Presentation is loading. Please wait.

Presentation is loading. Please wait.

Thinking Mathematically Number Representation and Calculation 4.1 Our Hindu-Arabic System and Early Positional Systems.

Similar presentations


Presentation on theme: "Thinking Mathematically Number Representation and Calculation 4.1 Our Hindu-Arabic System and Early Positional Systems."— Presentation transcript:

1 Thinking Mathematically Number Representation and Calculation 4.1 Our Hindu-Arabic System and Early Positional Systems

2 “Exponential” Notation An “exponent” is a small number written slightly above and just to the right of a number or an expression. When an exponent is a positive integer it stands for repeated multiplication = 10*10 = = 10*10*10 = = 10*10*10*10 = 10,000

3 Exponents, cont. Exercise Set 4.1, #3 2 3 = ? We will re-visit exponents in a more general sense in section 5.6 –0 exponent –Negative exponents –Fractional exponents

4 Our Hindu-Arabic Numeration System Introduced to Europe ~1200A.D. by Fionacci A base 10 system: 10 numerals (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) The value of each position is a power of 10 Why 10? How about 12 or 60?

5 Our Hindu-Arabic Numeration System With the use of exponents, Hindu-Arabic numerals can be written in expanded form in which the value of the digit in each position is made clear = (3x10 3 )+(4x10 2 )+(0x10 1 )+(7x1) or (3x1000)+(4x100)+(0x10)+(7x1) 53,525=(5x10 4 )+(3x10 3 )+(5x10 2 )+(2x10 1 )+(5x1) or (5x10,000)+(3x1000)+(5x100)+(2x10)+(5x1)

6 Examples: Expanded Form Exercise Set 4.1 #17, #29 Write in expanded form –3,070 Express as a Hindu-Arabic numeral –(7 x 10 3 ) + (0 x 10 2 ) + (0 x 10 1 ) + (2 x 1)

7 Thinking Mathematically Number Representation and Calculation 4.2 Number Bases in Positional Systems

8 Base of a Positional System Base n n numerals (0 through n-1) Powers of n define the place values Example – base digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) Positional values (right to left) 10 0 (=1), 10 1 (=10), 10 2 (=100), 10 3 (=1,000)… Example – base 16 (hexadecimal) 16 digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, c, d, e, f) Positional values (right to left) 16 0 (=1), 16 1 (=16), 16 2 (=256), 16 3 (=4,096)…

9 Counting in a Positional System Base 10 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11,... Base 4 0, 1, 2, 3, 10, 11, 12, 13, 20, 21, 22, 23, 30,... Base 16 (hexadecimal) 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, c, d, e, f, 10, 11,... Base 2 (binary) 0, 1, 10, 11, 100, 101, 110, 111, 1000, 1001,...

10 Converting to/from Base 10 Exercise Set 4.2 #3, #21, #37 –Convert 52 eight to base 10 –Convert 11 to base seven –Convert 19 to base two

11 Thinking Mathematically Number Representation and Calculation 4.3 Computation in Positional Systems

12 Computation in Other Bases Remember how its done in base 10 –Carry (addition and multiplication) –Borrow (subtraction) –Long Division

13 Examples: Computation in Other Bases Exercise Set 4.3 #5, # five five = 475 eight – 267 eight = Hexadecimal Arithmetic 4C6 sixteen sixteen = 694 sixteen – 53B sixteen =

14 Thinking Mathematically Chapter 4: Number Representation and Calculation


Download ppt "Thinking Mathematically Number Representation and Calculation 4.1 Our Hindu-Arabic System and Early Positional Systems."

Similar presentations


Ads by Google