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Units and Measurement Physical Science
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Math and Units Math- the language of Physics SI Units – International System MKS Length m Mass kg Time s National Bureau of Standards Prefixes
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Base SI Units QuantityUnitSymbol Lengthmeterm Masskilogramkg TemperaturekelvinK Timeseconds Amount of Substance molemol Luminous Intensitycandelacd Electric Currentamperea
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Derived SI Units (examples) QuantityunitSymbol Volumecubic meterm3m3 Densitykilograms per cubic meter kg/m 3 Speedmeter per secondm/s Newtonkg m/ s 2 N EnergyJoule (kg m 2 /s 2 )J PressurePascal (kg/(ms 2 )Pa
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Limits of Measurement Accuracy and Precision
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Example: Evaluate whether the following are precise, accurate or both. Accurate Not Precise Not Accurate Precise Accurate Precise
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Accuracy - a measure of how close a measurement is to the true value of whatever is being measured.
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Example: Accuracy Who is more accurate when measuring a book that has a true length of 17.0cm? Susan: 17.0cm, 16.0cm, 18.0cm, 15.0cm Amy: 15.5cm, 15.0cm, 15.2cm, 15.3cm
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Precision – a measure of how close a series of measurements are to one another. A measure of how exact a measurement is.
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Example: Precision Who is more precise when measuring the same 17.0cm book? Susan: 17.0cm, 16.0cm, 18.0cm, 15.0cm Amy: 15.5cm, 15.0cm, 15.2cm, 15.3cm
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Significant Figures The significant figures in a measurement include all of the digits that are known, plus one last digit that is estimated.
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Centimeters and Millimeters
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SI Unit Prefixes NameSymbolAnalogy giga-G10 9 mega-M10 6 kilo-k10 3 deci-d10 -1 centi-c10 -2 milli-m10 -3 micro-μ10 -6 nano-n10 -9 pico-p10 -12
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SI Unit Prefixes for Length NameSymbolAnalogy gigameterGm10 9 megameterMm10 6 kilometerkm10 3 decimeterdm10 -1 centimetercm10 -2 millimetermm10 -3 micrometerμmμm10 -6 nanometernm10 -9 picometerpm10 -12
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Scientific Notation M x 10 n M is the coefficient 1<M<10 10 is the base n is the exponent or power of 10
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1)Put the decimal after the first non- zero digit. Example: To convert 5,668,000 first write 5.668000 To write a number to scientific notation:
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2) To find the exponent count the number of places from the decimal to the end of the original number. In 5.668000 there are 6 places after the decimal. So the exponent is 6 or 10 6
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3) Drop the ending (or beginning) zeros (if any). So 5,668,000 is written as: 5.668x10 6
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Scientific Notation Exponents are often expressed using other notations. 5.668E+6 or 5.668 x 10^6
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Numbers less than 1 will have a negative exponent. A millionth of a second is: 0.000001 sec 1x10 -6 1.0E-6 1.0^-6
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Speed of Light 300,000,000 m/sec
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Example 1 Express the following in scientific notation: 73,822 m= 0.001234 g= 34,532.666 s= 0.447600 m=
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Example 2 Express the following in standard numerical form: 4.75 x 10 -3 m= 8.99 x 10 7 g= 1.44 x 10 1 s= 3.334 x 10 -6 m=
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Factor-Label Method of Unit Conversion Example: Convert 5km to m: NEW UNIT 5km x 1,000m =5,000m km OLD UNIT
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Factor-Label Method of Unit Conversion: Example Example: Convert 7,000m to km 7,000m x 1 km =0.007m = 7x10 -3 km 1,000m
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Problem Solving Method 1) Make a list of: knowns unknowns 2) a) If applicable, make a diagram. b) Write the related formula. c) Substitute the numbers with units and check that the units are uniform. 3) Write the answer with the units.
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Multiplication in Scientific Notation New coefficient= product of coefficients New exponent= sum of exponents Perform the following calculations: (9 x 10 5 )m· ( 7 x 10 -6 )m= (3 x 10 3 )m· ( 2. x 10 3 )m=
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Division in Scientific Notation New coefficient= quotient of coefficients New exponent= exponent of numerator -exponent of denominator Perform the following calculations: 12 x 10 2 kg / 8 x 10 2 m 3 = 24 x 10 4 kg/ 6 x 10 2 m 3 =
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Addition and Subtraction in Scientific Notation A. First express each number with the same exponent as the other B. New coefficient=sum of coefficients Perform the following calculations: 3 x 10 4 + 2 x 10 4 = 5 x 10 23 - 1. x 10 22 = 1.5 x 10 6 + 2.7 x 10 3 =
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