Topic 1.      Introductory Material

 

          a. Introducing scientific notation – “floating point numbers”

 

                   1. The decimal point of a number and how it is modified by positive and negative exponents.

 

                             123.4 = 1.234 x 102 = 12.34 x 101

                             0.01234 = 1.234 x 10-2

                             1 x 103 = 1000       sometimes written as 1e+3

                             1 x 10-3 = 0.001     sometimes written as 1e-3          (especially in computer listings)

                             6 x 1023 = 600,000,000,000,000,000,000,000

 

                   2. Multiplication and division of floating point numbers

 

                             Multiply numbers and add exponents to multiply:    (3x105)(4x103) = 12x108

                             Divide numbers and subtract exponents to divide:  (3x105)/(4x103) = ¾ x 102 = 0.75 x 102 = 75

 

                   3. Addition and subtraction of floating point numbers

 

                             Addition and subtraction of normal fixed-point numbers requires that the decimal points of

                             the two numbers be aligned, and this is true for floating point numbers as well.  This alignment

                             can be accomplished in two ways: (1) convert both numbers to fixed point or (2) convert one number

                             to the exponent of the other one so that they share a common exponent.

 

                             For example: 

Method 1:              1x103 + 1x102 = 1,000 + 100 = 1,100

Method 2:              1x103 + 1x102 = 10x102 + 1x102 = 11x102 = 1,100

 

          The floating point representation may not be very useful if the two numbers have very different exponents.

 

                                      Thus:                    1x105 - 1 = 100,000 - 1= 99,999

 

          There is no advantage to using the floating point representation in this case.

 

          In general, the floating point representation is most useful when the numbers are either very big or very small, so that using this representation saves writing lots of zeroes.

 

          b. The metric system of base units and prefixes: unit= prefix+base unit.

 

Example 1: kilo+meter=kilometer= 1,000 meters, abbreviated as 1 km

Example 2: 1 nanometer= 0.000 000 001 meters, abbreviated as 1 nm

                  

nano-           10-9    abbreviated as n + unit     example: nm for nanometers

micro-         10-6    abbreviated as m + unit    example: mm for micrometers

                   milli-            10-3    abbreviated as m + unit    example: mm for millimeters

                   centi-           10-2    abbreviated as c + unit     example: cm for centimeters

                   kilo-             103     abbreviated as k + unit     example: kHz for kilohertz

                   mega-          106     abbreviated as M + unit   example MHz for megahertz

                   giga-            109     abbreviated as G + unit    example GHz for gigahertz

                   tera-             1012    abbreviated as T + unit    example THz for Terahertz

 

          Important: In a calculation, most metric prefixes should be converted to the equivalent power of 10. See Useful equations for more about this.

 

 

 

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