Basic Math Conversions Math for Water Technology MTH 082 Fall 07 Chapters 1, 2, 4, and 7 Lecture 1 Math for Water Technology MTH 082 Fall 07 Chapters 1, 2, 4, and 7 Lecture 1

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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

Decimal Places Greater than 1 Less than 1

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

Rules of Power and Scientific Notation 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 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 and negative exponent values!

Rules of Scientific Notation Rule 4 = when you multiply the numbers in scientific notation, multiply the numbers but add the exponents. Rule 5 = when you divide the numbers in scientific notation, divide the numbers but subtract the exponents.

POWER Numeric 2 0 =1 2 1 =2 2 2 = 2 X 2 = = ( ) X ( ) X ( )= ________ Numeric 2 0 =1 2 1 =2 2 2 = 2 X 2 = = ( ) X ( ) X ( )= ________ 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

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

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

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

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

Multiplying in Scientific Notation Rule 4 = when you multiply the numbers in scientific notation, multiply the numbers but add the exponents. Your Turn

Dividing in Scientific Notation Rule 5 = when you divide the numbers in scientific notation, divide the numbers but subtract the exponents.. Rule 5 = when you divide the numbers in scientific notation, divide the numbers but subtract the exponents.. Your Turn

Basic Math Conversions Chapter 2 Dimensional Analysis Chapter 2 Dimensional Analysis

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

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

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

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

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

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.

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?

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?

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?

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

Decimal Places Greater than 1 Less than 1

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

Rounding Round 342,427 to the nearest thousandths 342,427 ≈ 342,400 Round 342,427 to the nearest thousandths 342,427 ≈ 342,400 Rounding place (less then 5 everything to right =0) hundredths 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 hundredth thousandths place Your Turn 1,342,427 ≈

Round 37,926 to the nearest tenth 37,926 ≈ 37,930 Round 37,926 to the nearest tenth 37,926 ≈ 37,930 Rounding place (greater then 5 increase value by 1) tenths 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 1,377,427 to the nearest hundredth thousandths place Your Turn 1,377,427 ≈

Round to the nearest tenth ≈ 5.7 Round to the nearest tenth ≈ 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 to the nearest unit Your Turn ≈

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, ≈ 60 X ≈ 400 X 7 63 ≈ 60 X ≈ 400 X 7 9 X 7

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

Basic Math Conversions Chapter 7 Percents Chapter 7 Percents

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.

Percents

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?

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?

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

Percent Word Problems A treatment plant was designed to treat 60 Ml/d. One day it treated 66 Ml. 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.

Basic Math Conversions Chapter 5 Ratios and Proportions Chapter 5 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 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)

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 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

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

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.