 Home
 INTERMEDIATE ALGEBRA
 Course Syllabus for Algebra I
 MidPlains Community College
 FRACTION OF A WHOLE NUMBER
 Systems of Linear Equations
 MATH FIELD DAY
 Course Outline for Finite Mathematics
 Calculus
 Algebra Final Examination
 Math 310 Exam #2
 Review of Trigonometric Functions
 Math 118 Practice test
 Precalculus Review
 Section 12
 Literal Equations
 Calculus Term Definitions
 Math 327A Exercise 2
 Public Key Algorithms II
 Maximizing Triangle Area
 Precalculus I Review for Midterm
 REVIEW OF A FIRST COURSE IN LINEAR ALGEBRA
 Math 6310 Homework 5
 Some Proofs of the Existence of Irrational Numbers
 ALGEBRAIC PROPERTIES OF MATRIX OPERATIONS
 Math 142  Chapter 2 Lecture Notes
 Math 112 syllabus
 Math 371 Problem Set
 Complex Numbers,Complex Functions and Contour Integrals
 APPLICATIONS OF LINEAR EQUATIONS
 Week 4 Math
 Fractions
 Investigating Liner Equations Using Graphing Calculator
 MATH 23 FINAL EXAM REVIEW
 Algebra 1
 PYTHAGOREAN THEOREM AND DISTANCE FORMULA
 Georgia Performance Standards Framework for Mathematics  Grade 6
 Intermediate Algebra
 Introduction to Fractions
 FACTORINGS OF QUADRATIC FUNCTIONS
 Elementary Algebra Syllabus
 Description of Mathematics
 Integration Review Solutions
 College Algebra  Applications
 A Tip Sheet on GREATEST COMMON FACTOR
 Syllabus for Elementary Algebra
 College Algebra II and Analytic Geometry
 Functions
 BASIC MATHEMATICS
 Quadratic Equations
 Language Arts, Math, Science, Social Studies, Char
 Fractions and Decimals
 ON SOLUTIONS OF LINEAR EQUATIONS
 Math 35 Practice Final
 Solving Equations
 Introduction to Symbolic Computation
 Course Syllabus for Math 935
 Fractions
 Fabulous Fractions
 Archimedean Property and Distribution of Q in R
 Algebra for Calculus
 Math112 Practice Test #2
 College Algebra and Trigonometry
 ALGEBRA 1A TASKS
 Description of Mathematics
 Simplifying Expressions
 Imaginary and Complex Numbers
 Building and Teaching a Math Enhancement
 Math Problems
 Algebra of Matrices Systems of Linear Equations
 Survey of Algebra
 Approximation of irrational numbers
 More about Quadratic Functions
 Long Division
 Algebraic Properties of Matrix Operation
 MATH 101 Intermediate Algebra
 Rational Number Project
 Departmental Syllabus for Finite Mathematics
 WRITTEN HOMEWORK ASSIGNMENT
 Description of Mathematics
 Rationalize Denominators
 Math Proficiency Placement Exam
 linear Equations
 Description of Mathematics & Statistics
 Systems of Linear Equations
 Algebraic Thinking
 Study Sheets  Decimals
 An Overview of Babylonian Mathematics
 Mathematics 115  College Algebra
 Complex Numbers,Complex Functions and Contour Integrals
 Growing Circles
 Algebra II Course Curriculum
 The Natural Logarithmic Function: Integration
 Rational Expressions
 QUANTITATIVE METHODS
 Basic Facts about Rational Funct
 Statistics
 MAT 1033 FINAL WORKSHOP REVIEW
 Measurements Significant figures
 PreCalculus 1
 Compositions and Inverses of Functions
Measurements Significant figures Scientific Notation
Read the following scales
3 units
Reading
3.4 units
Reading
3.41 units
Reading
Uncertainty in
measurement
Read the following
29.25°
Reading
Read the following scales
Uncertainity in a measured number
To determine the uncertainity in a number
–look at the last digit –this is the uncertain digit
–402.3 Last digit is 3 and is in the tenths place
The uncertainity is + 0.1
–402.34 Last digit is 4 and is in the hundredths place
The uncertainity is + 0.01
Uncertainity in a measured number
Examples: continued
–230 Last significant digit is 3. 3 is in the tens place
The uncertainity is + 10
This means our measurement is 230, 220 or 240
Errors in Measurement
Random errors are errors originating from
uncontrolled variables in the experiment.
Experimental values that fluctuate about the true value.
Systematic errors are errors originating from
controlled variables in the experiment.
constant errors
occur again and again
affect the accuracy of the measurements can occur due misscalibration of a
measuring device
are readings in variables such as temperature, pressure, flow, weight and alike
Driving down the thruway to MCC
Weight your car to the nearest 1 lb $50.00 
Weight your car to the nearest 10 lb $15.00 
Weight your car to the nearest 100 lb $2.00 
Cont.
Weight Limit 2556 and
we mean it!.
Car manual reads weight to be between 2421 to 2707
depending on # people in car and what’s in the trunk
At
$2.00 station weight is 2600 which
means car weight is 25002700 lbs
At $15.00 station
weight is 2550
which means car weight is 25402560 lbs
At $2.00 station
weight is 2549
which means car weight is 25482550 lbs
Will
the bridge collapse?
Discussion
Significant Figures
Significant Figures rules
•The digits 1 to 9 inclusive always count as
significant figures
14.23
3.112
244.62
Leading zeros and zeros that occur at the start of
a number , do not count for sig. figs. They only
indicate position
.004
.00036
0.00125
Zeros
between nonzero digits count for sig.fig.
3.075
1005
.030078
Zeros at the end of
the number are only
significant if they are after a decimal point
(trailing zeros)
100.030
50.0
.1000
If
you can transform the number to scientific
notation and the zeros are lost, they were not
significant
93,000,000 = 9.3 x
10^7
How many significant figures are in
each of the following measurements?
24 mL  2 significant figures 
3001 g  4 significant figures 
0.0320 m^{3}  3 significant figures 
6.4 x 10^{4} molecules  2 significant fig 
560 kg  2 significant figures 
Significant Figures
Addition or Subtraction
The answer cannot have more digits to the right of the decimal
point than any of the original numbers.
one significant figure after decimal point round off to 90.4 

two significant figures after decimal point round off to 0.79 
Problems:
Add 5.62 + 0.0223 + 9.831
Least precise quantity is 5.62 1/100^{th}place
Add 0.02457 + 1.00001 + 0.003
Least precise quantity is 0.003 1/1000^{th}place
Problems:
Substract 1632.1 58.2345
Least precise quantity is 1632.1 1/10^{th}place
Significant Figures
Multiplication or Division
The number of significant figures in the result is set by the original
number that has the smallest number of significant figures
3 sig figs  round to 3 sig figs 
2 sig figs  round to 2 sig figs 
Significant Figures
Exact Numbers
Numbers from definitions or numbers of objects are considered
to have an infinite number of significant figures
The average of three measured lengths; 6.64, 6.68 and 6.70?
Because 3 is an exact number
Scientific Notation
The number of atoms in 12 g of carbon:
602,200,000,000,000,000,000,000
6.022 x 10^{23}
The mass of a single carbon atom in grams:
0.0000000000000000000000199
1.99 x 10^{23}
N x 10^{n} 
Scientific Notation
consists of two parts.
Scientific notation: Adding exponents
Express 18 as 1.8 x 10^{1}  Add exponents 
Express 0.43 as 4.3 x 10^{1}  Add exponents 
Scientific Notation
568.762  0.00000772 
←move decimal left  →move decimal right 
n > 0  n < 0 
568.762 = 5.68762 x 10^{2}  0.00000772 = 7.72 x 10^{6} 
Addition or Subtraction  
1.Write each quantity with the same exponent n  4.31 x 10^{4}+ 3.9 x 10^{3}= 
2.Combine N_{1}and N_{2}  4.31 x 10^{4}+ 0.39 x 10^{4}= 
3.The exponent, n, remains the same  4.70 x 10^{4} 
Scientific Notation
1.86 x 10^{5}would be the
Number.
Scientific Notation
3.2 x 10^{20}
Scientific Notation
1.6 x 10^{3}would be the number
Scientific Notation
1.0 x 10^{7}would be the number
Scientific Notation
Multiplication
1.Multiply N_{1}and N_{2}  
2.Add exponents n_{1}and n_{2}  
Division  
1.Divide N_{1}and N_{2}  
2.Subtract exponents n_{1}and n_{2} 
Accuracy–how close a measurement is to the true value
Precision–how close a set of measurements are to each other
accurate & precise 
precise but not accurate 
not accurate & not precise 