Post on 24-Jun-2018
MathematicsFOR ELEMENTARY TEACHERS
A CONTEMPORARY APPROACH
Supplimentary Text
By Courtney Pindling
Department of Mathematics- SUNY New paltz
Mathematics for Elementary Teachers by Musser, Burger, Petersonand Pharo is a key source for the content of this paper Edited 6/04/2002
Cover page
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1. Introduction - Problem Solving Process
Polya's 4 Steps toProblem Solving:
1. UnderstandProblem
2. Devise a Plan
3. Carry Out Plan
4. Look Back
1. Introduction - Problem Solving Process
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Some Problem - Solving Strategies
1. Guess and test
2. Use a variable
3. Look for a pattern
4. Make a list
5. Solve a simplerproblem
6. Draw a picture
7. Draw a diagram
8. Use directreasoning
9. Use indirectreasoning
10. Use properties ofnumbers
11. Solve anequivalent problem
1. Introduction - Problem Solving Process
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12. Work backward
13. Use cases
14. Solve an equation
15. Look for aformula
16. Do a simulation
17. Use dimensionalanalysis
18. Identify subgoals
19. Use coordinates
20. Use symmetry
1. Introduction - Problem Solving Process
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2.1. Introduction to Set Theory
Definitions: Set { },
Union (either A or Bor Both)
Intersection(elements in commonto both)
Complement (allelements in U not inA) Â
Difference (A - B)
2.1. Introduction to Set Theory
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Disjointed ( ) Subset ( )
2.1. Introduction to Set Theory
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2.2. Whole Numbers & Numeration
Math History:http://www.seanet.com/~ksbrown/ihistory.htm
Translale Egyption Numbering System: (3400 BC)http://www.psinvention.com/zoetic/tr_egypt.htm
The Egyptians had a decimal system using seven different symbols.
1 is shown by a single stroke. 10 is shown by a drawing of a hobble for cattle. 100 is represented by a coil of rope. 1,000 is a drawing of a lotus plant. 10,000 is represented by a finger. 100,000 by a tadpole or frog 1,000,000 is the figure of a god with arms raised above his head.
1 10 100 1,000 10,000 100,000 Million
Roman Numeration System: (AD 100)
2.2. Whole Numbers & Numeration
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System
I - 1
V - 5
X - 10
L - 50
C - 100
D - 500
M - 1000
SubstractionMethod
IV - 4
IX - 9
XL - 40
XC - 90
CD - 400
CM - 900
Examples
CCLXXX1 - 281
MCVII - 1107
MCMXLIV >
M CM XL IV >
1000+900+40+4
Babylonian Numeration System: ( 3000 - 2000 BC)
2.2. Whole Numbers & Numeration
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Mayan Numbering System: (AD 300 - 900)
Abacus: (500 BC - Present) Basics - Calculations areperformed by placing the
abacus flat on a
table or one's lap and manipulating the beads with the fingers of one hand. Eachbead in the upper deck has a value of five; each bead in the lower deck has avalue of one. Beads are considered counted, when moved towards the beam thatseparates the two decks. The rightmost column is the ones column; the nextadjacent to the left is the tens column; the next adjacent to the left is the hundredscolumn, and so on. After 5 beads are counted in the lower deck, the result is"carried" to the upper deck; after both beads in the upper deck are counted, theresult (10) is then carried to the leftmost adjacent column. Floating pointcalculations are performed by designating a space between 2 columns as thedecimal-point and all the rows to the right of that space represent fractionalportions while all the rows to the left represent whole number digits
2.2. Whole Numbers & Numeration
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Hindu-Arabic System: (AD 800)
Digits {0,1,2,3,4,5,6,7,8,9}, Base 10 (decimal system),
Place value ( ..., million, thousands,hundred,tens,ones . tenth,hundredth, ...)
2.2. Whole Numbers & Numeration
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5. Number Theory
5.1 Primes, Composites, and Tests for Divisibility
Counting Numbers: 1, 2, 3, 4, 5, 6, .......
Prime Numbers: Divisable by itself and 1: 2, 3, 5, 7, 11, 13 , 17, 19, ...
Composite Numbers: at least 3 factors - e.g. 60 = 2 x 2 x 3 x 5
a | b means a divides b (quotient is a whole number)
Theorem:FundamentalTheorem ofArithmetic -Each Compositenumber can be afactor of primenumbers -
e.g. 60 = 2 x 2 x 3x 5
Theorem: Test for divisibilityby 2, 5 & 10 - Number divisible by 2 if ends in 0 or even digit
Number divisible by 5 if ends in 0 or 5
Number divisible by 10 if ends in 0
Theorem:Let a, m, nbe wholenumbers - If a | m & a | n, then a |(m+n)
If a | m & a | n, then a |(m-n) for m n
If a | m, then a | km(multiple of )
Theorem: Test for divisibilityby 4 & 8 - Number divisible by 4 if last 2 digits divisible by 4
Number divisible by 8 if last 3 digits divisible by 8
5.1 Primes, Composites, and Tests for Divisibility
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Theorem:Test fordivisibilityby 3 & 9 - Number divisible by 3if sum of digitsdivisible by 3
Number divisible by 9if sum of digitsdivisible by 9
Theorem: Test for divisibilityby 11 - Number divisible by 11 if ( sum of
digits in even positions) - (sum of digits in oddpositions) divisible by 11
e.g. 909381=>(9+9+8)-(0+3+1)=22 is / 11
Theorem:Test fordivisibilityby 6 -Passes testsfor divisibility by 2 &3
Theorem:Productdivisibility -Number divisibility byboth a & b, then a & bhas 1 as commonfactor
Theorem: Prime Factor Test -Test if n is prime: see if primes up to p is divisor ofn: where
Is 299 a prime ?
So
299 is a prime
5.2 Counting factors, Greatest Common Factor (GCF)& Least Common Multiple (LCM)
Theorem: Counting Factors - If counting number expressed as product of distinctprimes:
5.1 Primes, Composites, and Tests for Divisibility
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number of factors for 144=24 x 32=> (4+1)(2+1)=15
Greatest Common Factor (GCF): The GCF of 2 or more whole numbers is the largest whole number that is a factor of both (all)
1. Prime Factor Method: The product of highest prime common to both (all):
e.g. GCF(24, 36): 24= 23 x 3 and 36=22 x 32 so GCF=> 22x3 = 12
2. GCF Theorem Method: GCF(a,b) = GCF(a-b, b) when :
3. Remainder Method: Theorem: GCF(a, b) = GCF(r, b):
If a & b are whole numbers and a >= b and a = kb + r , where r < b
Least Common Multiple (LCM): The LCM of 2 or more whole numbers is the smallest whole number that is a multiple of each (all) of the numbers. 1. Set Intersection Method: Smallest element of the intersection of multiple of the set ofeach numbers:
e.g. LCM(24, 36): 24= {24,48,72,96,120,144..} 36={36,72,108,144..}= {72, 144} So
LCM(24, 36) = 72
5.1 Primes, Composites, and Tests for Divisibility
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2. Prime Factor Method: The product of largest prime exponent in each (all):
e.g. LCM (24, 36): 24= 23x 3 and 36=22 x 32 so GCF=> 23x32 = 72
3. Buildup Method: State all prime, select prime of one number and build up to largestexponent:
e.g. LCM(42, 24): 24= 23 x 3 and 42=23 x 3 x 7 so LCM(42,24)= 23x3x7 = 168
GCF and LCM - Theorems
Theorem: GCF & LCM: GCF(a, b) x LCM (a, b) = ab
For example, find LCM (36,56) if GCF(36,56)=4
LCM x GCF = 36 x 56, So
Theorem: Infinite Number of Primes: There is an infinite number ofprimes
Algorithm for primes: Sieve of Eratosthenes
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
Directions: Skip the number 1, circle 2 and cross out evry second number after 2,Circle 3 and cross out every 3rd number after 3 (even if it had been crossed out before).Continue this procedure with 5, 7, and each succeeding number not crossed out.Circled numbers are primes and crossed out numbers are compsites.
5.1 Primes, Composites, and Tests for Divisibility
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6. Fractions
Parts of Fractions:
Definition of Fractions: a number represented by ordered pair of a wholenumber:
(Relative amount, part of a whole, numeral)
Fractions Equality : (cross product):
Theorem: Given Fraction must be written in simplest form
Improper Fractions: when numerator > denominator (mixed number):
Ordering Fractions : (Theorems)
Theorem (<) Theorem CrossMultiplication
Theorem (in betweens)
Multiplication:
Properties of Fractions Multiplication:
Meaning: (cases: whole x Fraction & Fractions x Fraction)
Properties:
6. Fractions
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Closure: Fract. XFract. = Fract.
Cumutative:
Associative: Distributive:
Identity :
Division:
Division - CommonDenominator:
Division - DifferentDenominator:
6. Fractions
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7. Decimals (base ten) Another way of representing the fractional part of a whole:
Every fraction can be represented in decimal form:
Some Observations:
A fraction can be transformed into a terminating decimal
if the prime factor if b is divisible by either 2 or 5
Order decimal from smallest to largest via its position along the number line
Addition / Substraction of decimals:
Like whole number additions (add the decimal portion first keeping true tothe dot that separates the whole number from the fractional part.
Fractional Equivalence:
Every terminating decimal has a fractional equivalence:
Converting Termination to fraction:
Divide the decimal by 1; Multiply both numerator and denominator bymultiples of 10s to remove the remove the decimal; then factor and simplify
Example convert 0.125 to fractional equivalence:
7. Decimals (base ten)
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(power of ten and decimals / common fractionalequiv.)
7.2 Decimals Operations:
Multiplication: number of decimal place is expanded:
e.g 437.09 x 3.8 = 1600.942
Significant figure: By Example:
e.g. 437.0923 = 437.09 (since value of place after 9 is 2 < 5unchanged )
437.0961 = 437.10 (since value of place after 9 is >= 5 round up)
Division: number of decimal place is reduced to significance of smallestdecimal place: (practice)
e.g.. 437.09 / 3.8 = 115.0
Decimals with repeating series; repeating values called repetend
Number of values that repeats called period
For example:
Long Division Algorithm: preserve decimal place or introduce it:
e.g..
7. Decimals (base ten)
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Theorem: A repeating decimal doesnot terminate (NonterminatingDecimal Representation):
iff its fractional equivalent has primefactor other than 2 or 5 for itsdenominator
Theorem: Everyfraction has arepeating decimaland everyrepeating decimalhas a fractionalrepresentation
Fraction <==>RepeatingDecimal
If p is the period of a repetend:
Then with any given repeating decimal, n
(subtract n from both sides):
99n = 34, so (fractional equivalence)
In General to convert a repeating Decimal tofraction.
Introduce: Scientific Notation for decimals: 10-n
7.3 Ratio and Proportion
Ratio: a : b, with b not equal to 0 = denote relative size, comparison, rate,percent: a relative to b
Equality of Ratios: 2 ratios are equal if given:
7. Decimals (base ten)
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Proportion: a statement that 2 ratios are equal: e.g.
7.4 Percent
Another way of representing fractions or decimal:
(Number per hundred)
Cases:
Percent to Decimal
Percent to Fraction
Decimal to Percent
Fraction to Percent
Common Percent / Fraction Equivalence (Appendix B)
Approaches to solving problems with percent:
1. 10 x 10 Grid
2. Properties of proportion / ratios
7. Decimals (base ten)
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3. Solve equation
7. Decimals (base ten)
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8. Integers Negative representations: (discuss historic and present international)
Integers: set of numbers: {..,-3,-2,-1,0,1,2,3,..} Positive Integers, Zero, Negative Integers (Set View via models or Measurement view via the number line); concept of negative being opposite of positive across pivot point at Zero)
8.1 Addition & Subtraction:
Set Model: Cancel effect: 4 positives + 3 negatives [i.e. 3 (-) cancels 3 (+) leaving1 (+)]
Number Line Model: a positives + b negatives: move from Zero a units right and then b units left from new position
Addition Properties: (if a, b, c are integers)
Closure: a + b is an integer Cumutative:
a + b = b + a
Associative:
(a + b) + c = a + (b + c)
Additive Inverse:
a + (-a) = 0
Identity :
a + 0 = a = 0 + a for all a
Theorem - Additive Cancellation forIntegers:
If a + c = b + c, then a = b
Theorem - Inverse of opposite:
- ( - a ) = a
8.2 Multiplication, Division, and Ordering Integers:
8. Integers
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If a and b are integers:
1.
2.
3.
Multiplication Properties: (if a, b, c are integers)
Closure: ab is an integer Cumutative:
a x b = b x a
Associative:
(ab)c = a(bc)
Identity:
a x 1 = a
Distribution: (Multipilcation overaddition):
a( b + c ) = ab + ac
Multiplication Cancellation:
Ac = bc, then a = b
Zero Divisors:
ab = 0, iff a = 0 or b = 0 or both = 0
Theorem - Multiplication by -1:
a (-1) = - a
Theorem - Multiplication of (-):
Case 1: (-a)b = -(ab)
Case 2: (-a)(-b) = ab
Scientific Notation: An exponential representation of numbers in the form:
Where a is called the mantissa and n the characteristic of exponent
8. Integers
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Ordering Integers Properties: (if a, b, c are integers)
Transitive Properties:
If a < b and b < c, then a < c
< addition:
If a < b, then a + c < b + c
< Multiplication by (+):
If a < b, then ac < bc
< Multiplication by (-):
If a < b, then a(-c) > a(-c)
Use number line to order integers
8. Integers
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9.1 Rational Numbers
Real Number Line
-4 -3 -2 -1 0 ½ 1 2 3 4
_________________________________________________________________Negative real numbers Zero(neither + or -) Positive realnumbers
Set of Rational Numbers
Real numbers {Rational Numbers{Fraction / Integers{Whole numbers{Counting}, 0}} }
Real numbers {Irrational numbers}
Definition Rational Numbers: {fractions, whole numbers ( ), integers}
The set of rational numbers is : Q={
Equality of Rationals:Definition
Equality Theorem: n =nonzero integer
(smiplest form:
lowest term)
Addition of Rationals:Definition
Additive InverseTheorem:
(note -b
hard to interpret)
Properties (Rational Numbers Addition):
Closure: Fract. X Fract.= Fract.
Cumutative:
9.1 Rational Numbers
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Associative: Additive Inverse:
Identity:
Theorem:Additive cancellation OppositeofOpposite:
Subtraction:Adding Opp.
(common / uncommondenominators)
Multiplcation of Rational Numbers
Properties (Rational Numbers Multiplication):
Closure: Fract. X Fract. =Fract.
Cumutative:
Distributive of Multiplication /Addition:
MultiplicationInverse: (Theorem)
Every ratitionals has a
unique rationals such
that: (reciprocal)
9.1 Rational Numbers
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Identity: Associative:
Division of Rational Numbers
Division of Rationals: Theorem
1.
2.
3.
Ordering of Rationals:
Number line approach
Common-positive denominator a/b > c/d ifi a > c
Additive approach
Cross-Multiplication Theorem: (for b > 0 and d > 0)
9.1 Rational Numbers
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9.3 Functions and Their Graphs
xy-coordinates system Linear function
Step Function: Quadratic Max.
9.3 Functions and Their Graphs
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More FunctionsQuadratic Min. Exponential Growth:
9.3 Functions and Their Graphs
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Exponential Decay: Cubic Function:
9.3 Functions and Their Graphs
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Appendix A - Multiplication Table (12 x 12)
1 2 3 4 5 6 7 8 9 10 11 12
2 2 6 8 10 12 14 16 18 20 22 24
3 6 9 12 15 18 21 24 27 30 33 36
4 8 12 16 20 24 28 32 36 40 44 48
5 10 15 20 25 30 35 40 45 50 55 60
6 12 18 24 30 36 42 48 54 60 66 72
7 14 21 28 35 42 49 56 63 70 77 84
8 16 24 32 40 48 56 64 72 80 88 96
9 18 27 36 45 54 63 72 81 90 99 108
10 20 30 40 50 60 70 80 90 100 110 120
11 22 33 44 55 66 77 88 99 110 121 132
12 24 36 48 60 72 84 96 108 120 132 144
Remembering 9's
What's 9 x 7 ? Use the 9-method! Hold out all 10 fingers, and lower the 7th finger.There are 6 fingers to the left and 3 fingers on the right.
The answer is 63!
Appendix A - Multiplication Table (12 x 12)
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Appendix A - Multiplication Table (12 x 12)
1 2 3 4 5 6 7 8 9 10 11 12
2 2 6 8 10 12 14 16 18 20 22 24
3 6 9 12 15 18 21 24 27 30 33 36
4 8 12 16 20 24 28 32 36 40 44 48
5 10 15 20 25 30 35 40 45 50 55 60
6 12 18 24 30 36 42 48 54 60 66 72
7 14 21 28 35 42 49 56 63 70 77 84
8 16 24 32 40 48 56 64 72 80 88 96
9 18 27 36 45 54 63 72 81 90 99 108
10 20 30 40 50 60 70 80 90 100 110 120
11 22 33 44 55 66 77 88 99 110 121 132
12 24 36 48 60 72 84 96 108 120 132 144
Remembering 9's
What's 9 x 7 ? Use the 9-method! Hold out all 10 fingers, and lower the 7th finger.There are 6 fingers to the left and 3 fingers on the right.
The answer is 63!
Appendix A - Multiplication Table (12 x 12)
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Appendix B - Fraction to Decimal Comparison Table
Fraction Decimal Fraction Decimal
0.05 0.5
0.1 0.6
0.125
0.2 0.75
0.25 0.8
0.875
0.4 1.0
Need to convert arepeating decimal to afraction?
Follow these examples:
Note the followingpattern for repeatingdecimals:
0.22222222... =
0.54545454... =
0.298298298... =
Division by 9's causesthe repeating pattern.
Note the pattern if zeros
To convert a decimal that begins with a non-repeatingpart, such as 0.21456456456456456..., to a fraction, write it asthesum of the non-repeating part and the repeating part.
0.21 + 0.00456456456456456...
Next, convert each of these decimals to fractions.The first decimal has a divisor of power ten. The seconddecimal (which repeats) is convirted according to thepattern given above.
Appendix B - Fraction to Decimal Comparison Table
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preceed the repeatingdecimal:
0.022222222... = 2/90
0.00054545454... =54/99000
0.00298298298... =298/99900
Adding zero's to thedenominator addszero's before the repeatingdecimal.
21/100 + 456/99900
Now add these fraction by expressing both witha common divisor
Appendix B - Fraction to Decimal Comparison Table
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Appendix C - First 200 prime numbers
2 73 181 613 743 1231 1399 xxxx 2063 2221
3 79 191 617 751 1237 1409 1531 2069 2237
5 83 193 619 757 1249 1423 1543 2081 2243
7 89 197 631 761 1259 1427 1549 2083 2251
11 97 199 641 769 1277 1429 1553 2087 2267
13 101 211 643 773 1279 1433 1559 2089 2269
17 103 223 647 787 1283 1439 1567 2099 2281
19 107 227 653 797 1289 1447 1571 2111 2287
23 109 229 659 809 1291 1451 1579 2113 2293
29 113 547 661 811 1297 1453 1583 2129 2297
31 127 557 673 821 1301 1459 1993 2131 2309
37 131 563 677 823 1303 1471 1997 2137 2311
41 137 569 683 827 1307 1481 1999 2141 2333
43 139 571 691 829 1319 1483 2003 2143 2339
53 151 587 709 853 1327 1489 2017 2161 2347
59 157 593 719 857 1361 1493 2027 2179 2351
61 163 599 727 859 1367 1499 2029 2203 2357
67 167 601 733 863 1373 1511 2039 2207 2749
71 173
179
607 739 1229 1381 1523 2053 2213 2753
Appendix C - First 200 prime numbers
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Appendix D: Pascal's Triangle to Row 191
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21 7 1
1 8 28 56 70 56 28 8 1
1 9 36 84 126 126 84 36 9 1
1 10 45 120 210 252 210 120 45 10 1
1 11 55 165 330 462 462 330 165 55 11 1
1 12 66 220 495 792 924 792 495 220 66 12 1
1 13 78 286 715 1287 1716 1716 1287 715 286 78 13 1
1 14 91 364 1001 2002 3003 3432 3003 2002 1001 364 91 14 1
1 15 105 455 1365 3003 5005 6435 6435 5005 3003 1365 455 105 15 1
1 16 120 560 1820 4368 8008 11440 12870 11440 8008 4368 1820 560 120 16 1
1 17 136 680 2380 6188 12376 19448 24310 24310 19448 12376 6188 2380 680 136 17 1
1 18 153 816 3060 8568 18564 31824 43758 48620 43758 31824 18564 8568 3060 816 153 18 1
1 19 171 969 3876 11628 27132 50388 75582 92378 92378 75582 50388 27132 11628 3876 969 171 19 1
Appendix D: Pascal's Triangle to Row 19
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Appendix E. Data Powers of Ten
SI-Prefixes
Number Prefix Symbol Number Prefix Symbol
d deci- da deka-
c centi- h hecto-
m milli- k kilo-
u( ) micro- M mega-
n nano- G giga-
p pico- T teta-
f femto- P peta-
a atto- E exa-
z zepto- Z zeta-
y yocto- Y yotta-
The following list is a collection of estimates of the quantities of data contained by the various media.Each is rounded to be a power of 10 times 1, 2 or 5.
The numbers quoted are approximate. In fact a kilobyte is 1024 bytes not 1000 bytes.
(roy@caltech.edu)Bytes (8 bits) Terabyte (1 000 000 000 000 bytes)
0.1 bytes: A binary decision 1 Terabyte: An automated tape robot ORAll the X-ray films in a largetechnological into paper and printed ORDaily rate of EOS data (1998)
1 byte: A single character
10 bytes: A single word 2 Terabytes: An academic researchlibrary OR A cabinet full of Exabytetapes
Appendix E. Data Powers of Ten
file:///C|/HP/Math/Math_Teachers/Resource/suppl...endix_E_Power_of_10/Appendix_E_power_of_ten.htm (1 of 3) [05/25/2001 12:05:46 PM]
100 bytes: A telegram OR A punchedcard
10 Terabytes: The printed collection ofthe US Library of Congress
Kilobyte (1000 bytes) 50 Terabytes: The contents of a largeMass Storage System
1 Kilobyte: A very short story Petabyte (1 000 000 000 000 000 bytes)
2 Kilobytes: A Typewritten page 1 Petabyte: 3 years of EOS data (2001)
10 Kilobytes: An encyclopaedic pageOR A deck of punched cards
2 Petabytes: All US academic researchlibraries
50 Kilobytes: A compressed documentimage page
20 Petabytes: Production of hard-diskdrives in 1995
100 Kilobytes: A low-resolutionphotograph
200 Petabytes: All printed material OR
200 Kilobytes: A box of punched cards Production of digital magnetic tape in1995
500 Kilobytes: A very heavy box ofpunched cards
Exabyte (1 000 000 000 000 000 000bytes)
Megabyte (1 000 000 bytes) 5 Exabytes: All words ever spoken byhuman beings.
1 Megabyte: A small novel OR A 3.5inch floppy disk
Zettabyte (1 000 000 000 000 000 000000 bytes)
2 Megabytes: A high resolutionphotograph
Yottabyte (1 000 000 000 000 000 000000 000 bytes)
5 Megabytes: The complete works ofShakespeare OR 30 seconds ofTV-quality video
10 Megabytes: A minute of high-fidelitysound OR A digital chest X-ray
Etymology of Units
20 Megabytes: A box of floppy disks
50 Megabytes: A digital mammogram
100 Megabytes: 1 meter of shelvedbooks OR A two-volume encyclopaedicbook
200 Megabytes: A reel of 9-track tapeOR An IBM 3480 cartridge tape
1.Kilo Greek khilioi = 1000
Appendix E. Data Powers of Ten
file:///C|/HP/Math/Math_Teachers/Resource/suppl...endix_E_Power_of_10/Appendix_E_power_of_ten.htm (2 of 3) [05/25/2001 12:05:46 PM]
500 Megabytes: A CD-ROM OR Thehard disk of a 1995 PC
2.Mega Greek megas = great, e.g.,
Alexandros Megos
Gigabyte (1 000 000 000 bytes) 3.Giga Latin gigas = giant
1 Gigabyte: A pickup truck filled withpaper OR A symphony in high-fidelitysound OR A
4.Tera Greek teras = monster
2 Gigabytes: 20 meters of shelved booksOR A stack of 9-track tapes
5.Peta Greek pente = five, fifth prefix,peNta -
N = peta
5 Gigabytes: An 8mm Exabyte tape 6.Exa Greek hex = six, sixth prefix,Hexa - H = exa
10 Gigabytes: Remember, in standard French, theinitial H is silent, so they wouldpronounce Hexa as Exa. It is far easierto call it Exa for
20 Gigabytes: A good collection of theworks of Beethoven OR 5 Exabyte tapesOR A
everyone's sake, right?
50 Gigabytes: A floor of books ORHundreds of 9-track tapes
7.Zetta almost homonymic with GreekZeta, but last letter of the Latin alphabet
100 Gigabytes: A floor of academicjournals OR A large ID-1 digital tape
8.Yotta almost homonymic with Greekiota, but penultimate letter of the Latinalphabet.
200 Gigabytes: 50 Exabyte tapes
The first prefix is number-derived; second, third, and fourth are based on mythology.Fifth and sixth are supposed to be just that: fifth and sixth. But, with the seventh, another fork hasbeen taken.The General Conference of Weights and Measures (CGMP, from the French;they have been headquartered, since 1874, in Sevres on the outskirts of Paris) has now decided toname the
prefixes, starting with the seventh, with the letters of the Latin alphabet, but starting from the end.Now,that makes it all clear! Remember, both according to CGMP and SI, the prefixes refer to powers of 10.Mega is 106 , exactly 1,000,000, kilo is exactly 1000, not 1024.
Appendix E. Data Powers of Ten
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Appendix F. Hierarchy of Numbers
0(zero) 1(one) 2(two) 3(three) 4(four)
5(five) 6(six) 7(seven) 8(eight) 9(nine)
101(ten) 102(hundred) 103(thousand)
Name American-French English -German
Million 106 106
Billion 109 109
Trillion 1012 1018
Quadrillion 1015 1024
Quintillion 1018 1030
Sextillion 1021 1036
Septillion 1024 1042
Octillion 1027 1048
Nonillion 1030 1054
Decillion 1033 1060
Undecillion 1036 1066
Duodecillion 1039 1072
Tredecillion 1042 1078
Quatuordecillion 1045 1084
Quindecillion 1048 1090
Sexdecillion 1051 1096
Appendix F. Hierarchy of Numbers
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Septendecillion 1054 10102
Octodecillion 1057 10108
Novemdecillion 1060 10114
Vigintillion 1063 10120
Googol 10100
Googolplex
Appendix F. Hierarchy of Numbers
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Appendix - z-score percentile for normal distribution
Percentile z-Score Percentile z-Score Percentile z-Score
1 -2.326 34 -0.412 67 0.44
2 -2.054 35 -0.385 68 0.468
3 -1.881 36 -0.358 69 0.496
4 -1.751 37 -0.332 70 0.524
5 -1.645 38 -0.305 71 0.553
6 -1.555 39 -0.279 72 0.583
7 -1.476 40 -0.253 73 0.613
8 -1.405 41 -0.228 74 0.643
9 -1.341 42 -0.202 75 0.674
10 -1.282 43 -0.176 76 0.706
11 -1.227 44 -0.151 77 0.739
12 -1.175 45 -0.126 78 0.772
13 -1.126 46 -0.1 79 0.806
14 -1.08 47 -0.075 80 0.842
15 -1.036 48 -0.05 81 0.878
16 -0.994 49 -0.025 82 0.915
17 -0.954 50 0 83 0.954
18 -0.915 51 0.025 84 0.994
19 -0.878 52 0.05 85 1.036
20 -0.842 53 0.075 86 1.08
21 -0.806 54 0.1 87 1.126
22 -0.772 55 0.126 88 1.175
23 -0.739 56 0.151 89 1.227
24 -0.706 57 0.176 90 1.282
25 -0.674 58 0.202 91 1.341
Appendix - z-score percentile for normal distribution
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26 -0.643 59 0.228 92 1.405
27 -0.613 60 0.253 93 1.476
28 -0.583 61 0.279 94 1.555
29 -0.553 62 0.305 95 1.645
30 -0.524 63 0.332 96 1.751
31 -0.496 64 0.358 97 1.881
32 -0.468 65 0.385 98 2.054
33 -0.44 66 0.412 99 2.326
Appendix - z-score percentile for normal distribution
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Appendix H - primes: Sieve of Eratosthenes (circle primes)
1
2 3 4 5 6 7 8 9 10
11
12 13 14 15 16 17 18 19 20
21
22 23 24 25 26 27 28 29 30
31
32 33 34 35 36 37 38 39 40
41
42 43 44 45 46 47 48 49 50
51
52 53 54 55 56 57 58 59 60
61
62 63 64 65 66 67 68 69 70
71
72 73 74 75 76 77 78 79 80
81
82 83 84 85 86 87 88 89 90
91
92 93 94 95 96 97 98 99 100
Directions: Skip the number 1, circle 2 and cross out evry second number after 2,Circle 3 and cross out every 3rd number after 3 (even if it had been crossed out before).Continue this procedure with 5, 7, and each succeeding number not crossed out.
Appendix H - primes: Sieve of Eratosthenes
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