4 1 Day II Additive Multiplicative and Ciphered

4. 1 Day II: Additive, Multiplicative and Ciphered Systems of Numeration By the end of class you will be able to convert numbers among Hindu-Arabic, Chinese and Greek

Some Chinese Examples: =63 So What Do You Notice? ? =725

Chinese Numeration System: • Read from bottom up • Group numbers in 2: top number is multiplied by bottom number which is a power of 10 • The bottom number is the units digit (not multiplied by anything • Need to add zeros if they appear consecutively in the middle of the number • 11 -19 not written as powers of 10

Examples of Special Rules: =9001 =16

Conversions 1) 3) 577 2) 4) 703

Iconic Greek System • Ciphered System: there are numerals for numbers up to the base, and numerals for multiples of the base (multiples of 10 in this case) • Uses Greek letters of alphabet • Has a multiplicative property: place I as a superscript in front of a number to multiply by 1000

Write in Hindu Arabic • 1) • 2) • 3) • 4)

Write in Greek • 1) 285 • 2) 311 • 3) 1012

Summarizer • 1) Create a 4 -foldable with labels “Egyptian”, “Roman”, “Chinese” “Greek” • 2) Write a different numeral in each box • 3) Your partner will convert the numerals to Hindu-Arabic, and write a fact about each numeration system • 4) Check your partner’s work