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Mathematics
FOR ELEMENTARY TEACHERS
A CONTEMPORARY APPROACH
Supplimentary Text
By Courtney Pindling
Department of Mathematics
- SUNY New paltz
Mathematics for Elementary Teachers by Musser, Burger, Peterson
and Pharo is a key source for the content of this paper Edited 6/04/2002
file:///C|/HP/Math/Math_Teachers/Resource/supplimentary/1_cover/cover.htm [05/25/2001 11:48:21 AM]
1. Introduction - Problem Solving Process
1. Introduction - Problem Solving Process
Polya's 4 Steps to
Problem Solving:
1. Understand
Problem
2. Devise a Plan
3. Carry Out Plan
4. Look Back
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1. Introduction - Problem Solving Process
Some Problem - Solving Strategies
1. Guess and test
2. Use a variable
3. Look for a pattern
4. Make a list
5. Solve a simpler
problem
6. Draw a picture
7. Draw a diagram
8. Use direct
reasoning
9. Use indirect
reasoning
10. Use properties of
numbers
11. Solve an
equivalent problem
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1. Introduction - Problem Solving Process
12. Work backward
13. Use cases
14. Solve an equation
15. Look for a
formula
16. Do a simulation
17. Use dimensional
analysis
18. Identify subgoals
19. Use coordinates
20. Use symmetry
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2.1. Introduction to Set Theory
2.1. Introduction to Set Theory
Definitions: Set { },
Union (either A or B
or Both)
Intersection
(elements in common
to both)
Complement (all
elements in U not in
A) Â
Difference (A - B)
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2.1. Introduction to Set Theory
Disjointed (
)
Subset (
)
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2.2. Whole Numbers & Numeration
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)
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2.2. Whole Numbers & Numeration
System
I-1
Substraction Examples
Method
CCLXXX1 - 281
V-5
IV - 4
MCVII - 1107
X - 10
IX - 9
MCMXLIV >
L - 50
XL - 40
M CM XL IV >
C - 100
XC - 90
1000+900+40+4
D - 500
CD - 400
M - 1000
CM - 900
Babylonian Numeration System: ( 3000 - 2000 BC)
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2.2. Whole Numbers & Numeration
Mayan Numbering System: (AD 300 - 900)
Abacus: (500 BC - Present) Basics - Calculations are
performed by placing the
abacus flat on a
table or one's lap and manipulating the beads with the fingers of one hand. Each
bead in the upper deck has a value of five; each bead in the lower deck has a
value of one. Beads are considered counted, when moved towards the beam that
separates the two decks. The rightmost column is the ones column; the next
adjacent to the left is the tens column; the next adjacent to the left is the hundreds
column, 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, the
result (10) is then carried to the leftmost adjacent column. Floating point
calculations are performed by designating a space between 2 columns as the
decimal-point and all the rows to the right of that space represent fractional
portions while all the rows to the left represent whole number digits
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2.2. Whole Numbers & Numeration
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, ...)
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5.1 Primes, Composites, and Tests for Divisibility
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:
Theorem: Test for divisibility
Fundamental by 2, 5 & 10 Theorem of Number divisible by 2 if ends in 0 or even digit
Arithmetic - Number divisible by 5 if ends in 0 or 5
Each Composite
number can be a
factor of prime
numbers -
Number divisible by 10 if ends in 0
e.g. 60 = 2 x 2 x 3
x5
Theorem:
Let a, m, n
be whole
numbers -
Theorem: Test for divisibility
by 4 & 8 Number divisible by 4 if last 2 digits divisible by 4
Number divisible by 8 if last 3 digits divisible by 8
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 )
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5.1 Primes, Composites, and Tests for Divisibility
Theorem:
Test for
divisibility
by 3 & 9 -
Theorem: Test for divisibility
by 11 - Number divisible by 11 if ( sum of
digits in even positions) - (sum of digits in odd
positions) divisible by 11
e.g. 909381=>(9+9+8)-(0+3+1)=22 is / 11
Number divisible by 3
if sum of digits
divisible by 3
Number divisible by 9
if sum of digits
divisible by 9
Theorem:
Theorem: Prime Factor Test Test if n is prime: see if primes up to p is divisor of
Test for
n: where
divisibility
by 6 -Passes tests Is 299 a prime ?
for divisibility by 2 &
3
So
299 is a prime
Theorem:
Product
divisibility Number divisibility by
both a & b, then a & b
has 1 as common
factor
5.2 Counting factors, Greatest Common Factor (GCF)
& Least Common Multiple (LCM)
Theorem: Counting Factors
- If counting number expressed as product of distinct
primes:
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5.1 Primes, Composites, and Tests for Divisibility
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 of
each 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
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5.1 Primes, Composites, and Tests for Divisibility
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 largest
exponent:
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 of
primes
Algorithm for primes: Sieve of Eratosthenes
1
2 3
11 12 13
21 22
23
31 32 33
41 42 43
51 52
53
4
5
6
14
15
16
24
25
26
27
28
34
35
36
44
45
46
37
47
54
55
56
57
7
17
8
9
10
18
19
29
20
38
39
40
48
49
50
58
59
60
30
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.
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6. Fractions
6. Fractions
Parts of Fractions:
Definition of Fractions: a number represented by ordered pair of a whole
number:
(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 Cross
Theorem (in betweens)
Multiplication
Multiplication:
Properties of Fractions Multiplication:
Meaning:
(cases: whole x Fraction & Fractions x Fraction)
Properties:
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6. Fractions
Closure: Fract. X
Fract. = Fract.
Cumutative:
Associative:
Distributive:
Identity :
Division:
Division - Common
Denominator:
Division - Different
Denominator:
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7. Decimals (base ten)
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 to
the
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 by
multiples of 10s
to remove the remove the decimal; then factor and simplify
Example convert 0.125 to fractional equivalence:
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7. Decimals (base ten)
(power of ten and decimals / common fractional
equiv.)
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 < 5
unchanged )
437.0961 = 437.10 (since value of place after 9 is >= 5 round up)
Division: number of decimal place is reduced to significance of smallest
decimal 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..
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7. Decimals (base ten)
Theorem: A repeating decimal does
not terminate (Nonterminating
Decimal Representation):
iff its fractional equivalent has prime
factor other than 2 or 5 for its
denominator
Theorem: Every
fraction has a
repeating decimal
and every
repeating decimal
has a fractional
representation
Fraction <==>
Repeating
Decimal
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 to
fraction.
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:
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7. Decimals (base ten)
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
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7. Decimals (base ten)
3. Solve equation
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8. Integers
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 (+) leaving
1 (+)]
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:
Additive Inverse:
(a + b) + c = a + (b + c)
a + (-a) = 0
Identity :
a + 0 = a = 0 + a for all a
Theorem - Additive Cancellation for
Integers:
Theorem - Inverse of opposite:
-(-a)=a
If a + c = b + c, then a = b
8.2 Multiplication, Division, and Ordering Integers:
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8. Integers
If a and b are integers:
1.
2.
3.
Multiplication Properties: (if a, b, c are integers)
Closure: ab is an integer
Cumutative:
axb=bxa
Associative:
Identity:
(ab)c = a(bc)
ax1=a
Distribution: (Multipilcation over
addition):
Multiplication Cancellation:
Ac = bc, then a = b
a( b + c ) = ab + ac
Zero Divisors:
ab = 0, iff a = 0 or b = 0 or both = 0
Theorem - Multiplication by -1:
Theorem - Multiplication of (-):
a (-1) = - a
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
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8. Integers
Ordering Integers Properties: (if a, b, c are integers)
Transitive Properties:
< addition:
If a < b and b < c, then a < c
If a < b, then a + c < b + c
< Multiplication by (+):
< Multiplication by (-):
If a < b, then ac < bc
If a < b, then a(-c) > a(-c)
Use number line to order integers
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9.1 Rational Numbers
9.1 Rational Numbers
Real Number Line
-4
-3
-2
-1
0
½
1
2
3
4
_________________________________________________________________
Negative real numbers
Zero(neither + or -)
Positive real
numbers
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:
Equality Theorem: n =
Definition
nonzero integer
(smiplest form:
lowest term)
Addition of Rationals:
Definition
Additive Inverse
Theorem:
(note -b
hard to interpret)
Properties (Rational Numbers Addition):
Closure: Fract. X Fract.
= Fract.
Cumutative:
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9.1 Rational Numbers
Associative:
Additive Inverse:
Identity:
Theorem:Additive cancellation
Opposite Subtraction:
of
Adding Opp.
Opposite:
(common / uncommon
denominators)
Multiplcation of Rational Numbers
Properties (Rational Numbers Multiplication):
Closure: Fract. X Fract. =
Fract.
Cumutative:
Distributive of Multiplication / Multiplication
Addition:
Inverse: (Theorem)
Every ratitionals
unique rationals
has a
such
that: (reciprocal)
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9.1 Rational Numbers
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)
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9.3 Functions and Their Graphs
9.3 Functions and Their Graphs
xy-coordinates system
Linear function
Step Function:
Quadratic Max.
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9.3 Functions and Their Graphs
More Functions
Quadratic Min.
Exponential Growth:
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9.3 Functions and Their Graphs
Exponential Decay:
Cubic Function:
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Appendix A - Multiplication Table (12 x 12)
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
8
9
10
11
12
14
21
28
35
42
49
56
63
70
77
84
16
24
32
40
48
56
64
72
80
88
96
18
27
36
45
54
63
72
81
90
99
108
20
30
40
50
60
70
80
90
100
110
120
22
33
44
55
66
77
88
99
110
121
132
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!
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Appendix A - Multiplication Table (12 x 12)
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
8
9
10
11
12
14
21
28
35
42
49
56
63
70
77
84
16
24
32
40
48
56
64
72
80
88
96
18
27
36
45
54
63
72
81
90
99
108
20
30
40
50
60
70
80
90
100
110
120
22
33
44
55
66
77
88
99
110
121
132
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!
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Appendix B - Fraction to Decimal Comparison Table
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 a
repeating decimal to a
fraction?
Follow these examples:
Note the following
pattern for repeating
decimals:
0.22222222... =
0.54545454... =
0.298298298... =
Division by 9's causes
the repeating pattern.
Note the pattern if zeros
To convert a decimal that begins with a non-repeating
part,
such as 0.21456456456456456..., to a fraction, write it as
the
sum 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 second
decimal (which repeats) is convirted according to the
pattern given above.
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Appendix B - Fraction to Decimal Comparison Table
preceed the repeating
decimal:
0.022222222... = 2/90
21/100 + 456/99900
Now add these fraction by expressing both with
a common divisor
0.00054545454... =
54/99000
0.00298298298... =
298/99900
Adding zero's to the
denominator adds
zero's
before the repeating
decimal.
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Appendix C - First 200 prime numbers
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
607
739
1229
1381
1523
2053
2213
2753
179
file:///C|/HP/Math/Math_Teachers/Resource/supplimentary/Appendix_C_prime_numbers/appendix_C.htm [05/25/2001 12:02:44 PM]
Appendix D: Pascal's Triangle to Row 19
Appendix D: Pascal's Triangle to Row 19
1
1
1
1
1
1
1
1
1
1
1
1
13
1
15
1
1
1
1
105
455
560
136
153
171
680
816
969
364
3060
1365
1820
2380
330
715
1001
3003
4368
5005
28
330
6435
1
9
45
165
55
11
13
1
91
14
455
15
560
16
680
3060
3876 11628 27132 50388 75582 92378 92378 75582 50388 27132 11628
1
120
2380
8568
1
105
1820
6188
8568 18564 31824 43758 48620 43758 31824 18564
1
78
364
1365
4368
6188 12376 19448 24310 24310 19448 12376
1
12
286
1001
3003
1
66
715
8008
1
10
220
2002
5005
8008 11440 12870 11440
8
495
1287
3003
1
36
120
792
1716
1
7
84
462
6435
6
210
924
3432
1
21
56
252
1716
3003
15
126
462
1
5
35
70
792
1287
2002
10
126
210
1
4
20
56
495
286
91
120
17
18
19
16
165
3
35
84
120
220
78
14
45
66
15
28
1
6
10
21
36
55
12
1
1
10
11
1
6
8
9
3
4
5
7
1
2
136
816
3876
1
17
153
969
1
18
171
file:///C|/HP/Math/Math_Teachers/Resource/supplimentary/Appendix_D_pascal_triangle/appendix_D_2.htm [05/25/2001 12:04:19 PM]
1
19
1
Appendix E. Data Powers of Ten
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.
([email protected])
Bytes (8 bits)
Terabyte (1 000 000 000 000 bytes)
0.1 bytes: A binary decision
1 Terabyte: An automated tape robot OR
All the X-ray films in a large
technological into paper and printed OR
Daily rate of EOS data (1998)
1 byte: A single character
10 bytes: A single word
2 Terabytes: An academic research
library OR A cabinet full of Exabyte
tapes
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]
Appendix E. Data Powers of Ten
100 bytes: A telegram OR A punched
card
10 Terabytes: The printed collection of
the US Library of Congress
Kilobyte (1000 bytes)
50 Terabytes: The contents of a large
Mass 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 page
OR A deck of punched cards
2 Petabytes: All US academic research
libraries
50 Kilobytes: A compressed document
image page
20 Petabytes: Production of hard-disk
drives in 1995
100 Kilobytes: A low-resolution
photograph
200 Petabytes: All printed material OR
200 Kilobytes: A box of punched cards
Production of digital magnetic tape in
1995
500 Kilobytes: A very heavy box of
punched cards
Exabyte (1 000 000 000 000 000 000
bytes)
Megabyte (1 000 000 bytes)
5 Exabytes: All words ever spoken by
human beings.
1 Megabyte: A small novel OR A 3.5
inch floppy disk
Zettabyte (1 000 000 000 000 000 000
000 bytes)
2 Megabytes: A high resolution
photograph
Yottabyte (1 000 000 000 000 000 000
000 000 bytes)
5 Megabytes: The complete works of
Shakespeare OR 30 seconds of
TV-quality video
10 Megabytes: A minute of high-fidelity
sound 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 shelved
books OR A two-volume encyclopaedic
book
200 Megabytes: A reel of 9-track tape
OR An IBM 3480 cartridge tape
1.Kilo Greek khilioi = 1000
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]
Appendix E. Data Powers of Ten
500 Megabytes: A CD-ROM OR The
hard disk of a 1995 PC
2.Mega Greek megas = great, e.g.,
Gigabyte (1 000 000 000 bytes)
3.Giga Latin gigas = giant
1 Gigabyte: A pickup truck filled with
paper OR A symphony in high-fidelity
sound OR A
4.Tera Greek teras = monster
Alexandros Megos
2 Gigabytes: 20 meters of shelved books 5.Peta Greek pente = five, fifth prefix,
OR A stack of 9-track tapes
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, the
initial H is silent, so they would
pronounce Hexa as Exa. It is far easier
to call it Exa for
20 Gigabytes: A good collection of the
everyone's sake, right?
works of Beethoven OR 5 Exabyte tapes
OR A
50 Gigabytes: A floor of books OR
Hundreds of 9-track tapes
7.Zetta almost homonymic with Greek
Zeta, but last letter of the Latin alphabet
100 Gigabytes: A floor of academic
journals OR A large ID-1 digital tape
8.Yotta almost homonymic with Greek
iota, but penultimate letter of the Latin
alphabet.
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 has
been 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 to
name 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.
file:///C|/HP/Math/Math_Teachers/Resource/suppl...endix_E_Power_of_10/Appendix_E_power_of_ten.htm (3 of 3) [05/25/2001 12:05:46 PM]
Appendix F. Hierarchy of Numbers
Appendix F. Hierarchy of Numbers
0(zero)
1(one)
5(five)
6(six)
101(ten)
2(two)
7(seven)
102(hundred)
Name
3(three)
4(four)
8(eight)
9(nine)
103(thousand)
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
file:///C|/HP/Math/Math_Teachers/Resource/suppli...ntary/Appendix_F_number_hierarchy/appendix_F.htm (1 of 2) [05/25/2001 12:06:51 PM]
Appendix F. Hierarchy of Numbers
Septendecillion
1054
10102
Octodecillion
1057
10108
Novemdecillion
1060
10114
Vigintillion
1063
10120
Googol 10100
Googolplex
file:///C|/HP/Math/Math_Teachers/Resource/suppli...ntary/Appendix_F_number_hierarchy/appendix_F.htm (2 of 2) [05/25/2001 12:06:51 PM]
Appendix - z-score percentile for normal distribution
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
file:///C|/HP/Math/Math_Teachers/Resource/supplimentary/Appendix_G_z_score/z_scores.htm (1 of 2) [05/25/2001 12:09:15 PM]
Appendix - z-score percentile for normal distribution
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
file:///C|/HP/Math/Math_Teachers/Resource/supplimentary/Appendix_G_z_score/z_scores.htm (2 of 2) [05/25/2001 12:09:15 PM]
Appendix H - primes: Sieve of Eratosthenes
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.
file:///C|/HP/Math/Math_Teachers/Resource/supplimentary/Appednix_H_primes/appendix_H.htm (1 of 2) [06/05/2001 11:12:40 AM]