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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? ft s ? ft s 95 mi h 5280 ft mi 1 h _ 60 min 1 min 60 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 = d t t = d v 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? d t 60 ft 1 s 60 s_ 1 min 60 min 1 h 1 mi_ 5280 ft ? v = = * * * = = 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) 532.6 ≈ 536.7 4.02 (as determined by**

≈ 536.7 (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 _ _ 1 _ 1000 10 = = 10 __ 1 __ _ 1 _ 0.00001 10**

-3 = 10 3 __ 1 __ _ 1 _ 5 = = 10 -5

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**Addition and Subtraction**

A * 10 ± B * 10 = (A ± B) * 10 Example: = (6.3 * 10 ) + (75 * 10 ) = ( ) * 10 = 81.3 * 10 3 3 3 3

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Multiplication n m n + m (a* 10 ) (B * 10 ) = (A)(B) * 10 Example: (0.0002) ( ) = (2) * 10 * (7) * 10 = 14 * 10 -4 -6 -10

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**Division A * 10_ A B * 10 B = * 10 Example: 0.00047 0.002 47 * 10_**

n-m = * 10 m Example: -5 0.002 47 * 10_ 2 * 10 -2 = 23.5 * 10 = -3

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**( ) Powers = 125 * 10 (A * 10 ) = A * 10 Example: __1___ 0.0005 =**

n m nm Example: ( ) __1___ 0.0005 3 3 -5 3 -15 = (5 * 10 ) = 5 * 10 -15 = 125 * 10

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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 1 3 1 16 = 0.333 = 0.063 2300 2 =

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**Floating Point Number of significant figures varies 1 3**

= … 1 16 = 2300 2 = 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 10. 1 3 = E-1 1 16 = 6.25 E-2 2300 2 = 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 1000 1 3 = E-3 1 16 = 62.5 E-3 2300 2 = 1.15 E3

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**Engineering Notation and Accuracy**

Using engineering notation with two-place accuracy will result in: 1 3 = E-3 1 16 = E-3 2300 2 = 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**

20 kHz = ______________ MHz 20 * 10_ Hz 3 -6 -3 * = * 10 = 0.02 MHz

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**Conversion: Continued**

0.04 ms = ___________ μs -2 4 * 10_ s +1 -3 6 * 10 * = * 10 μs or 40 μs

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**( ) ( ) 1.9 Conversion 0.5 day = _____ min 0.5 day 24 h 60 min**

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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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**Rate = 14.4 kbps, Capacity = 1.44 MB 1.44 MB = 1.44 * 2 * 8 bit**

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 20 1.44 MB = 1.44 * * 8 bit Capacity Rate Capacity Time so Time = Rate = bytes 20 bits (1.44 MB) ( ) (8 _) (14.4 * )(60 ) MB byte = min t = bits 3 sec sec min

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**Number Systems (N) = [(integer part) . (fractional part)]**

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

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**Juxtapositional (N) = (a a … a a a a … a )**

Radix point (N) = (a a … a a a a … a ) n n-1 n-2 1 0. -1 n-2 -m R = Radix of the number system n = number of digits in the integer portion m = number of digits in the fractional portion a = MSD n-1 a = LSD -m

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Base Conversion = ( ) 10 2 1 _ 1010 1 _ 1010 1 _ 1010 [(0001 * 1010) + (1001 * 0001) + (0111 * ) * ] 2 ___ 1 2___1 2___0 19 9 4 2 1 10011 0.75 2 1.50 1.00 ______x = 1 ______x 1 .11

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Measurements and Their Uncertainty 3.1

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