Math 2008 Ch 3
Tally Number System
Easy to use even today. Grouping is 5 makes numbers easier to read and count. Not the best for large numbers, no way to write zero, multiplication and division are difficult to model.
Factor
If a is any number and n is any natural number, then
Egyptian Number System
Improvement over the tally. Powers of ten. adding is easy, shorter way to represent numbers from tallies. disadvantages: no way to write zero multiple ways to represent a single number, Still hard to Multiply and Divide
Roman Numbers
Still used today. Uses letter to represent numbers. Advantages= uses 7 symbols, makes use of 10's and 5's. Subtraction allows for shorter numbers representation. Disadvantages= difficult to add, subtract, multiply and divide, no way to write zero, multiple ways to represent the same number.
Base two Binary system - only two digits
Base two is especially important because of its use in computers. One of the two digits is represented by the presence of an electrical signal and the other by the absence of an electrical signal
Hindu-Arabic Numeration System
1.All numerals are constructed from the 10 digits. 2.Place value is based on powers of 10.
Base-ten blocks
1 long →101 = 1 row of 10 units 1 flat →102 = 1 row of 10 longs, or 100 units 1 block →103 = 1 row of 10 flats, or 100 longs, or 1000 units
Tally Numeration System
Uses single strokes (tally marks) to represent each object that is counted
Use the Roman numeration system to represent 15,478
XVCDLXXVIII The first X and V have a line over the top of them
Numeration system
a collection of properties and symbols agreed upon to represent numbers systematically
Place value
assigns a value to a digit depending on its placement in a numeral
Mayan system
groups their symbols vertically and its always base 20. 0-19 represented through three symbols a dot for one, a line for 5 and an pie for zero. The pie with a dot over it represents 20.
Babylonian system
groups their symbols vertically and its always base 60. 1st to develop the place value system. Additive System as are Egyptian and Tally. Can also be subtractive. Advantages= uses only two symbols and a space, very large numbers can be easily represented, adding, subtraction, multiplication and division are easier to accomplish. Disadvantages= lack a zero symbol
Numerals
written symbols to represent cardinal numbers.
