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1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
Introduction to Number Systems
January 16, 2019
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
How We Use Numbers
I cardinal numbers
I how many numbers are in a set
I ordinal numbersI positionI which comes first
I identification numbers
Numbers are abstract ideas and it is sometimes difficult todiscern for students the difference between a number andthe symbol that represents a number ...
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
How We Use Numbers
I cardinal numbersI how many numbers are in a set
I ordinal numbersI positionI which comes first
I identification numbers
Numbers are abstract ideas and it is sometimes difficult todiscern for students the difference between a number andthe symbol that represents a number ...
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
How We Use Numbers
I cardinal numbersI how many numbers are in a set
I ordinal numbers
I positionI which comes first
I identification numbers
Numbers are abstract ideas and it is sometimes difficult todiscern for students the difference between a number andthe symbol that represents a number ...
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
How We Use Numbers
I cardinal numbersI how many numbers are in a set
I ordinal numbersI positionI which comes first
I identification numbers
Numbers are abstract ideas and it is sometimes difficult todiscern for students the difference between a number andthe symbol that represents a number ...
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
How We Use Numbers
I cardinal numbersI how many numbers are in a set
I ordinal numbersI positionI which comes first
I identification numbers
Numbers are abstract ideas and it is sometimes difficult todiscern for students the difference between a number andthe symbol that represents a number ...
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
How We Use Numbers
I cardinal numbersI how many numbers are in a set
I ordinal numbersI positionI which comes first
I identification numbers
Numbers are abstract ideas and it is sometimes difficult todiscern for students the difference between a number andthe symbol that represents a number ...
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
How We Use Numbers
I cardinal numbersI how many numbers are in a set
I ordinal numbersI positionI which comes first
I identification numbers
Numbers are abstract ideas and it is sometimes difficult todiscern for students the difference between a number andthe symbol that represents a number ...
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Tally System
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Tally System
Properties
I most simplistic
I a line represents 1, crossing represents 5
I grouping is to make counting easier
I very tedious
I additive system
DefinitionAn additive system is one in which the number representedby a particular set of numerals is simply the sum of thevalues of the numerals.
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Tally System
Properties
I most simplistic
I a line represents 1, crossing represents 5
I grouping is to make counting easier
I very tedious
I additive system
DefinitionAn additive system is one in which the number representedby a particular set of numerals is simply the sum of thevalues of the numerals.
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Tally System
Properties
I most simplistic
I a line represents 1, crossing represents 5
I grouping is to make counting easier
I very tedious
I additive system
DefinitionAn additive system is one in which the number representedby a particular set of numerals is simply the sum of thevalues of the numerals.
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Tally System
Properties
I most simplistic
I a line represents 1, crossing represents 5
I grouping is to make counting easier
I very tedious
I additive system
DefinitionAn additive system is one in which the number representedby a particular set of numerals is simply the sum of thevalues of the numerals.
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Tally System
Properties
I most simplistic
I a line represents 1, crossing represents 5
I grouping is to make counting easier
I very tedious
I additive system
DefinitionAn additive system is one in which the number representedby a particular set of numerals is simply the sum of thevalues of the numerals.
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Tally System
Properties
I most simplistic
I a line represents 1, crossing represents 5
I grouping is to make counting easier
I very tedious
I additive system
DefinitionAn additive system is one in which the number representedby a particular set of numerals is simply the sum of thevalues of the numerals.
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Egyptian Numeration System
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Egyptian Numeration System
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Egyptian Numeration System
Properties
I base 10 system
I additive system
I multiple symbols is an improvement
I order does not matter
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Egyptian Numeration System
Properties
I base 10 system
I additive system
I multiple symbols is an improvement
I order does not matter
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Egyptian Numeration System
Properties
I base 10 system
I additive system
I multiple symbols is an improvement
I order does not matter
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Egyptian Numeration System
Properties
I base 10 system
I additive system
I multiple symbols is an improvement
I order does not matter
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
Examples Using Egyptian Hieroglyphics
Example
What decimal number is represented here?
2008
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
Examples Using Egyptian Hieroglyphics
Example
What decimal number is represented here?
2008
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
Examples Using Egyptian Hieroglyphics
Example
What decimal number is represented here?
2,320,111
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
Examples Using Egyptian Hieroglyphics
Example
What decimal number is represented here?
2,320,111
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
Examples Using Egyptian Hieroglyphics
Example
Write the number 245 using Egyptian hieroglyphics.
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
Examples Using Egyptian Hieroglyphics
Example
Write the number 245 using Egyptian hieroglyphics.
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Roman Numeration System
Decimal Roman
1
I5 V
10 X50 L
100 C500 D
1000 M
Where do we see Roman numerals in modern day?
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Roman Numeration System
Decimal Roman
1 I5
V10 X50 L
100 C500 D
1000 M
Where do we see Roman numerals in modern day?
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Roman Numeration System
Decimal Roman
1 I5 V
10
X50 L
100 C500 D
1000 M
Where do we see Roman numerals in modern day?
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Roman Numeration System
Decimal Roman
1 I5 V
10 X50
L100 C500 D
1000 M
Where do we see Roman numerals in modern day?
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Roman Numeration System
Decimal Roman
1 I5 V
10 X50 L
100
C500 D
1000 M
Where do we see Roman numerals in modern day?
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Roman Numeration System
Decimal Roman
1 I5 V
10 X50 L
100 C500
D1000 M
Where do we see Roman numerals in modern day?
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Roman Numeration System
Decimal Roman
1 I5 V
10 X50 L
100 C500 D
1000
M
Where do we see Roman numerals in modern day?
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Roman Numeration System
Decimal Roman
1 I5 V
10 X50 L
100 C500 D
1000 M
Where do we see Roman numerals in modern day?
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Roman Numeration System
Decimal Roman
1 I5 V
10 X50 L
100 C500 D
1000 M
Where do we see Roman numerals in modern day?
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Roman Numeration System
Properties
I not a base 10 system
I additive system
I subtractive system
I multiplicative - we place a bar over a number torepresent 1000 times that numberM = 1, 000, 000
I positional system - where we place the symbols changesthe value
VI = 6 IV = 4
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Roman Numeration System
Properties
I not a base 10 system
I additive system
I subtractive system
I multiplicative - we place a bar over a number torepresent 1000 times that numberM = 1, 000, 000
I positional system - where we place the symbols changesthe value
VI = 6 IV = 4
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Roman Numeration System
Properties
I not a base 10 system
I additive system
I subtractive system
I multiplicative - we place a bar over a number torepresent 1000 times that numberM = 1, 000, 000
I positional system - where we place the symbols changesthe value
VI = 6 IV = 4
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Roman Numeration System
Properties
I not a base 10 system
I additive system
I subtractive system
I multiplicative - we place a bar over a number torepresent 1000 times that number
M = 1, 000, 000
I positional system - where we place the symbols changesthe value
VI = 6 IV = 4
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Roman Numeration System
Properties
I not a base 10 system
I additive system
I subtractive system
I multiplicative - we place a bar over a number torepresent 1000 times that numberM = 1, 000, 000
I positional system - where we place the symbols changesthe value
VI = 6 IV = 4
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Roman Numeration System
Properties
I not a base 10 system
I additive system
I subtractive system
I multiplicative - we place a bar over a number torepresent 1000 times that numberM = 1, 000, 000
I positional system - where we place the symbols changesthe value
VI = 6 IV = 4
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Roman Numeration System
Properties
I not a base 10 system
I additive system
I subtractive system
I multiplicative - we place a bar over a number torepresent 1000 times that numberM = 1, 000, 000
I positional system - where we place the symbols changesthe value
VI = 6 IV = 4
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
More Roman Numerals
Example
Write the following using Roman numerals.
1. 2
II
2. 4 IV
3. 9 IX
4. 40 XL
5. 49 XLIX
6. 99 XCIX
7. 1489 MCDLXXXIX
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
More Roman Numerals
Example
Write the following using Roman numerals.
1. 2 II
2. 4
IV
3. 9 IX
4. 40 XL
5. 49 XLIX
6. 99 XCIX
7. 1489 MCDLXXXIX
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
More Roman Numerals
Example
Write the following using Roman numerals.
1. 2 II
2. 4 IV
3. 9
IX
4. 40 XL
5. 49 XLIX
6. 99 XCIX
7. 1489 MCDLXXXIX
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
More Roman Numerals
Example
Write the following using Roman numerals.
1. 2 II
2. 4 IV
3. 9 IX
4. 40
XL
5. 49 XLIX
6. 99 XCIX
7. 1489 MCDLXXXIX
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
More Roman Numerals
Example
Write the following using Roman numerals.
1. 2 II
2. 4 IV
3. 9 IX
4. 40 XL
5. 49
XLIX
6. 99 XCIX
7. 1489 MCDLXXXIX
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
More Roman Numerals
Example
Write the following using Roman numerals.
1. 2 II
2. 4 IV
3. 9 IX
4. 40 XL
5. 49 XLIX
6. 99
XCIX
7. 1489 MCDLXXXIX
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
More Roman Numerals
Example
Write the following using Roman numerals.
1. 2 II
2. 4 IV
3. 9 IX
4. 40 XL
5. 49 XLIX
6. 99 XCIX
7. 1489
MCDLXXXIX
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
More Roman Numerals
Example
Write the following using Roman numerals.
1. 2 II
2. 4 IV
3. 9 IX
4. 40 XL
5. 49 XLIX
6. 99 XCIX
7. 1489 MCDLXXXIX
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
More Roman Numerals
Example
Write the following as decimal numbers.
1. CDXXIII
423
2. DCXIV 614
3. CCII 200,002
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
More Roman Numerals
Example
Write the following as decimal numbers.
1. CDXXIII 423
2. DCXIV 614
3. CCII 200,002
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
More Roman Numerals
Example
Write the following as decimal numbers.
1. CDXXIII 423
2. DCXIV
614
3. CCII 200,002
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
More Roman Numerals
Example
Write the following as decimal numbers.
1. CDXXIII 423
2. DCXIV 614
3. CCII 200,002
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
More Roman Numerals
Example
Write the following as decimal numbers.
1. CDXXIII 423
2. DCXIV 614
3. CCII
200,002
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
More Roman Numerals
Example
Write the following as decimal numbers.
1. CDXXIII 423
2. DCXIV 614
3. CCII 200,002
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Babylonian Numeration System
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Babylonian Numeration System
For the sake of simplicity, we will use symbols that look likethe following:
Properties
I base 60 system
I additive system
I place valued system
I positional
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Babylonian Numeration System
For the sake of simplicity, we will use symbols that look likethe following:
Properties
I base 60 system
I additive system
I place valued system
I positional
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Babylonian Numeration System
For the sake of simplicity, we will use symbols that look likethe following:
Properties
I base 60 system
I additive system
I place valued system
I positional
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Babylonian Numeration System
For the sake of simplicity, we will use symbols that look likethe following:
Properties
I base 60 system
I additive system
I place valued system
I positional
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Babylonian Numeration System
For the sake of simplicity, we will use symbols that look likethe following:
Properties
I base 60 system
I additive system
I place valued system
I positional
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Babylonian Numeration System
Base 60
603 602 601 600
Example
Write 53 using Babylonian cuneiform.
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Babylonian Numeration System
Base 60
603 602 601 600
Example
Write 53 using Babylonian cuneiform.
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Babylonian Numeration System
Base 60
603 602 601 600
Example
Write 53 using Babylonian cuneiform.
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Babylonian Numeration System
Example
What decimal number is represented here?
Example
What decimal number is represented here?
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Babylonian Numeration System
Example
What decimal number is represented here?
Example
What decimal number is represented here?
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Babylonian Numeration System
Example
What decimal number is represented here?
The Babylonians realized they needed a place holder torepresent that they had a place with nothing in it whenwriting their numbers.
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Babylonian Numeration System
Example
What decimal number is represented here?
The Babylonians realized they needed a place holder torepresent that they had a place with nothing in it whenwriting their numbers.
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Babylonian Numeration System
Example
Write 3821 using Babylonian cuneiform.
To figure this out, we want to write this in expanded form.What is the largest power of 60 that goes into 3821?
602( ) + 601( ) + 600( )
602(1) + 601( ) + 600( )
602(1) + 601(3) + 600( )
602(1) + 601(3) + 600(41)
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Babylonian Numeration System
Example
Write 3821 using Babylonian cuneiform.
To figure this out, we want to write this in expanded form.What is the largest power of 60 that goes into 3821?
602( ) + 601( ) + 600( )
602(1) + 601( ) + 600( )
602(1) + 601(3) + 600( )
602(1) + 601(3) + 600(41)
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Babylonian Numeration System
Example
Write 3821 using Babylonian cuneiform.
To figure this out, we want to write this in expanded form.What is the largest power of 60 that goes into 3821?
602( ) + 601( ) + 600( )
602(1) + 601( ) + 600( )
602(1) + 601(3) + 600( )
602(1) + 601(3) + 600(41)
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Babylonian Numeration System
Example
Write 3821 using Babylonian cuneiform.
To figure this out, we want to write this in expanded form.What is the largest power of 60 that goes into 3821?
602( ) + 601( ) + 600( )
602(1) + 601( ) + 600( )
602(1) + 601(3) + 600( )
602(1) + 601(3) + 600(41)
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Babylonian Numeration System
Example
Write 3821 using Babylonian cuneiform.
To figure this out, we want to write this in expanded form.What is the largest power of 60 that goes into 3821?
602( ) + 601( ) + 600( )
602(1) + 601( ) + 600( )
602(1) + 601(3) + 600( )
602(1) + 601(3) + 600(41)
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Babylonian Numeration System
Example
Write 3821 using Babylonian cuneiform.
To figure this out, we want to write this in expanded form.What is the largest power of 60 that goes into 3821?
602( ) + 601( ) + 600( )
602(1) + 601( ) + 600( )
602(1) + 601(3) + 600( )
602(1) + 601(3) + 600(41)
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Babylonian Numeration System
Example
Write 3821 using Babylonian cuneiform.
To figure this out, we want to write this in expanded form.What is the largest power of 60 that goes into 3821?
602( ) + 601( ) + 600( )
602(1) + 601( ) + 600( )
602(1) + 601(3) + 600( )
602(1) + 601(3) + 600(41)
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Babylonian Numeration System
Example
Write 3821 using Babylonian cuneiform.
To figure this out, we want to write this in expanded form.What is the largest power of 60 that goes into 3821?
602( ) + 601( ) + 600( )
602(1) + 601( ) + 600( )
602(1) + 601(3) + 600( )
602(1) + 601(3) + 600(41)
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Babylonian Numeration System
Example
Write 7205 using Babylonian cuneiform.
What is the largest power of 60 that goes into 7205?
7205 = 602( ) + 601( ) + 600( )
= 602(2) + 601( ) + 600( )
= 602(2) + 601(0) + 600( )
= 602(2) + 601(0) + 600(5)
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Babylonian Numeration System
Example
Write 7205 using Babylonian cuneiform.
What is the largest power of 60 that goes into 7205?
7205 = 602( ) + 601( ) + 600( )
= 602(2) + 601( ) + 600( )
= 602(2) + 601(0) + 600( )
= 602(2) + 601(0) + 600(5)
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Babylonian Numeration System
Example
Write 7205 using Babylonian cuneiform.
What is the largest power of 60 that goes into 7205?
7205 = 602( ) + 601( ) + 600( )
= 602(2) + 601( ) + 600( )
= 602(2) + 601(0) + 600( )
= 602(2) + 601(0) + 600(5)
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Babylonian Numeration System
Example
Write 7205 using Babylonian cuneiform.
What is the largest power of 60 that goes into 7205?
7205 = 602( ) + 601( ) + 600( )
= 602(2) + 601( ) + 600( )
= 602(2) + 601(0) + 600( )
= 602(2) + 601(0) + 600(5)
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Babylonian Numeration System
Example
Write 7205 using Babylonian cuneiform.
What is the largest power of 60 that goes into 7205?
7205 = 602( ) + 601( ) + 600( )
= 602(2) + 601( ) + 600( )
= 602(2) + 601(0) + 600( )
= 602(2) + 601(0) + 600(5)
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Babylonian Numeration System
Example
Write 7205 using Babylonian cuneiform.
What is the largest power of 60 that goes into 7205?
7205 = 602( ) + 601( ) + 600( )
= 602(2) + 601( ) + 600( )
= 602(2) + 601(0) + 600( )
= 602(2) + 601(0) + 600(5)
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Babylonian Numeration System
Example
Write 7205 using Babylonian cuneiform.
What is the largest power of 60 that goes into 7205?
7205 = 602( ) + 601( ) + 600( )
= 602(2) + 601( ) + 600( )
= 602(2) + 601(0) + 600( )
= 602(2) + 601(0) + 600(5)
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Mayan Numeration System
Properties
1. additive system
2. positional system
3. place valued system
4. symbol for 0
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Mayan Numeration System
Properties
1. additive system
2. positional system
3. place valued system
4. symbol for 0
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Mayan Numeration System
Properties
1. additive system
2. positional system
3. place valued system
4. symbol for 0
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Mayan Numeration System
Properties
1. additive system
2. positional system
3. place valued system
4. symbol for 0
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Mayan Numeration System
Properties
1. additive system
2. positional system
3. place valued system
4. symbol for 0
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Mayan Numeration System
1’s
20’s
18 · 20’s
18 · 202’s
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Mayan Numeration System
1’s
20’s
18 · 20’s
18 · 202’s
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Mayan Numeration System
1’s
20’s
18 · 20’s
18 · 202’s
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Mayan Numeration System
1’s
20’s
18 · 20’s
18 · 202’s
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Mayan Numeration System
Example
Write 7 in Mayan.
• •
Example
Write 45 in Mayan.
• •
Spacing is very important ...
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Mayan Numeration System
Example
Write 7 in Mayan.
• •
Example
Write 45 in Mayan.
• •
Spacing is very important ...
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Mayan Numeration System
Example
Write 7 in Mayan.
• •
Example
Write 45 in Mayan.
• •
Spacing is very important ...
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Mayan Numeration System
Example
Write 7 in Mayan.
• •
Example
Write 45 in Mayan.
• •
Spacing is very important ...
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Mayan Numeration System
Example
Write 7 in Mayan.
• •
Example
Write 45 in Mayan.
• •
Spacing is very important ...
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Mayan Numeration System
Example
Write 611 in Mayan
First, we need to write 611 in expanded form.
611 = 360 + 251
= 360 + 240 + 11
= 18 · 20 + 12 · 20 + 11
•
• •
•
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Mayan Numeration System
Example
Write 611 in Mayan
First, we need to write 611 in expanded form.
611 = 360 + 251
= 360 + 240 + 11
= 18 · 20 + 12 · 20 + 11
•
• •
•
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Mayan Numeration System
Example
Write 611 in Mayan
First, we need to write 611 in expanded form.
611 =
360 + 251
= 360 + 240 + 11
= 18 · 20 + 12 · 20 + 11
•
• •
•
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Mayan Numeration System
Example
Write 611 in Mayan
First, we need to write 611 in expanded form.
611 = 360 + 251
= 360 + 240 + 11
= 18 · 20 + 12 · 20 + 11
•
• •
•
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Mayan Numeration System
Example
Write 611 in Mayan
First, we need to write 611 in expanded form.
611 = 360 + 251
= 360 + 240 + 11
= 18 · 20 + 12 · 20 + 11
•
• •
•
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Mayan Numeration System
Example
Write 611 in Mayan
First, we need to write 611 in expanded form.
611 = 360 + 251
= 360 + 240 + 11
= 18 · 20 + 12 · 20 + 11
•
• •
•
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Mayan Numeration System
Example
Write 611 in Mayan
First, we need to write 611 in expanded form.
611 = 360 + 251
= 360 + 240 + 11
= 18 · 20 + 12 · 20 + 11
•
• •
•
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Hindu-Arabic Numeration System
Properties
1. base 10 system
2. positional system
3. place-valued system
4. additive system (values for various numerals added)
5. 10 symbols called digits
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Hindu-Arabic Numeration System
Properties
1. base 10 system
2. positional system
3. place-valued system
4. additive system (values for various numerals added)
5. 10 symbols called digits
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Hindu-Arabic Numeration System
Properties
1. base 10 system
2. positional system
3. place-valued system
4. additive system (values for various numerals added)
5. 10 symbols called digits
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Hindu-Arabic Numeration System
Properties
1. base 10 system
2. positional system
3. place-valued system
4. additive system (values for various numerals added)
5. 10 symbols called digits
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
The Hindu-Arabic Numeration System
Properties
1. base 10 system
2. positional system
3. place-valued system
4. additive system (values for various numerals added)
5. 10 symbols called digits
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
Sets of Numbers
Let’s define the following sets:
I The Natural Numbers N
Why is 0 not a natural number? Because we don’t startcounting from 0 ...
I The Integers ZI The Rational Numbers QI The Irrational Numbers
I The Real Numbers RI The Complex Numbers C
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
Sets of Numbers
Let’s define the following sets:
I The Natural Numbers NWhy is 0 not a natural number?
Because we don’t startcounting from 0 ...
I The Integers ZI The Rational Numbers QI The Irrational Numbers
I The Real Numbers RI The Complex Numbers C
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
Sets of Numbers
Let’s define the following sets:
I The Natural Numbers NWhy is 0 not a natural number? Because we don’t startcounting from 0 ...
I The Integers Z
I The Rational Numbers QI The Irrational Numbers
I The Real Numbers RI The Complex Numbers C
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
Sets of Numbers
Let’s define the following sets:
I The Natural Numbers NWhy is 0 not a natural number? Because we don’t startcounting from 0 ...
I The Integers ZI The Rational Numbers Q
I The Irrational Numbers
I The Real Numbers RI The Complex Numbers C
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
Sets of Numbers
Let’s define the following sets:
I The Natural Numbers NWhy is 0 not a natural number? Because we don’t startcounting from 0 ...
I The Integers ZI The Rational Numbers QI The Irrational Numbers
I The Real Numbers RI The Complex Numbers C
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
Sets of Numbers
Let’s define the following sets:
I The Natural Numbers NWhy is 0 not a natural number? Because we don’t startcounting from 0 ...
I The Integers ZI The Rational Numbers QI The Irrational Numbers
I The Real Numbers R
I The Complex Numbers C
1 How We UseNumbers
2 The TallySystem
3 The EgyptianNumerationSystem
4 The RomanNumerationSystem
5 The BabylonianNumerationSystem
6 The MayanNumerationSystem
7 TheHindu-ArabicNumerationSystem
8 Sets of Numbers
Sets of Numbers
Let’s define the following sets:
I The Natural Numbers NWhy is 0 not a natural number? Because we don’t startcounting from 0 ...
I The Integers ZI The Rational Numbers QI The Irrational Numbers
I The Real Numbers RI The Complex Numbers C
