Units and Measurement Physical Science

Math and Units Math- the language of Physics SI Units – International System  MKS Length m Mass kg Time s National Bureau of Standards Prefixes

Base SI Units QuantityUnitSymbol Lengthmeterm Masskilogramkg TemperaturekelvinK Timeseconds Amount of Substance molemol Luminous Intensitycandelacd Electric Currentamperea

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

Limits of Measurement Accuracy and Precision

Example: Evaluate whether the following are precise, accurate or both. Accurate Not Precise Not Accurate Precise Accurate Precise

Accuracy - a measure of how close a measurement is to the true value of whatever is being measured.

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

Precision – a measure of how close a series of measurements are to one another. A measure of how exact a measurement is.

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

Significant Figures The significant figures in a measurement include all of the digits that are known, plus one last digit that is estimated.

Centimeters and Millimeters

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

SI Unit Prefixes for Length NameSymbolAnalogy gigameterGm10 9 megameterMm10 6 kilometerkm10 3 decimeterdm10 -1 centimetercm10 -2 millimetermm10 -3 micrometerμmμm10 -6 nanometernm10 -9 picometerpm10 -12

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

1)Put the decimal after the first non- zero digit. Example: To convert 5,668,000 first write To write a number to scientific notation:

2) To find the exponent count the number of places from the decimal to the end of the original number. In there are 6 places after the decimal. So the exponent is 6 or 10 6

3) Drop the ending (or beginning) zeros (if any). So 5,668,000 is written as: 5.668x10 6

Scientific Notation Exponents are often expressed using other notations E+6 or x 10^6

Numbers less than 1 will have a negative exponent. A millionth of a second is: sec 1x E-6 1.0^-6

Speed of Light 300,000,000 m/sec

Example 1 Express the following in scientific notation: 73,822 m= g= 34, s= m=

Example 2 Express the following in standard numerical form: 4.75 x m= 8.99 x 10 7 g= 1.44 x 10 1 s= x m=

Factor-Label Method of Unit Conversion Example: Convert 5km to m: NEW UNIT 5km x 1,000m =5,000m km OLD UNIT

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

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.

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 )m= (3 x 10 3 )m· ( 2. x 10 3 )m=

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 =

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 x 10 4 = 5 x x = 1.5 x x 10 3 =