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55 Cards in this Set

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What comp must you recognize, use and relate the various sets of numbrs with the complex number system?
Competencay 10
10
Which competency states that you need to use different concrete, pictorial and symbolic forms of a number
10
What comp must you recognize and use the verious characteristics of the sets with the complex number syste
10
define the classicfication of all real numbers
SET OF REAL NUMBERS DENOTED BY R CONTAINS ALL FORMS AND STRUCTURES OF NUMBERS USED IN MATHMATICS
R
HOW ARE REAL NUMBERS CLASSIFUED
ACCURACY, FORM AND VALUE
A, C, R,
ANY REAL NUMBER MAY BE EITHER RATIONAL, IRRARATION, POSTIVE, OR NEGATIVE
RATIONAL, IRRARATION, POSTIVE, OR NEGATIVE
R, iR, P, N
CLASSIFICATION OF REAL NUMBERS IN TERMS OF ACCURACY.
WHAT IS THE FIRST TYPE
RATIONAL NUMBERS-IS A REAL NUMBER THAT CAN BE WRITTIN OR EXPRESSED AS A RATIO OF TWO INTERGERS AND AND DECIMALS ARE REPEATING FOR RATINAL NUMBERS EXP. 5/2, -10 1/4, 1.333, 42234(line above 234) etc
examples: EXP. 5/2, -10 1/4, 1.333, 42234(line above 234) etc
Which of the following three are real numbers 2.4, 1/7, Pie
2.4, and 1/7
1.7 can be expressed as 0.142857 with a small line above the one to the seven
Why is pie not a rational number
pie=3.14159265 it does not repeat anytime early
define a fraction strip
a piece of paper with lines, with lines on one level over the other.
what type 5/8
rational
r
what type 5=5/1
rational
r
25=1/4
ratioanl
r
.333=1/3
ratioanl
r
CLASSIFICATION OF REAL NUMBERS IN TERMS OF ACCURACY.
WHAT IS THe second type
Irrational numbers-are always non terminating or nonrepeating Irrational numbers can be denoted as I.
What are the following classafied numbers? 5 under raical sign, 1.23476..., 2 under the radical, e, Pie,
Irractional numberrs
Please classify 25 under the radical sign
Rational because it =5.0. which has a fixed repeating PART OF O
4 RADICAL SIGN (1/3) UNDR RADICAL SIGN
=0.75983568565 NO DECIMAL REPEATS SO THIS IS IRRATIOAL
2.451451451
RATIONAL VALUE
WHAT IS IT r OR i=RADICAL SIGN 5
IR-NONREPEATING
NAME SOME CLASSIFICATIONS OF REAL NUMBERS IN TERMS OF THERE..........FORM?
DECIAMAL, FRACTIONAL NUMBERS
If a fraction looks like this a/0, whats it considered?
Undefined
what is the symbol W?
Whole numbrs
define an integers? Are they infinate yes
Whole numbers with their opposites generate a set of integers denoted by Z where Z ={-4,-3,-2,-1,0,1,2,3,4}Yes they are infinite, and don't have a max or min value
Identify the communative proberty
Order doesnt matter
Identify Associative
Grouping does not matter
What is Closure?
Operating on two elements of a set results in an element in and element in the set
example of closure
5+3=8 adding two numbers will give you a WHOLE NUMBER, Subtracting any two whole numbers will not give you a whole number
What is a IDENTITY ELEMENT?
Operating on an element in a set, with this element leaves the first unchanged exps
0 is the identity element for add. of intergers 1 is the identity element for multiplication
Define the Density Property
order does not make a diffrence in the result
MODES OF REPRESENTATION-BASE TEN BLOCKS=1.42
CONCRETE OR PICTORIAL
A) 4 BLOCKS SITTING SIDEWAYS
b) One huge square sitting on a plane
c) and two little square blocks
MODES OF REPRESENTATION-Pattern of Blocks-If the hexagon is 1, what part of it has been shaded
Take a picture represted by a pie? One slice of the pie is taken away, what do you have left 5 shaded symbols for regular pie and one piece that is white that has been taken away
MODES OF REPRESENTATION
what is 25% of a circle
a full cirlce with 1/ 4covered in black. to show 25% is gone
Which of the follwing below is not closed for the operation of division? Rationals, Integers, C) Natural Numbers, D) Whole Numbers
The only set of numbers closed for diviison is the RAtional
Applciations of real Numbers:
Mass of 1/20 kilogram=
1/20 kg
Speed of 60 miles per hour=
60 mph
time interval of 3.5 hours?
3.5 h
Percent and its Applicaits. A class contains 25 students. If 20 of them are present, what percent would be present
first constrruct a ration:
PART/WHOLE QUANTITY= 20/25 THEN MULTIPLY * 100)=80%, TOTAL STUDENTS PRESTEN WAS 80%
wHAT IS THE RELATIVE PERCENT CHANGE FORMULA?
rpc =
(INAL VALUE-INITIAL VALUE/iNITIAL VALUE )x 100%
Give an example of relative percent change formula. Ex. Due to a heavy rain, a water level in a tank raised from 1.2 m to 1.5 m. Calculate precent change of teh water level?
Initial vale is 1.2 m and the final 1.5 m. When you sub these values into the formula above yeilds RPC=
(.5-1.5/1.2) * 100%
Relative % err in science formula
Measured value-Accepted value/Accepted Value} X 100%
Example of relative Percent in Error: A Physics student measured the acceleration due to gravity to be 9.0 m/s^2. If the expected value is 9.8m/s^2, calculate the percent error of measurement.
ANSWER: EXPECTED VALUE =9.8M/S^2, MEASURED VALUE=9.0M/S^2
RELATIVE PERCENT ERROR=*100=8.2%
8.2%
ROOTS IN ALGEBRA
Roots have a triple meaning in mathmatics and they represent:
Zeros of a function
Solutions of an algebiac equation
Result of expnenttiantion when the expoent is a fractioanl proper or inproper
Roots:
FIND THE ZEROS OF f(x)=x^2-4 and classify them as rational or irrational
EQUATE F(X) TO 0, F(X)=0 YIELDS 0=X^2-4. Seperate x^2 and taking the SQUARE root of both sides, produces X=+-2 tHE 0'S OF THE FUCNTION ARE RATIONAL
ALGEBRAIC Roots: FIND THE ROOTS OF THE NUMBERS OF X^2-4X=0?
bY APPLYING COMMON FACTORIN WE GET X(X-4)=0
WHAT IS Y^2 DEFINE IT?
y * Y
EXPLAIN SCIENTIFIC NOTATION
A *B^10
• Powers and Scientific Notation
Power is an expression of the form ab where a is called to base of the power and b is the exponent. If the
exponent is a whole number, then it tells how many times the base must be multiplied by itself to evaluate
the power.
Examples: Write in the expanded form and evaluate if possible.
a. 43
b. y2
c. (1.4)5 (1.5)=1.4x1.4x1.4x1.4x1.4=5.3784=5.4
, Answer 43=4x4x4=63
b. y2, Answer y2–yxy
c. (1.4)5, Answer (1.4)5=1.4x1.4x1.4x1.4x1.4=5.3784=5.4
• Scientific Notation
Scientific notation is used to express very large or very small quantities by applying a power with the base
of 10. A quantity expressed in a scientific notation has the following form:
a x bn where
a is called the magnitude of the value: -10 < a <1 0
b is called the base: b=10
n is the exponent: n must be an integer, THEN HOW IS DONE
Domain I
by applying a power with the base
of 10. A quantity expressed in a scientific notation has the following form:
a x bn where
a is called the magnitude of the value: -10 < a <1 0
b is called the base: b=10
n is the exponent: n must be an integer
Domain I
Quantity can be expressed as a fraction or a decimal.
A quantity properly described contains a magnitude
and the unit.
• Decimal numbers 1.3, 4.1, - 7.278 etc.
Decimal numbers contain a decimal point that separates
the place value of ones from tenths. They can
also contain commas that underline other place values.
They can
also contain commas that underline other place values.
1. Convert to fractions:
a. 3.2 b. 2.004 c. 00.027
Answers. Identifying the place value of each digit
and converting each to a fraction one gets:
A,3.2=3+2 * 1/10= 3 2/5=3 1/5
b> 2.004 +2+4 X 1/1000=2 4/1000= 2 1/250

C)0.027+2 x 1/100+ 7/1000=27/1000
Quantity can be expressed as a fraction or a decimal.
A quantity properly described contains a magnitude
and the unit.
• Decimal numbers 1.3, 4.1, - 7.278 etc.
Decimal numbers contain a decimal point that separates
the place value of ones from tenths. They can
also contain commas that underline other place values.
They can
also contain commas that underline other place values.
1. Convert to fractions:
a. 3.2 b. 2.004 c. 00.027
Answers. Identifying the place value of each digit
and converting each to a fraction one gets:
A,3.2=3+2 * 1/10= 3 2/5=3 1/5
b> 2.004 +2+4 X 1/1000=2 4/1000= 2 1/250

C)0.027+2 x 1/100+ 7/1000=27/1000