The Evolution of Numeration Systems Section 4.1 The Evolution of Numeration Systems

Objectives Understand and use the Egyptian System. Understand and use the Roman system. Understand and use the Chinese system. Understand and use the Ionic Greek system.

Key Terms Number: 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 System An 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 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: 1,320,401 Convert to Egyptian Hieroglyphics

Example 5: 421,536 Convert to Egyptian Hieroglyphics

Example 6: 1,752 Convert 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 I Classwork: TB pg. 204/1 – 24 All Must write problem and show ALL work to receive credit for this assignment.

The Evolution of Numeration Systems Part II Section 4.1 The Evolution of Numeration Systems Part II

Egyptian Method of Doubling Power of 2 Value Times 21 20 1 21 2 21 + 21 = 42 22 4 42 + 42 = 84 23 8 84 + 84 = 168 24 16 168 + 168 = 336 25 32 336 + 336 = 672 26 64 672 + 672 = 1344

Example 11: 13 X 43 Doubling Method

Example 12: 35 X 21 Doubling Method

Roman Numerals Number Roman Numeral 1 I 5 V 10 X 50 L 100 C 500 D 1,000 M NOTE: See pg. 202 in TB

Example 13: MCMXCVI Convert to Hindu-Arabic

Example 14: MCDXLVII Convert to Hindu-Arabic

Example 15: 931 Convert to Roman Numerals

Example 16: 87,423 Convert to Roman Numerals

Section 4.1 Assignment II Classwork: TB pg. 205/ Must write problem and show ALL work to receive credit for this assignment.

The Evolution of Numeration Systems Part III Section 4.1 The Evolution of Numeration Systems Part III

Chinese Number System 1 2 3 4 5 6 7 8 9 10 100 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: 87 Translate to Chinese

Example 21: 358 Translate to Chinese

Example 22: 3264 Translate to Chinese

Section 4.1 Assignment III Classwork: TB pg. 205/59 – 72 All Must write problem and show ALL work to receive credit for this assignment.