Chapter 3: Scientific Measurement 3.1: Measurements and Their Uncertainty

I. Scientific Notation Review Try These: 680 = 70.75 = 0.0063 =

II. Using your Calculator A. To perform calculations using scientific notation, you need to use the EE, EXP, or x10x button. B. For 3.5x103, you type 3.5E3 Do not multiply by 10!

III. Error A. Error: Numerical difference between accepted and experimental value B. Percent error: (error/accepted value) x 100

IV. Uncertainty in Measurements A. Measurements always have some amount of uncertainty based on the measuring device 4.36 cm B. Correct measurements always have only one “estimated digit”

V. Identifying Significant Figures Rules: All non-zero #’s [0.005468] Zeros between non-zero [202000] Zeros behind numbers [202.000] (if any decimal is visible) 4. Exactly defined #’s have infinite sig. figs. (ex. 60 minutes in a hour)

VI. Examples Identify which of the numbers in the following values are significant. 2.5000 3000 205 100.0 0.00300 10.

VII. Sig. Figs. In Calculations A. Addition/ Subtraction: round answer to least number of decimals in problem Ex. 12.52 + 1.2 = 13.72 rounded to 13.7 B. Multiplication/ Division: round answer to least number of sig. figs in problem Ex. 10.5 x 5.5 = 57.75 rounded to 58

VIII. Examples Solve the following using significant figures. 4.5 + 3.31 = 5.0 – 2.44 = 100. x 2.0 = 15.00 ÷ 3.0 =

3.2 International System of Units

I. Units of Length A. SI: International System of Units, metric, based on multiples of 10 B. Prefixes indicate size of measurement C. Kilo: 1000, Centi: 1/100, Milli: 1/1000 D. Length: distance, measured in meters (m)

II. Units of A. Volume: space occupied by matter B. Measured in Liters (L) or Meters3 (m3)

III. Units of A. Mass: amount of matter, grams (g) B. Weight: force of gravity on mass

IV. Units of Temperature A. Definition: degree of hotness or coldness B. Temp. Scales I. Celsius (ºC): freezing pt. water at 0°C, boiling pt. at 100°C II. Kelvin (K): 273 degrees more than Celsius, set by absolute zero (-273°C) III. Kelvin = Celsius + 273 Galileo Thermometer

3.3 Conversion Problems

I. Conversion Factors 1 meter = 100 centimeters A. Ratio of equal measurements Ex. 12 inches = 1 foot, 60 seconds = 1 minute B. In metric system one measurement will usually be “root” (meter, gram, liter, etc.) other will have prefix 1 meter = 100 centimeters 1 meter = 100 centimeters

II. Unit Cancellation (“Cross Method”) 1. Make cross 2. Given info. on top left 3. Desired unit at end of cross 4. Starting unit in bottom right (to cancel) 5. Corresponding unit on top right 6. Enter numbers to make conversion factor 7. Multiply #’s on top, divide on bottom

Example Convert 3.75 yards to inches.

III. Complex Units A. Ratio units (Miles/hour, gram/ml) B. Need to change one or both units C. Use bottom of cross for denominator unit D. Ex. 20 miles/hour  miles/minute 20 miles 1 hour = miles/minute 0.3 60 hour minute

V. Example Convert 10.0 kilometers/hour  meters/second.

3.4: Density Floating in the Dead Sea

Determining Density A. Density: mass/volume B. SI units are gram/centimeter3 or gram/milliliter C. Density increases as temp. decreases D. Water is exception, ice less dense than liquid water