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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 NUMBERSIS 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 numbersare 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

IRNONREPEATING



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 REPRESENTATIONBASE 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 REPRESENTATIONPattern of BlocksIf 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 VALUEINITIAL 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=
(.51.5/1.2) * 100% 


Relative % err in science formula

Measured valueAccepted 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^24 and classify them as rational or irrational 
EQUATE F(X) TO 0, F(X)=0 YIELDS 0=X^24. 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^24X=0?

bY APPLYING COMMON FACTORIN WE GET X(X4)=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 
