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.