basic math conversions math for water technology mth 082 fall 08 chapters 1, 2, 4, and 7 lecture 1...
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Basic Math ConversionsBasic Math Conversions
Math for Water TechnologyMTH 082
Fall 08Chapters 1, 2, 4, and 7
Lecture 1
Math for Water TechnologyMTH 082
Fall 08Chapters 1, 2, 4, and 7
Lecture 1
Why are you here?
Lai
d of
f/ret
ra...
Mili
tary
Just
ent
erin
g ...
Dec
ided
to g
o ...
25% 25%25%25%
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
What is your education level?
Hig
h Sch
ool o
r GED
Ass
ociat
es D
egre
e
BS o
r BA/C
olle
ge D...
Gra
duate
Level
33%
0%
67%
0%
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
How much math have you taken?
Hig
h Sch
ool M
a...
Colle
ge M
ath (.
..
Colle
ge A
lgeb
r...
Inte
rmed
iate
A...
Cal
culu
s or h
i...
20% 20% 20%20%20%
1. High School Math2. 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 Math2. College Math (MTH10-
MTH50)3. College Algebra I (MTH
060)4. Intermediate Algebra II
(MTH 065)5. Calculus or higher (MTH
251+)
Have you taken the Math Placement Exam for incoming students in the testing center?
Have you taken the Math Placement Exam for incoming students in the testing center?
1. Yes
2. No
1. Yes
2. No
I have had MTH 065 (Intermediate College Algebra II) and thus
completed the prerequisite for this course?
I have had MTH 065 (Intermediate College Algebra II) and thus
completed the prerequisite for this course?
Tru
e
Fal
se
0%0%
1. True
2. False
1. True
2. False
Although I have not completed the prerequisite for this course, I am
willing to work _________% harder than my teammates?
Although I have not completed the prerequisite for this course, I am
willing to work _________% harder than my teammates?
100% 50
%25
% 0%
25% 25%25%25%
1. 100%
2. 50%
3. 25%
4. 0%
1. 100%
2. 50%
3. 25%
4. 0%
ObjectivesObjectives
Review and demonstrate proficiency in math problems that include:
1. manipulation of fractions and decimals2. percent and unit conversions
Review and demonstrate proficiency in math problems that include:
1. manipulation of fractions and decimals2. percent and unit conversions
RULES TO SOLVING MATH PROBLEMS
RULES TO SOLVING MATH PROBLEMS
1.READ THE PROBLEM FIRST (AND PUT IT INTO YOUR OWN WORDS)
2.LAY OUT THE PROBLEM=DRAW A DIAGRAM3.DETERMINE WHAT YOU HAVE AND WHAT YOU
NEED (YOU MAY HAVE EXTRA)4.PERFORM CONVERSIONS5.ARTICULATE THE REASON FOR USING AN
EQUATION 6.DO DIMENSIONAL ANALYSIS FIRST7.APPLY THE EQUATION---DO NOT PLUG AND
CHUG8.SOLVE THE PROBLEM9.CHECK YOUR WORK
1.READ THE PROBLEM FIRST (AND PUT IT INTO YOUR OWN WORDS)
2.LAY OUT THE PROBLEM=DRAW A DIAGRAM3.DETERMINE WHAT YOU HAVE AND WHAT YOU
NEED (YOU MAY HAVE EXTRA)4.PERFORM CONVERSIONS5.ARTICULATE THE REASON FOR USING AN
EQUATION 6.DO DIMENSIONAL ANALYSIS FIRST7.APPLY THE EQUATION---DO NOT PLUG AND
CHUG8.SOLVE THE PROBLEM9.CHECK YOUR WORK
Decimal PlacesDecimal Places
http://www.gomath.com/htdocs/lesson/decimal_lesson1.htmhttp://www.gomath.com/htdocs/lesson/decimal_lesson1.htm
Greater than 1Greater than 1 Less than 1Less than 1
10
1100
1
1000
1110100
Basic Math ConversionsBasic Math Conversions
Chapter 1Power and Scientific Notation
Chapter 1Power and Scientific Notation
Rules of Power and Scientific Notation
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!
Rules of Scientific NotationRules of Scientific Notation
Rule 4 = when you divide the numbers in scientific notation, divide the numbers but subtract the exponents.
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.Rule 3 = when you multiply the numbers in scientific notation, multiply the numbers but add the exponents.
POWERPOWERNumeric20=121 =222= 2 X 2 = 423 = 2 X 2 X 2= 8
Numeric20=121 =222= 2 X 2 = 423 = 2 X 2 X 2= 8
Englishft2= ft X ftm3= meter X meter X meter
Englishft2= ft X ftm3= meter X meter X meter
POWERPOWER
Numeric Expanded and Exponential FormNumeric Expanded and Exponential Form
)3
2)(
3
2()
3
2( 2
)3
1(3
22
))8)(8(
1()
8
1(8
22
))5)(5)(5(
)4)(4(()
5
4(
3
2
English Expanded and Exponential FormEnglish Expanded and Exponential Form
)) )( )( (
) )( (()(
3
2
m
km22
2
)()))((
))((()(
ft
in
ftft
inin
ft
in
Your TurnYour Turn
Scientific NotationScientific Notation
Scientific Notation = number multiplied by power of tenScientific Notation = number multiplied by power of ten
54)104.5(104.5 1
200,1))10)(10)(10(2.1(102.1 3
0362.0)10
62.3())
10
1)(
10
1(62.3(1062.3
22
Your Turn (Write It All out!!!)Your Turn (Write It All out!!!)
10800.4 3 10350 3
Scientific NotationScientific Notation
Scientific Notation = Taken out!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!
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!
10039.0 2
Your TurnYour Turn
105200.0 3
890,977890.910789.9 4 17890.01789010890,17 5
Positive four places to rightPositive four places to right Negative five places to leftNegative five places to left
25 X 10-4 = ?
25.0
025
2500
00
None
of the
ab.
..
0%
13%13%
73%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
Scientific NotationScientific Notation
Scientific Notation = Put Into!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!
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!
110 5.775
420
Your TurnYour Turn
0041.0
310 2.11200
-210 62.30362.
0.0058 = ?
5.8
X 1
0-3
58
X 10-
4
0.5
8 X 1
0-2
All
of the
abo...
47%
40%
0%
13%
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
Multiplying in Scientific Notation
Multiplying in Scientific Notation
Rule 3 = when you multiply the numbers in scientific notation, multiply the numbers but add the exponents.Rule 3 = when you multiply the numbers in scientific notation, multiply the numbers but add the exponents.
7)34(34 1012)10()43()104()10 3(
7)34(3-4 1030)10()65()106()10 5(
)106()102()103()0006.0()2.0()003(. 413
8)413( 1036)10()36()62 3( Your TurnYour Turn
)002.0()2.0()02(.
Dividing in Scientific NotationDividing in Scientific Notation
Rule 4 = when you divide the numbers in scientific notation, divide the numbers but subtract the exponents.
Rule 4 = when you divide the numbers in scientific notation, divide the numbers but subtract the exponents.
1)34(3
4
102)10()2
4(
)102(
)10 4(
3)1(21
2
104)102
8()
102
108(
)2.0(
)800(
Your TurnYour Turn
)3.0(
)006.0(
Basic Math ConversionsBasic Math Conversions
Chapter 2Dimensional Analysis
Chapter 2Dimensional Analysis
MATT’S RULE
ALWAYS USE DIMENSIONAL ANALYSIS BEFORE YOU PLUG AND
CHUG!
MATT’S RULE
ALWAYS USE DIMENSIONAL ANALYSIS BEFORE YOU PLUG AND
CHUG!
Dimensional AnalysisDimensional Analysis
33
ft
galor
(ft) (ft) ft)(
galftgal
3
3
ftgalmingal
t)(ft)(ft)(fgalmingal
gal/ft
gal/min
3
232
mm
kmor
(mm) (mm) (mm)
(km)(km)mmkm
m
(sec)(sec)
(mm) (mm) (mm)
(km)(km)
(sec)(sec)
(mm) (mm) (mm)(km)(km)
sec/
mmkm2
32
mm
Dividing is the same as multiplying by the INVERSEDividing is the same as multiplying by the INVERSEYour TurnYour Turn
sec/
sec/3
ft
ft
Dimensional AnalysisMultiplication and Division
Dimensional AnalysisMultiplication and Division
gal1
gal
1
t)(ft)(ft)(f
(ft) (ft) (ft)
gal))(ftft(gal 33
Need answer in gallonsNeed answer in gallons
Need answer in square feetNeed answer in square feet
WRONG!(sec)
ft
(sec)
(ft)
(sec)
t)(ft)(ft)(fft/sec) (3.5)secft (80
2
43
23 ft(ft)
(sec)
(sec)
t)(ft)(ft)(f
sec
(sec)t)(ft)(ft)(f
ft/sec) )/(3.5secft (80 ft
Dimensional AnalysisMultiplication and Division
Dimensional AnalysisMultiplication and Division
Need answer in cubic meters per secondNeed answer in cubic meters per second
YEP!(sec)
m
(1)
)(m
(sec)
(m))m (5)secm (100
322
UGLY!(sec)m
m
m
1
(sec)
(m)
1(m)(m)(sec)(m)
)m )/(5secm (10022
2
WORD PROBLEMWORD PROBLEMThe flow rate in a water line is 2.3 ft3/sec. What is the flow rate as gallons per minute? The flow rate in a water line is 2.3 ft3/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 problemStep 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 diagramStep 2: Draw a diagram2.3 ft3/sec2.3 ft3/sec gal/min?gal/min?
Step 3: Conversions? GIVEN: 2.3 ft3/sec NEED: gal/minCONVERSIONS:
7.48 ft3/gal 60 sec/min
Step 3: Conversions? GIVEN: 2.3 ft3/sec NEED: gal/minCONVERSIONS:
7.48 ft3/gal 60 sec/min
WORD PROBLEMWORD PROBLEMThe flow rate in a water line is 2.3 ft3/sec. What is the flow rate as gallons per minute? The flow rate in a water line is 2.3 ft3/sec. What is the flow rate as gallons per minute?
Step 4: Convert ft3/sec to gal min. Dimensional Analysis First. To multiply or divide?
Step 4: Convert ft3/sec to gal min. Dimensional Analysis First. To multiply or divide?
2.3 ft3/sec2.3 ft3/sec gal/min?gal/min?
)(min
gal
min
sec
t)(ft)(ft)(f
gal
sec
t)(ft)(ft)(fsec/min 60 )
ft
gal (7.48 )secft (2.3
33 Yes
Step 5: Solve the problem.Step 5: Solve the problem.
min
gal1032sec/min 60 )
ft
gal (7.48 )secft (2.3
33
WORD PROBLEMWORD PROBLEMA 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?
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 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 diagramStep 2: Draw a diagram
Step 3: Conversions? GIVEN: 1.8 ft/sec , 3ft, 2 ft NEED: ft3/secCONVERSIONS:
None necessary
Step 3: Conversions? GIVEN: 1.8 ft/sec , 3ft, 2 ft NEED: ft3/secCONVERSIONS:
None necessary
1.8 ft/sec1.8 ft/sec3 ft
2 ftft3/sec?ft3/sec?
WORD PROBLEMWORD PROBLEMA 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?
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: ft3/secCONVERSIONS: 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: ft3/secCONVERSIONS: None necessary
Step 4 Equation : flow in channel (FC) = f X w X d
Step 5: Solve Dimensional Analysis First!
1.8 ft/sec1.8 ft/sec3 ft
2 ftft3/sec?ft3/sec?
YES!sec
ft
1
ft
1
ft
sec
ftft) (2 ft) (3 )secft (1.8
3
WORD PROBLEMWORD PROBLEMA 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?
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/sec1.8 ft/sec3 ft
2 ftft3/sec?ft3/sec?
sec
ft8.10ft) (2 ft) (3 )secft (1.8
3
Basic Math ConversionsBasic Math Conversions
Chapter 3Rounding and Estimating
Chapter 3Rounding and Estimating
Decimal PlacesDecimal Places
http://www.gomath.com/htdocs/lesson/decimal_lesson1.htmhttp://www.gomath.com/htdocs/lesson/decimal_lesson1.htm
Greater than 1Greater than 1 Less than 1Less than 1
10
1100
1
1000
1110100
Basic Rulesof RoundingBasic Rulesof 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
RoundingRounding
Round 342,427 to the nearest thousands342,427 ≈ 342,000
Round 342,427 to the nearest thousands342,427 ≈ 342,000
Rounding place (less then 5 everything to right =0)Rounding place (less then 5 everything to right =0)
hundreds placehundreds 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.
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 placeRound 1,342,427 to the nearest hundred thousands place
Your TurnYour Turn
1,342,427 ≈
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)Rounding place (greater then 5 increase value by 1)
tens placetens place
RoundingRoundingRule 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 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 placeRound 248,722 to the nearest thousands place
Your TurnYour Turn
248,722 ≈
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)Rounding place (greater then 5 increase value by 1)
tenths placetenths place
RoundingRoundingRule 3: When rounding decimal numbers to the right of the decimal point, drop the rounded digits.Rule 3: When rounding decimal numbers to the right of the decimal point, drop the rounded digits.
Round 483.16 to the nearest unitRound 483.16 to the nearest unit
Your TurnYour Turn
483.16 ≈
Round 549,012 to the nearest ten thousands
5500
00
5490
12
5490
00
Not e
nough in
f...
94%
0%6%
0%
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
Estimate the value of 20 X 30 = (2 X 3) = 6 with two zeros at the end =600Estimate the value of 20 X 30 = (2 X 3) = 6 with two zeros at the end =600
EstimatingEstimatingFactoid: 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 =24,000Estimate 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 =400,000Estimate 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 =28,000,000Estimate 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 79 X 7
EstimatingEstimatingFactoid: 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=200Estimate 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 700/6,000 = cancel zeros 7/60= 1.01.00.760
Estimate the value of (20)(400)/(50)(80) = cancel zeros =(20)(4)/(5)(8)= 80/40= cancel zeros =8/4=2Estimate the value of (20)(400)/(50)(80) = cancel zeros =(20)(4)/(5)(8)= 80/40= cancel zeros =8/4=2
Basic Math ConversionsBasic Math Conversions
Chapter 4Solving for the Unknown
“Basic Algebra”
Chapter 4Solving for the Unknown
“Basic Algebra”
Solving For The UnknownSolving For The Unknown
12X2
24X
)24((X) (2)
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!
A
VAQ
V
Q
A THE ISOLATE 1 RULE
A FOR SOLVE
208642
8X
64220X
XFor Solve 20X642
WORKCHECK
2016642
16X
64220X
XFor Solve 20X642
WORKCHECK
Solving For The UnknownSolving For The UnknownRule 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
2X
2412X
SIDE ONE TO X ISOLATE :1 RULE
8)(3)((6)(x)(2)
MULTIPLY CROSS :2 ULE
X FOR SOLVE )6
3()
8
)2)(((
R
x
Solving For The UnknownSolving For The Unknown
1
)32
1(322)3
32
1(
23(32)
(8)(4)(X) (16)(2)
SIDE ONE TO X ISOLATE :1 RULE
1
(8)(X))4(
(8)(X)
(16)(2)
1
(8)(X)
other) the todue side one todoyou (Whatever NUMERATOR TO X ISOLATE :1 ULE
))(8(
X FOR SOLVE )4()2)(16(
X
X
XFORSOLVE
X
R
X
Chlorine DosageChlorine DosageChlorine 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?
DemandChlorinelmg
Xlmglmg
LmgXlmg
Dose
/8.6
/2.0/7
/2.0/7
Residual Demand
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?
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?
55.
5 m
g/L
49.
5 m
g/l
50.
5 m
g/l
0%8%
92%
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
(X) – 12 = 6 Solve for X? 3
X=2
7
X=3
0
X=5
4
X =
21
10%0%
90%
0%
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:
20 ft2 = (15 ft X H) Solve for H? 2
27.
5 ft
2.6
7 ft
1.4
7 ft
0% 0%
100%A= (B X H) 2 2A=(B)(H)2A= H B
2(20ft2)=(15 ft)(H)40 ft2 =(15 ft)(H)40ft2 = (H)15 ft
2.67 ft =H
A= (B X H) 2 2A=(B)(H)2A= H B
2(20ft2)=(15 ft)(H)40 ft2 =(15 ft)(H)40ft2 = (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
Basic Rulesof PercentsBasic Rulesof Percents
100WHOLE
PARTPERCENT
FACTOID. The term efficacy refers to a percentFACTOID. 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.
Rule 1. In calculations greater than 100 percent, the numerator of the percent equation must always be larger than the denominator.
Percents Fractions DecimalsPercents Fractions Decimals
2000
1
10000
5
100
1
100
5
100100
5
or 0005.0100
05.%05.
250
1
1000
4
100
1
10
4
100104
or 004.0100
4.0%4.0
02.0100
2%2
%9595.0100
95or 95.0
100
95%95
%2020.0100
20or 20.0
100
20%20
PercentsPercents
08.0100
8%8
:StateYork Newfor Tax Sales
005.0100
05.%05.
95.0100
95%95
%2020.0100
20or 20.0
100
20%20
Percent Word ProblemsPercent Word ProblemsA certain piece of equipment is having mechanical difficulties. If the equipment fails 6 times out of 25 tests, what percent failure does this represent?
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?
100WHOLE
PARTPERCENT
failure 24% 100 0.24 10025
6PERCENT
Percent Word ProblemsPercent Word ProblemsThe 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.
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.
100WHOLE
PARTPERCENT
efficacy removal turbidity95% 10010
9.5PERCENT
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
Percent Word ProblemsPercent 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.
A treatment plant was designed to treat 60 Mgd. One day it treated 66 Mgd. What % of the design capacity does this represent.
100WHOLE
PARTPERCENT
110%1001.1 10060
66PERCENT
Rule 1. In calculations greater than 100 percent, the numerator of the percent equation must always be larger than the denominator.
Rule 1. In calculations greater than 100 percent, the numerator of the percent equation must always be larger than the denominator.
Percent Word ProblemsPercent Word Problems16 is 80% of what?16 is 80% of what?
200.8
16W
160.8W
)1
W(
W
16(W) 0.8
160.8
8.0 100
80%80
W
P%
W
Find 90% of 5?Find 90% of 5?
P4.5
)1
5(
5
P(5) 0.9
5
P0.9
9.0 100
90%90
W
P%
High test hypochlorite or HTH has 32.5 lbs of active chlorine in a 50 lb container. What is the % active in
the container?
High test hypochlorite or HTH has 32.5 lbs of active chlorine in a 50 lb container. What is the % active in
the container?
25% 10 50
65%
0%
100%
0%0%
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%
Basic Math ConversionsBasic Math Conversions
Chapter 5Ratios and Proportions
Chapter 5Ratios and Proportions
Rules of Ratios and Proportions
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 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 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)
Rule 3 = Make the two remaining values of the problem into the second fraction. (smaller in numerator, larger in denominator)
Ratios and ProportionsRatios and Proportions
uelarger val
luesmaller va
uelarger val
luesmaller va
ey...........mon ...........lbs
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 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
hrsx
x
hrsx
65
30
3055men
3men
hr 10
xhr
Ratios and ProportionsRatios and Proportions
uelarger val
luesmaller va
uelarger val
luesmaller va
ey...........mon ...........lbs
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 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
lbgal
gallbx
gal
allbx
allbx
252
)10)(5(
000,2
)g 000,0(1 )5(
)g 000,0(1 )5(000,2
gal 10,000
gal 2,000
x
lb 5
Ratios and ProportionsRatios and Proportions
yes! so 4 (4)(1) and 4)2)(2(
?4
2
2
1 Are
alproportionand
yes! so 294 (7)(42) and 294)98)(3(
?98
42
7
3 Are
alproportionand
x
x
x
xand
46.1813
(6)(40)
))(13()40)(6(
for x. solve 4013
6
Ratios and ProportionsRatios and Proportions
uelarger val
luesmaller va
uelarger val
luesmaller va
ey...........mon ...........lbs
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 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
hrsx
x
hrsx
65
30
3055
3
hr 10
x
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?
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
5.2
hrs
2.1
6 hrs
2.5
hrs
32.
5 hrs
75%
25%
0%0%
uelarger val
luesmaller va
uelarger val
luesmaller va
...........gpm ...........hrs
X hrs = 6 gpm13 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 gpm13 Hrs 15 gpm
(15 gpm)(X HRS) = (6 gpm)(13 hrs)
( X hrs) = (6 gpm)(13 hrs) (15 gpm)Hrs = 5.2
Mixed numbersMixed numbersMixed 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 .
8
51
8
51
8
5
8
8
8
13
http://www.visualfractions.com/MixtoFrCircle.html
42/5 is what mixed number? 42/5 is what mixed number?
4 2/
51
3/5
1 1/
5 0
...
88%
0%0%
13%
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
Sig FigsSig 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
Sig FigsSig FigsRule 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
Sig FigsSig FigsRule: 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 m135.28 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 m135.28 m (2 decimal places)
http://www.sciencebyjones.com/multiply_sig_figs.htm
Sig FigsSig FigsRule: 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 m2
but must be recorded as 2.52 m2 (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 m2
but must be recorded as 2.52 m2 (3 sig figs)
http://www.sciencebyjones.com/multiply_sig_figs.htm
How many Sig Figs are in 108,602?
How many Sig Figs are in 108,602?
4 6 1 3
0% 0%0%
100%
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
How many Sig Figs are in 108.00108?
How many Sig Figs are in 108.00108?
3 8 4 3
0% 0%0%
100%
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
Basic Math ConversionsBasic Math Conversions
Unit ConversionsMathematics Chapter 2 Dimensional Analysis
Unit ConversionsMathematics Chapter 2 Dimensional Analysis
RULES FOR CONVERSIONSRULES 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
Unit ConversionsUnit ConversionsExample 1. Convert 4,000 cu. Inches to cu. yardsExample 1. Convert 4,000 cu. Inches to cu. yards
)!(8.0)27
1)(
1728
1)(000,4(
)!(........)3
1)(
12
1)(000,4(
)3
1)(
12
1)(000,4(
)3
1()
12
1)(000,4(
33
3
3
33
33
3
3
33
3
3
3
33
333
yesydft
yd
in
ftin
yesydft
yd
in
ftin
ft
yd
in
ftin
ft
yd
in
ftin
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
Unit ConversionsUnit ConversionsExample 2. Convert 5000 gallons to cu. yardsExample 2. Convert 5000 gallons to cu. yards
)!(7.24)27
1)(
48.7
1)(000,5(
)!(........)27
1)(
48.7
1)(000,5(
)3
1)(
48.7
1)(000,5(
)3
1)(
48.7
1)(000,5(
33
33
33
33
3
33
33
yesydft
yd
gal
ftgal
yesydft
yd
gal
ftgal
ft
yd
gal
ftgal
ft
yd
gal
ftgal
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
How many gallons are there in 82 ft3?
10.
9 g
613
gal
I don’t
know
18%
0%
82%
7.48g (82 ft3) =613 or 610 g rounded 1 ft3 7.48g (82 ft3) =613 or 610 g rounded 1 ft3
1. 10.9 g
2. 613 gal
3. I don’t know
1. 10.9 g
2. 613 gal
3. I don’t know
Convert 3.2 ft3/sec to million gallons per day?
3.2
mgd
2.1
mgd
5.0
mgd
I don’t
know
0% 0%0%
100%
3.2 ft3 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 ft3 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
Basic Math ConversionsBasic Math Conversions
% to mg/L
REMEMBER: 1 ppm = 1mg/L% to mg/L
REMEMBER: 1 ppm = 1mg/L
% to Mg/L Word Problems% to Mg/L Word ProblemsYou can memorize or set up a ratio. Its your choiceYou can memorize or set up a ratio. Its your choice
Rule 1. to convert mg/L (ppm) to % multiply by 0.0001Rule 1. to convert mg/L (ppm) to % multiply by 0.0001
Rule 2. to convert % to mg/L (ppm) multiply by 10,000 Rule 2. to convert % to mg/L (ppm) multiply by 10,000
Rule 3. Ratio for percent to mg/L:Rule 3. Ratio for percent to mg/L:
l
mgx
l
mg%
000,10
%1
% to Mg/L Word Problems% to Mg/L Word ProblemsExample 1. Convert 0.55% to mg/LExample 1. Convert 0.55% to mg/L
l
mg
l
mgC
l
mg
l
mgC
l
mgC
l
mg
l
mgx
l
mg
500,5)(
%)55.0)(000,10()%)(1(
%55.0
000,10
%1
%
000,10
%1
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
% to Mg/L Word Problems% to Mg/L Word ProblemsExample 2. Convert 2,000 mg/L to percentExample 2. Convert 2,000 mg/L to percent
%)(%2.0
%)()10(
)2(
%)()000,10(
)000,2%)(1(
%))(000,10()000,2%)(1(
000,2
%
000,10
%1
%
000,10
%1
P
P
l
mgl
mg
P
l
mgl
mg
Pl
mg
l
mgl
mgP
l
mg
l
mgP
l
mg
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
A solution was found to be 1.3% alum. How many milligrams per liter of alum are in the solution?
13,
000
mg/L
1.3
mg/L
130
,000
mg/L
I don’t
know
86%
0%7%7%
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
Temperature ConversionsTemperature Conversions
oF= (9 * oC) + 32 5
oF= (9 * oC) + 32 5
oC= 5 * (oF – 32) 9
oC= 5 * (oF – 32) 9
Convert 17oC to Fahrenheit Convert 17oC to Fahrenheit
Convert 451oF to degrees CelsiusConvert 451oF to degrees Celsius
oF= (9 *17)+32=62.6oF= 63oF 5
oF= (9 *17)+32=62.6oF= 63oF 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 Celsius1. Begin by subtracting 32 from the Fahrenheit #. 2. Divide the answer by 9. 4. Then multiply that answer by 5.
Fahrenheit to Celsius1. Begin by subtracting 32 from the Fahrenheit #. 2. Divide the answer by 9. 4. Then multiply that answer by 5.
oC= 5* (oF -32)=232.7oC= 233oC 9
oC= 5* (oF -32)=232.7oC= 233oC 9
Convert 75oF to degrees Celsius?
24
oC
107
oC
I don’t
know
50%
0%
50%
1. 24 oC
2. 107 oC
3. I don’t know
1. 24 oC
2. 107 oC
3. I don’t know
oC=5/9 (oF - 32)oC=5/9 (o75 - 32)oC=0.55 (43)oC = 24
oC=5/9 (oF - 32)oC=5/9 (o75 - 32)oC=0.55 (43)oC = 24
The objectives for this week were met with the assignment
and lecture?
Stro
ngly A
gree
Agre
e
Dis
agre
e
Stro
ngly D
isag
ree
46%
0%
8%
46%
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 decimals2. Percent and unit conversions
Review and demonstrate proficiency in math problems that include:
1. Manipulation of fractions and decimals2. Percent and unit conversions