Section 4.1The Evolution

of Numeration Systems

Objectives

1. Understand and use the Egyptian System.

2. Understand and use the Roman system.

3. Understand and use the Chinese system.

4. Understand and use the Ionic Greek system.

Key TermsNumber: tell us how many objects

we are counting.Numeral: a symbol which

represents a number.System of Numeration: a set of

basic numerals and rules for combining them to represent numbers.

Hindu-Arabic Numerals: a system of writing numerals that were invented in India and brought to Europe by Arabs, which we use today.

Hindu-Arabic SystemAn important characteristic of our

Hindu-Arabic system is that we can write the numeral for any number, large or small, using only ten symbols.

The ten symbols are as follows:0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

These symbols are called digits.

Egyptian Hieroglyphic System

Number Power of 10

Symbol Name

1 100 Stroke/Staff

10 101 Heel bone

100 102 Scroll

1,000 103 Lotus Flower

10,000 104 Pointing Finger

100,000 105 Fish/Tadpole

1,000,000 106 Astonished Person

Example 1:Convert to Hindu-Arabic Notation

Example 2:Convert to Hindu-Arabic Notation

Example 3:Convert to Hindu-Arabic Notation

Example 4: 1,320,401Convert to Egyptian Hieroglyphics

Example 5: 421,536Convert to Egyptian Hieroglyphics

Example 6: 1,752Convert to Egyptian Hieroglyphics

Example 7:Adding in the Egyptian System.

Example 8:Adding in the Egyptian System.

Example 9:Subtracting in the Egyptian

System

Example 10:Subtracting in the Egyptian

System

Section 4.1 Assignment IClasswork:

◦TB pg. 204/1 – 24 All Must write problem and show ALL work to

receive credit for this assignment.

Section 4.1

The Evolution of

Numeration Systems

Part II

Egyptian Method of Doubling

Power of 2 Value Times 21

20 1 2121 2 21 + 21 = 4222 4 42 + 42 = 8423 8 84 + 84 = 16824 16 168 + 168 = 33625 32 336 + 336 = 67226 64 672 + 672 = 1344

Example 11: 13 X 43Doubling Method

Example 12: 35 X 21Doubling Method

Roman Numerals

Number Roman Numeral

1 I5 V

10 X50 L

100 C

500 D

1,000 M

NOTE: See pg. 202 in TB

Example 13: MCMXCVIConvert to Hindu-Arabic

Example 14: MCDXLVIIConvert to Hindu-Arabic

Example 15: 931Convert to Roman Numerals

Example 16: 87,423Convert to Roman Numerals

Section 4.1 Assignment IIClasswork:

◦TB pg. 205/ Must write problem and show ALL work

to receive credit for this assignment.

Section 4.1

The Evolution of

Numeration Systems

Part III

Chinese Number System

123456789

10100

1000

NOTE:The Chinese did not have a

symbol for the zero in the traditional notation, and they did not use the concept of place value. So they had to specify whether they were talking about 6 tens, 6 hundreds, or 6 thousands, etc.

This required an extra symbol.

Example 17:Translate to Hindu-Arabic

Example 18:Translate to Hindu-Arabic

Example 19:Translate to Hindu-Arabic

Example 20: 87Translate to Chinese

Example 21: 358Translate to Chinese

Example 22: 3264Translate to Chinese

Section 4.1 Assignment IIIClasswork:

◦TB pg. 205/59 – 72 All Must write problem and show ALL work

to receive credit for this assignment.