWN WORDS) 2.LAY OUT THE PROBLEM=DRAW A DIAGRAM 3.DETERMINE WHAT YOU HAVE AND WHAT YOU NEED (YOU MAY HAVE EXTRA) 4.PERFORM CONVERSIONS 5.ARTICULATE THE REASON FOR USING AN EQUATION 6.DO DIMENSIONAL ANALYSIS FIRST 7.APPLY THE EQUATION---DO NOT PLUG AND CHUG 8.SOLVE THE PROBLEM 9.CHECK YOUR WORK

10. Decimal Places http://www.gomath.com/htdocs/lesson/decimal_lesson1.htm Greater than 1 Less than 1

11. Basic Math Conversions Chapter 1 Power and Scientific Notation Chapter 1 Power and Scientific Notation

12. Rules of Power and Scientific Notation Rule 1 = when a number is TAKEN out of scientific notation Positive exponent value move decimal point to the right Negative exponent value move decimal point to the left! Rule 1 = when a number is TAKEN out of scientific notation Positive exponent value move decimal point to the right Negative exponent value move decimal point to the left! Rule 2 = when a number is PUT into scientific notation Decimal point to the left indicates a positive exponent Decimal point move to the right indicates negative exponent values! Rule 2 = when a number is PUT into scientific notation Decimal point to the left indicates a positive exponent Decimal point move to the right indicates negative exponent values!

13. Rules of Scientific Notation Rule 4 = when you divide the numbers in scientific notation, divide the numbers but subtract the exponents. Rule 3 = when you multiply the numbers in scientific notation, multiply the numbers but add the exponents.

14. POWER Numeric 2 0 =1 2 1 =2 2 2 = 2 X 2 = 4 2 3 = 2 X 2 X 2= 8 Numeric 2 0 =1 2 1 =2 2 2 = 2 X 2 = 4 2 3 = 2 X 2 X 2= 8 English ft 2 = ft X ft m 3 = meter X meter X meter English ft 2 = ft X ft m 3 = meter X meter X meter

15. 3 3 =? 3 X 3 X 3 = 27 1.9 2.27 3.1 4.0 1.9 2.27 3.1 4.0

16. POWER Numeric Expanded and Exponential Form English Expanded and Exponential Form Your Turn

17. Scientific Notation Scientific Notation = number multiplied by power of ten Your Turn (Write It All out!!!)

18. Scientific Notation Scientific Notation = Taken out! Rule 1 = when a number is taken out of scientific notation a positive exponent value indicates a move of the decimal point to the right and a negative exponent value indicates a decimal point move to the left! Your Turn Positive four places to right Negative five places to left

19. 25 X 10 -4 = ? 25 X 10 -4 = Move decimal four spots to left.0025 25 X 10 -4 = Move decimal four spots to left.0025 1.25 2..0025 3.250,000 4.None of the above 1.25 2..0025 3.250,000 4.None of the above

20. Scientific Notation Scientific Notation = Put Into! Rule 2 = when a number is PUT into scientific notation a decimal point to the left indicates a positive exponent and a decimal point move to the right indicates a negative exponent values! Your Turn

21. 0.0058 = ? 1.5.8 X 10 -3 2.58 X 10 -4 3.0.58 X 10 -2 4.All of the above 1.5.8 X 10 -3 2.58 X 10 -4 3.0.58 X 10 -2 4.All of the above

22. Multiplying in Scientific Notation Rule 3 = when you multiply the numbers in scientific notation, multiply the numbers but add the exponents. Your Turn

23. Dividing in Scientific Notation Rule 4 = when you divide the numbers in scientific notation, divide the numbers but subtract the exponents. Your Turn

24. Basic Math Conversions Chapter 2 Dimensional Analysis Chapter 2 Dimensional Analysis

25. MATT’S RULE ALWAYS USE DIMENSIONAL ANALYSIS BEFORE YOU PLUG AND CHUG!

26. Dimensional Analysis Dividing is the same as multiplying by the INVERSE Your Turn

27. Dimensional Analysis Multiplication and Division Dimensional Analysis Multiplication and Division Need answer in gallons Need answer in square feet

28. Dimensional Analysis Multiplication and Division Dimensional Analysis Multiplication and Division Need answer in cubic meters per second

29. WORD PROBLEM The flow rate in a water line is 2.3 ft 3 /sec. What is the flow rate as gallons per minute? Step 1: Use your own words. Got a pipe with a known flow rate, need to convert that value from one unit to another. This is a simple conversion problem Step 2: Draw a diagram 2.3 ft 3 /sec gal/min? Step 3: Conversions? GIVEN: 2.3 ft 3 /secNEED: gal/min CONVERSIONS: 7.48 ft 3 /gal 60 sec/min Step 3: Conversions? GIVEN: 2.3 ft 3 /secNEED: gal/min CONVERSIONS: 7.48 ft 3 /gal 60 sec/min

30. WORD PROBLEM The flow rate in a water line is 2.3 ft 3 /sec. What is the flow rate as gallons per minute? Step 4: Convert ft 3 /sec to gal min. Dimensional Analysis First. To multiply or divide? 2.3 ft 3 /sec gal/min? Step 5: Solve the problem.

31. WORD PROBLEM A channel is 3 ft wide with water flowing to a depth of 2 ft. The velocity in the channel is found to be 1.8 ft/sec. What is the flow rate in the channel in cubic feet per second? Step 1: Use your own words. Got a channel with known dimensions and a flow rate, need to convert that value from one unit to another. This is a simple conversion problem Step 2: Draw a diagram Step 3: Conversions? GIVEN: 1.8 ft/sec, 3ft, 2 ft NEED: ft 3 /sec CONVERSIONS: None necessary Step 3: Conversions? GIVEN: 1.8 ft/sec, 3ft, 2 ft NEED: ft 3 /sec CONVERSIONS: None necessary 1.8 ft/sec 3 ft 2 ft ft 3 /sec?

32. WORD PROBLEM A channel is 3 ft wide with water flowing to a depth of 2 ft. The velocity in the channel is found to be 1.8 ft/sec. What is the flow rate in the channel in cubic feet per second? Step 3: Conversions? GIVEN: f=1.8 ft/sec, w=3ft, d=2 ft NEED: ft 3 /sec CONVERSIONS: None necessary Step 4 Equation : flow in channel (FC) = f X w X d Step 5: Solve Dimensional Analysis First! Step 3: Conversions? GIVEN: f=1.8 ft/sec, w=3ft, d=2 ft NEED: ft 3 /sec CONVERSIONS: None necessary Step 4 Equation : flow in channel (FC) = f X w X d Step 5: Solve Dimensional Analysis First! 1.8 ft/sec 3 ft 2 ft ft 3 /sec?

33. WORD PROBLEM A channel is 3 ft wide with water flowing to a depth of 2 ft. The velocity in the channel is found to be 1.8 ft/sec. What is the flow rate in the channel in cubic feet per second? Step 6: Solve Problem Equation : flow in channel (FC) = f X w X d where f = flow w = width of channel d = depth of channel Step 6: Solve Problem Equation : flow in channel (FC) = f X w X d where f = flow w = width of channel d = depth of channel 1.8 ft/sec 3 ft 2 ft ft 3 /sec?

34. Basic Math Conversions Chapter 3 Rounding and Estimating Chapter 3 Rounding and Estimating

35. Decimal Places http://www.gomath.com/htdocs/lesson/decimal_lesson1.htm Greater than 1 Less than 1

36. Basic Rules of Rounding A ≈ indicates a number or answer has been rounded Rule 1: When rounding to any desired place if the digit directly to the right of that place is less then 5 replace all digits to the right with zeros. Rule 2: When rounding to any desired place if the digit directly to the right of that place is greater then 5, increase the digit in the rounding place by 1 and replace all digits to the right of the increase with zeros. Rule 3: When rounding decimal numbers to the right of the decimal point, drop the rounded digits A ≈ indicates a number or answer has been rounded Rule 1: When rounding to any desired place if the digit directly to the right of that place is less then 5 replace all digits to the right with zeros. Rule 2: When rounding to any desired place if the digit directly to the right of that place is greater then 5, increase the digit in the rounding place by 1 and replace all digits to the right of the increase with zeros. Rule 3: When rounding decimal numbers to the right of the decimal point, drop the rounded digits

37. Rounding Round 342,427 to the nearest thousands 342,427 ≈ 342,000 Round 342,427 to the nearest thousands 342,427 ≈ 342,000 Rounding place (less then 5 everything to right =0) hundreds place Rule 1: When rounding to any desired place if the digit directly to the right of that place is less then 5 replace all digits to the right with zeros. Round 1,342,427 to the nearest hundred thousands place Your Turn 1,342,427 ≈

38. Round 37,926 to the nearest tens 37,926 ≈ 37,930 Round 37,926 to the nearest tens 37,926 ≈ 37,930 Rounding place (greater then 5 increase value by 1) tens place Rounding Rule 2: When rounding to any desired place if the digit directly to the right of that place is greater then 5, increase the digit in the rounding place by 1 and replace all digits to the right of the increase with zeros. Round 248,722 to the nearest thousands place Your Turn 248,722 ≈

39. Round 5.654 to the nearest tenth 5.654 ≈ 5.7 Round 5.654 to the nearest tenth 5.654 ≈ 5.7 Rounding place (greater then 5 increase value by 1) tenths place Rounding Rule 3: When rounding decimal numbers to the right of the decimal point, drop the rounded digits. Round 483.16 to the nearest unit Your Turn 483.16 ≈

40. Round 549,012 to the nearest ten thousands 1.550,000 2.549,012 3.549,000 4.Not enough info given 1.550,000 2.549,012 3.549,000 4.Not enough info given

41. Estimate the value of 20 X 30 = (2 X 3) = 6 with two zeros at the end =600 Estimating Factoid: Estimating indicates the approximate size of a calculated answer. Factoid: Estimating indicates the approximate size of a calculated answer. Estimate the value of 40 X 600 = (4 X 6) = 24 with three zeros at the end =24,000 Estimate the value of 40 X 20 X 500 = (4 X 2 X 5) = 40 with four zeros at the end =400,000 Estimate the value of 9 X 700 X 60 X 70 = 2800 with four zeros at the end =28,000,000 63 ≈ 60 X 6 360 ≈ 400 X 7 63 ≈ 60 X 6 360 ≈ 400 X 7 9 X 7

42. Estimating Factoid: Estimating indicates the approximate size of a calculated answer. Factoid: Estimating indicates the approximate size of a calculated answer. Estimate the value of 40,000/200 = cancel zeros 400/2=200 Estimate the value of 700/6,000 = cancel zeros 7/60= Estimate the value of (20)(400)/(50)(80) = cancel zeros =(20)(4)/(5)(8)= 80/40= cancel zeros =8/4=2

43. Basic Math Conversions Chapter 4 Solving for the Unknown “Basic Algebra” Chapter 4 Solving for the Unknown “Basic Algebra”

44. Solving For The Unknown Rule 1 = ISOLATE THE X TO THE NUMERATOR AND/OR ONE SIDE OF THE PROBLEM!! WHATEVER YOU DO TO ONE SIDE DUE TO THE OTHER! Rule 1 = ISOLATE THE X TO THE NUMERATOR AND/OR ONE SIDE OF THE PROBLEM!! WHATEVER YOU DO TO ONE SIDE DUE TO THE OTHER!

45. Solving For The Unknown Rule 2 = In multiplication or division equations with unknown in numerator CROSS MULTIPLY AND THEN ISOLATE/SOLVE THE X Go from the top of one side to the bottom of the other Rule 2 = In multiplication or division equations with unknown in numerator CROSS MULTIPLY AND THEN ISOLATE/SOLVE THE X Go from the top of one side to the bottom of the other

46. Solving For The Unknown

47. Chlorine Dosage Chlorine Dosage = Chlorine Demand +Chlorine Residual The residual in a distribution system is measured to be 0.2 mg/L using a HACH DPD Colorimeter. If the original dose was 7.0 mg/L what is the chlorine demand for the system? Chlorine Dosage = Chlorine Demand +Chlorine Residual The residual in a distribution system is measured to be 0.2 mg/L using a HACH DPD Colorimeter. If the original dose was 7.0 mg/L what is the chlorine demand for the system?

48. A well system was dosed with a slug of 50 mg/L chlorine for 24 hours. The residual in a distribution system is measured to be 0.5 mg/L using a HACH DPD Colorimeter. How much chlorine was gobbled up by organics and inorganics (i.e., chlorine demand) in the water? 1.55.5 mg/L 2.49.5 mg/l 3.50.5 mg/l 1.55.5 mg/L 2.49.5 mg/l 3.50.5 mg/l

49. (X) – 12 = 6 Solve for X? 3 1.X=27 2.X=30 3.X=54 4.X =21 1.X=27 2.X=30 3.X=54 4.X =21 (X) - 12= 6 3 (X) = 6+12 3 (X) = 18 3 (X) = 18 * 3 (X)= 54 ---------------- (54) - 12= 6 3 18-12=6 6=6 (X) - 12= 6 3 (X) = 6+12 3 (X) = 18 3 (X) = 18 * 3 (X)= 54 ---------------- (54) - 12= 6 3 18-12=6 6=6 FORMULA: SOLVED: FORMULA: SOLVED:

50. 20 ft 2 = (15 ft X H) Solve for H? 2 A= (B X H) 2 2A=(B)(H) 2A= H B 2(20ft 2 )=(15 ft)(H) 40 ft 2 =(15 ft)(H) 40ft 2 = (H) 15 ft 2.67 ft =H A= (B X H) 2 2A=(B)(H) 2A= H B 2(20ft 2 )=(15 ft)(H) 40 ft 2 =(15 ft)(H) 40ft 2 = (H) 15 ft 2.67 ft =H 1.27.5 ft 2.2.67 ft 3.1.47 ft 1.27.5 ft 2.2.67 ft 3.1.47 ft

51. Basic Math Conversions Chapter 7 Percents Chapter 7 Percents

52. Basic Rules of Percents FACTOID. The term efficacy refers to a percent Rule 1. In calculations greater than 100 percent, the numerator of the percent equation must always be larger than the denominator.

53. Percents Fractions Decimals

54. Percents

55. Percent Word Problems A certain piece of equipment is having mechanical difficulties. If the equipment fails 6 times out of 25 tests, what percent failure does this represent?

56. Percent Word Problems The raw water entering a treatment plant has a turbidity of 10 ntu. If the turbidity of the finished water is 0.5 ntu, what is the turbidity removal efficacy of the treatment plant. Percent is unknown and 10 ntu = whole. However, 0.5 ntu is not the part removed. It is the turbidity still in the water. Thus, 10 ntu-0.5 ntu= 9.5 ntu Percent is unknown and 10 ntu = whole. However, 0.5 ntu is not the part removed. It is the turbidity still in the water. Thus, 10 ntu-0.5 ntu= 9.5 ntu

57. Percent Word Problems A treatment plant was designed to treat 60 Mgd. One day it treated 66 Mgd. What % of the design capacity does this represent. Rule 1. In calculations greater than 100 percent, the numerator of the percent equation must always be larger than the denominator.

58. Percent Word Problems 16 is 80% of what? Find 90% of 5?

59. High test hypochlorite or HTH has 32.5 lbs of active chlorine in a 50 lb container. What is the % active in the container? 1.25% 2.10 3.50 4.65% 1.25% 2.10 3.50 4.65% P/W * 100 = % 32.5 lbs X 100 = % 50 lbs 0.65 * 100 = % 65% P/W * 100 = % 32.5 lbs X 100 = % 50 lbs 0.65 * 100 = % 65%

60. Basic Math Conversions Chapter 5 Ratios and Proportions Chapter 5 Ratios and Proportions

61. Rules of Ratios and Proportions Rule 1 = If the unknown is expected to be smaller than the known value, put an x in the numerator of the first fraction, and put the known value of the same unit in the denominator. Rule 2 = If the unknown is expected to be larger than the known value, put an x in the denominator of the first fraction, and put the known value of the same unit in the numerator. Rule 3 = Make the two remaining values of the problem into the second fraction. (smaller in numerator, larger in denominator)

62. Ratios and Proportions Rule 1 = If the unknown is expected to be smaller than the known value, put an x in the numerator of the first fraction, and put the known value of the same unit in the denominator. Problem = If 3 men can do a certain job in 10 hours, how long would it take 5 men to do the same job? What is the unknown? Time and it will be smaller…so Problem = If 3 men can do a certain job in 10 hours, how long would it take 5 men to do the same job? What is the unknown? Time and it will be smaller…so

63. Ratios and Proportions Rule 2 = If the unknown is expected to be larger than the known value, put an x in the denominator of the first fraction, and put the known value of the same unit in the numerator. Problem = If 5 lb of chemical are mixed with 2,000 gallons of water to obtain a desired solution, how many pounds of chemical would be mixed with 10,000 gallons of water to obtain a solution of the same concentration? What is the unknown? lbs…so Problem = If 5 lb of chemical are mixed with 2,000 gallons of water to obtain a desired solution, how many pounds of chemical would be mixed with 10,000 gallons of water to obtain a solution of the same concentration? What is the unknown? lbs…so

64. Ratios and Proportions

65. Rule 1 = If the unknown is expected to be smaller than the known value, put an x in the numerator of the first fraction, and put the known value of the same unit in the denominator. Problem = If three men can do a certain job in 10 hours, how long would it take five men to do the same job? What is the unknown? Time and it will be smaller…so Problem = If three men can do a certain job in 10 hours, how long would it take five men to do the same job? What is the unknown? Time and it will be smaller…so

66. If a pump will fill a tank in 13 hours at 6 gpm, how long will it take a 15 gpm pump to fill the same tank? 1.5.2 hrs 2.2.16 hrs 3.2.5 hrs 4.32.5 hrs 1.5.2 hrs 2.2.16 hrs 3.2.5 hrs 4.32.5 hrs X hrs = 6 gpm 13 Hrs 15 gpm (15 gpm)(X HRS) = (6 gpm)(13 hrs) ( X hrs) = (6 gpm)(13 hrs) (15 gpm) Hrs = 5.2 X hrs = 6 gpm 13 Hrs 15 gpm (15 gpm)(X HRS) = (6 gpm)(13 hrs) ( X hrs) = (6 gpm)(13 hrs) (15 gpm) Hrs = 5.2

67. Mixed numbers Mixed Numbers as Fractions uses Circles to demonstrate how a fraction can be renamed from mixed form to fraction form. The circles below show the mixed number 2 2/5. You are to write 2 2/5 in fraction form with only a numerator and denominator. To write the example, you can think of each whole number as 5/5. So in the above example you would have: On the pretest, you can think of 13/8. Mixed Numbers as Fractions uses Circles to demonstrate how a fraction can be renamed from mixed form to fraction form. The circles below show the mixed number 2 2/5. You are to write 2 2/5 in fraction form with only a numerator and denominator. To write the example, you can think of each whole number as 5/5. So in the above example you would have: On the pretest, you can think of 13/8. http://www.visualfractions.com/MixtoFrCircle.html

68. 4 2/5 is what mixed number? 1.22/5 2.8/5 3.6/5 4.2/20 1.22/5 2.8/5 3.6/5 4.2/20 4 (2/5) =? (4)(5)+2= 22 22 5 4 (2/5) =? (4)(5)+2= 22 22 5

69. Basic Math Significant Figures

70. Sig Figs 1. Non-zero digits are always significant 2. Any zeros between two significant digits are significant. 3. A final zero or trailing zeros in the decimal portion ONLY are significant. 1. Non-zero digits are always significant 2. Any zeros between two significant digits are significant. 3. A final zero or trailing zeros in the decimal portion ONLY are significant. http://www.sciencebyjones.com/multiply_sig_figs.htm

71. Sig Figs Rule 1: All non-zero digits are significant. 12.83 cm [4] 16935 g [5] Rule 2: Zeros between other significant figures are significant. 12,038 cm [5] 169.04 g [5] 70,304 g [ ] 395.01 kg [ ] Rule 3: Zeros to the right of a decimal point and to the right of a number are significant. 12.380 cm [5] 169.00 m [5] 3.010 mL [4] 1.30 kg [ ] 1691.100 cm [ ] Rule 4: A zero standing alone to the left of a decimal point is not significant. 0.421 g [3] 0.5 m [ ] Rule 5: Zeros to the right of the decimal and to the left of a number are not significant. 0.000421 mg [3] 0.00180 cm [3] 0.010 kg [ ] 0.01010 m [ ] Rule 1: All non-zero digits are significant. 12.83 cm [4] 16935 g [5] Rule 2: Zeros between other significant figures are significant. 12,038 cm [5] 169.04 g [5] 70,304 g [ ] 395.01 kg [ ] Rule 3: Zeros to the right of a decimal point and to the right of a number are significant. 12.380 cm [5] 169.00 m [5] 3.010 mL [4] 1.30 kg [ ] 1691.100 cm [ ] Rule 4: A zero standing alone to the left of a decimal point is not significant. 0.421 g [3] 0.5 m [ ] Rule 5: Zeros to the right of the decimal and to the left of a number are not significant. 0.000421 mg [3] 0.00180 cm [3] 0.010 kg [ ] 0.01010 m [ ] http://www.sciencebyjones.com/multiply_sig_figs.htm

72. Sig Figs Rule: When adding and subtracting numbers that come from measurements, arrange the numbers in columnar form. The final answer can contain only as many decimal places as found in the measurement with the fewest number of decimal places. Example: 134.050 m + 1.23 m = 134.050 m + 1.23 m 135.28 m (2 decimal places) Rule: When adding and subtracting numbers that come from measurements, arrange the numbers in columnar form. The final answer can contain only as many decimal places as found in the measurement with the fewest number of decimal places. Example: 134.050 m + 1.23 m = 134.050 m + 1.23 m 135.28 m (2 decimal places) http://www.sciencebyjones.com/multiply_sig_figs.htm

73. Sig Figs Rule: In multiplication and division, the result may have no more significant figures than the factor with the fewest number of significant figures. Example: 2.52 m x 1.0004243 m = 2.521069236 m 2 but must be recorded as 2.52 m 2 (3 sig figs) Rule: In multiplication and division, the result may have no more significant figures than the factor with the fewest number of significant figures. Example: 2.52 m x 1.0004243 m = 2.521069236 m 2 but must be recorded as 2.52 m 2 (3 sig figs) http://www.sciencebyjones.com/multiply_sig_figs.htm

74. How many Sig Figs are in 108,602? 1.4 2.6 3.1 4.3 1.4 2.6 3.1 4.3 108,602 All numbers are significant 108,602 All numbers are significant

75. How many Sig Figs are in 108.00108? 1.3 2.8 3.4 4.3 1.3 2.8 3.4 4.3 108.00108 All numbers are significant 108.00108 All numbers are significant

76. Basic Math Conversions Unit Conversions Mathematics Chapter 2 Dimensional Analysis Unit Conversions Mathematics Chapter 2 Dimensional Analysis

77. RULES FOR CONVERSIONS 1.SHOW ALL WORK 2.CARRY YOUR UNITS TILL THE END 3.FOLLOW PROPER ORDER OF OPERATIONS 4.CARRY OUT ALL SQUARING OR CUBING ACTIONS 5.DO NOT JUST WRITE DOWN ANSWERS WITHOUT WORK 6.USE YOUR UNITS TO GUIDE YOU 1.SHOW ALL WORK 2.CARRY YOUR UNITS TILL THE END 3.FOLLOW PROPER ORDER OF OPERATIONS 4.CARRY OUT ALL SQUARING OR CUBING ACTIONS 5.DO NOT JUST WRITE DOWN ANSWERS WITHOUT WORK 6.USE YOUR UNITS TO GUIDE YOU

78. Unit Conversions Example 1. Convert 4,000 cu. Inches to cu. yards Step 1. Set up conversion Step 2. Carry out unit order of operations (cube) Step 3. Cancel units (do you have the right answer??) Step 4. perform numerical order of operations (square and cube numbers) Final 2 Steps. Multiply denominator together and then divide (2 steps=less likely for mistake with the TI calculator) Step 1. Set up conversion Step 2. Carry out unit order of operations (cube) Step 3. Cancel units (do you have the right answer??) Step 4. perform numerical order of operations (square and cube numbers) Final 2 Steps. Multiply denominator together and then divide (2 steps=less likely for mistake with the TI calculator) Step 1 Step 2 Step 4 Step 3

79. Unit Conversions Example 2. Convert 5000 gallons to cu. yards Step 1. Set up conversion Step 2. Carry out unit order of operations (cube) Step 3. Cancel units (do you have the right answer??) Step 4. perform numerical order of operations (square and cube numbers) Final 2 Steps. Multiply denominator together and then divide (2 steps=less likely for mistake with the TI calculator) Step 1. Set up conversion Step 2. Carry out unit order of operations (cube) Step 3. Cancel units (do you have the right answer??) Step 4. perform numerical order of operations (square and cube numbers) Final 2 Steps. Multiply denominator together and then divide (2 steps=less likely for mistake with the TI calculator) Step 1 Step 2 Step 4 Step 3

80. How many gallons are there in 82 ft 3 ? 7.48g (82 ft 3 ) =613 or 610 g rounded 1 ft 3 7.48g (82 ft 3 ) =613 or 610 g rounded 1 ft 3 1.10.9 g 2.613 gal 3.I don’t know 1.10.9 g 2.613 gal 3.I don’t know

81. Convert 3.2 ft 3 /sec to million gallons per day? 3.2 ft 3 60 sec 1,440 min 7.48 gal 1 million gallon sec 1 min 1d 1 ft3 1,000,000 gallons 2.1 mgd 3.2 ft 3 60 sec 1,440 min 7.48 gal 1 million gallon sec 1 min 1d 1 ft3 1,000,000 gallons 2.1 mgd 1.3.2 mgd 2.2.1 mgd 3.5.0 mgd 4.I don’t know 1.3.2 mgd 2.2.1 mgd 3.5.0 mgd 4.I don’t know

82. Basic Math Conversions % to mg/L REMEMBER: 1 ppm = 1mg/L % to mg/L REMEMBER: 1 ppm = 1mg/L

83. % to Mg/L Word Problems You can memorize or set up a ratio. Its your choice Rule 1. to convert mg/L (ppm) to % multiply by 0.0001 Rule 2. to convert % to mg/L (ppm) multiply by 10,000 Rule 3. Ratio for percent to mg/L:

84. % to Mg/L Word Problems Example 1. Convert 0.55% to mg/L Step 1. Show formula Step 2. Set up ratio Step 3. Cross multiply Step 4. Solve for variable Final Step. Are units correct? Step 1. Show formula Step 2. Set up ratio Step 3. Cross multiply Step 4. Solve for variable Final Step. Are units correct? Step 1 Step 2 Step 3 Step 4

85. % to Mg/L Word Problems Example 2. Convert 2,000 mg/L to percent Step 1. Show formula Step 2. Set up ratio Step 3. Cross multiply Step 4. Solve for variable Step 5. Reduce Fraction Final Step. Solve….Are units correct? Step 1. Show formula Step 2. Set up ratio Step 3. Cross multiply Step 4. Solve for variable Step 5. Reduce Fraction Final Step. Solve….Are units correct? Step 1 Step 2 Step 3 Step 4 Step 5

86. A solution was found to be 1.3% alum. How many milligrams per liter of alum are in the solution? 10,000 mg/L = X 1% 1.3% 10,000 mg/L (1.3) = X 13000 mg/L = x 10,000 mg/L = X 1% 1.3% 10,000 mg/L (1.3) = X 13000 mg/L = x 1.13,000 mg/L 2.1.3 mg/L 3.130,000 mg/L 4.I don’t know 1.13,000 mg/L 2.1.3 mg/L 3.130,000 mg/L 4.I don’t know

87. Basic Math Conversions Temperature Conversions

88. o F= (9 * o C) + 32 5 o F= (9 * o C) + 32 5 o C= 5 * ( o F – 32) 9 o C= 5 * ( o F – 32) 9 Convert 17 o C to Fahrenheit Convert 451 o F to degrees Celsius o F= (9 *17)+32=62.6 o F= 63 o F 5 o F= (9 *17)+32=62.6 o F= 63 o F 5 Celsius to Fahrenheit 1. Begin by multiplying the Celsius temperature by 9. 2. Divide the answer by 5. 3. Now add 32. Celsius to Fahrenheit 1. Begin by multiplying the Celsius temperature by 9. 2. Divide the answer by 5. 3. Now add 32. Fahrenheit to Celsius 1. Begin by subtracting 32 from the Fahrenheit #. 2. Divide the answer by 9. 4. Then multiply that answer by 5. Fahrenheit to Celsius 1. Begin by subtracting 32 from the Fahrenheit #. 2. Divide the answer by 9. 4. Then multiply that answer by 5. o C= 5* ( o F -32)=232.7 oC = 233 o C 9 o C= 5* ( o F -32)=232.7 oC = 233 o C 9

89. Convert 75 o F to degrees Celsius? 1.24 o C 2.107 o C 3.I don’t know 1.24 o C 2.107 o C 3.I don’t know o C=5/9 ( o F - 32) o C=5/9 ( o 75 - 32) o C=0.55 (43) o C = 24 o C=5/9 ( o F - 32) o C=5/9 ( o 75 - 32) o C=0.55 (43) o C = 24

90. The objectives for this week were met with the assignment and lecture? 1.Strongly Agree 2.Agree 3.Disagree 4.Strongly Disagree 1.Strongly Agree 2.Agree 3.Disagree 4.Strongly Disagree Review and demonstrate proficiency in math problems that include: 1. Manipulation of fractions and decimals 2. Percent and unit conversions Review and demonstrate proficiency in math problems that include: 1. Manipulation of fractions and decimals 2. Percent and unit conversions