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Units of Measurement (1.3) & (1.4) Systems of Units

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Table 1.1 (p. 9) English, Metric, & SI Units English – inch, mile, pound, ounce Metric – base-10, CGS and MKS CGS – Based on centimeter, gram, second MKS – Based on meter, kilogram, second SI – International System, modern metric

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Problem 6 (p. 29) A pitcher has the ability to throw a baseball at 95 mph. What is the speed in ft/s? 95 mi h 95 mi h 5280 ft mi 5280 ft mi * 1 h _ 60 min 1 h _ 60 min * 1 min 60 s 1 min 60 s * = ? ? ft s ft s ft s ft s

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Problem 6 (p. 29) part b How long does the hitter have to make a decision about swinging at the ball if the plate and the mound are separated by 60 feet? v = dtdt t = dvdv 60 ft _ ft/s = ?= ? = s

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Problem 6 (p. 29) part c. If the batter wanted a full second to make a decision, what would the speed in mph have to be? v = dtdt = 60 ft 1 s * 60 s_ 1 min * 60 min 1 h * 1 mi_ 5280 ft = ? = mph

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1.5 Significant figures, accuracy, and rounding off 1.2 V and 1.20 V Imply different levels of accuracy

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Accuracy and Precision Accuracy = freedom from error (exactness) Precision = The degree of refinement with which an operation is performed or a measure stated The precision of a reading can be determined by the number of significant figures (digits) present.

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When adding a quantity accurate only to the tenths place to a number accurate to the thousandths place will result in a total having accuracy only to the tenths place. In the addition or subtraction of approximate numbers, the entry with the lowest level of accuracy determines the format of the solution.

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Example 1.1 (p. 12) a (as determined by ) =

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Example 1.1 (p. 12) b (as determined by 0.04) =

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1.6 Powers of Ten _ 1 _ = 10 = __ 1 __ _ 1 _ = =

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Addition and Subtraction A * 10 ± B * 10 = (A ± B) * 10 Example: = (6.3 * 10 ) + (75 * 10 ) = ( ) * 10 = 81.3 * n n n

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Multiplication (a* 10 ) (B * 10 ) = (A)(B) * 10 Example: (0.0002) ( ) = (2) * 10 * (7) * 10 = 14 * 10 nmn + m

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Division A * 10_ A B * 10 B * 10 = n m n-m Example: * 10_ 2 * 10 = 23.5 * =

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Powers (A * 10 ) = A * 10 n m mnm (5 * 10 ) = 5 * __1___ () 3 = = 125 * Example:

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1.7: Fixed-Point, Floating Point, Scientific, and Engineering Notation * Fixed Point – Choose the level of accuracy for the output – example: tenths, hundredths or thousandths place 1313 = = =

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Floating Point Number of significant figures varies 1313 = … 1 16 = = 1150

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Scientific Notation Scientific notation requires that the decimal point appear directly after the first digit greater than or equal to 1, but let than = E = 6.25 E = 1.15 E3

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Engineering Notation Engineering notation specifies that all powers of ten must be multiples of 3, and the mantissa must be greater than or equal to 1 but less than = E = 62.5 E = 1.15 E3

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Engineering Notation and Accuracy Using engineering notation with two-place accuracy will result in: 1313 = E = E = 1.15 E3

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Look at table 1-2 for prefixes

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1.8 Conversion Between Levels of Powers of Ten a.20 kHz = ______________ MHz 20 * 10_ Hz 3 * 10 = 20 * = 0.02 MHz

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Conversion: Continued b.0.04 ms = ___________ μs * 10 * 10 = 4 * μsμs or 40 μs 6 4 * 10_ s

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1.9 Conversion 0.5 day = _____ min 0.5 day 24 h60 min = 720 min 1 day 1 h ( ())

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Determine the speed in miles per hour of a competitor who can run a 4-min mile. 1 mi 4 min 60 min 1 h 60 mi 4 hr 15 mi h (()) == 15 mph

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Data is being collected automatically from an experiment at a rate of 14.4 kbps. How long will it take to completely fill a diskette whose capacity is 1.44 MB? Rate = 14.4 kbps, Capacity = 1.44 MB Rate = 1.44 MB = 1.44 * 2 * 8 bit 20 Capacity Time so Time = Capacity Rate t = (1.44 MB) (2 ) (8 _) (14.4 * 10 )(60 ) 20bytes MB bits byte bits sec min = min 3

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Number Systems (N) = [(integer part). (fractional part)] n Radix point Two common number representations Juxtapositional – placing digit side-by-side Non-juxtapositional

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Juxtapositional n-1 (N) = (a a … a a a a … a ) n n-210.n-2-m R = Radix of the number system Radix point n = number of digits in the integer portion m = number of digits in the fractional portion a = MSD a = LSD n-1 -m

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Base Conversion = ( ) 10 2 [(0001 * 1010) + (1001 * 0001) + (0111 * ) * + ] 2 ___ 1 2___0 2___1 1 _ _ _ ______x =

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