Units and Measurement Physics Mrs. Coyle International Space Station

It All Starts with a Ruler!!!

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

SI Unit Prefixes - Part I NameSymbolFactor tera-T10 12 giga-G10 9 mega-M10 6 kilo-k10 3 hecto-h10 2 deka-da10 1

SI Unit Prefixes- Part II NameSymbolFactor deci-d10 -1 centi-c10 -2 milli-m10 -3 micro-μ10 -6 nano-n10 -9 pico-p femto-f10 -15

The Seven 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

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

Other Examples: 5.45E+6 or 5.45 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

Factor-Label Method of Unit Conversion Example: Convert 5km to m: Multiply the original measurement by a conversion factor. NEW UNIT 85km x 1,000m = 85,000m 1km OLD UNIT

Factor-Label Method of Unit Conversion: Example Example: Convert 789m to km: 789m x 1km =0.789km= 7.89x10 -1 km 1000m

Convert km/h to m/s km x 1000 m x 1 h___ = 20.83m/s h 1 km 3600 s

Limits of Measurement Accuracy and Precision

Accuracy - a measure of how close a measurement is to the true value of the quantity 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

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

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

Finding the Number of Sig Figs: When the decimal is present, start counting from the left. When the decimal is absent, start counting from the right. Zeroes encountered before a non zero digit do not count.

How many sig figs? x10 4

Sig Figs in Addition/Subtraction Express the result with the same number of decimal places as the number in the operation with the least decimal places. Ex: 2.33 cm cm 5.3 cm (Result is rounded to one decimal place)

Sig Figs in Multiplication/Division Express the answer with the same sig figs as the factor with the least sig figs. Ex: 3.22 cm x 2.0 cm 6.4 cm 2 (Result is rounded to two sig figs)

Counting Numbers Counting numbers have infinite sig figs. Ex: 3 apples

Solving Word Problems Analyze –List knowns and unknowns. –Draw a diagram. –Devise a plan. –Write the math equation to be used. Calculate –If needed, rearrange the equation to solve for the unknown. –Substitute the knowns with units in the equation and express the answer with units. Evaluate –Is the answer reasonable?