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Scientific Measurements SI Units Significant Figures

SI Units Measurement system universal to scientists. Measurement standards (base vs. derived) Base unit— Quantity we can MEASURE Derived unit-- Quantity provided by CALCULATION

SI Units (cont.) Base Mass = kilogram (kg) Length = Meter (m) Time = Second (s) Temperature = Kelvin (°K) Derived Volume = m 3, we will use cm 3 /ml ml is NOT an SI unit (1ml = 1cm 3 ) Density = kg/m 3, we will use g/cm 3 or g/ml

Scientific Measurements SI Units Significant Figures ALWAYS WRITE YOUR UNITS ON YOUR ANSWER !!!!----units provide meaning to numbers.

Significant Figures The number of digits in a scientific measurement known with certainty and one estimated or uncertain digit. Method of reporting scientific measurements and calculations.

Significant Figure Basic Rules 1. All numbers that are NOT zeroes are significant Ex. 211, 345 =3 2. All zeroes BETWEEN 2 significant figures are significant. Ex. 2003, 1203 = 4 3. All zeros that are FINAL and PAST a decimal are significant. Ex =2 4. Final zeros are only significant if a DECIMAL POINT is added to the end of the number. Ex. 100 = 1 Ex = 3 Ex = 6

Examples 1) 567 2) ) ) 200

Significant Figures: Adding/Subtracting # of digits to RIGHT of decimal = # of digits RIGHT of decimal from number with the LEAST digits. Ex kg kg = 75.3 kg Ex g – g = g

Significant Figures: Multiplying/Dividing # of significant figures = # of significant figures in number with LEAST significant figures. Ex / 3.1 = ~ 3.9 Ex * 1.23 = ~ 56.2

Significant Figure Practice---If Necessary 1) 9006) ) 10207) ) ) ) ) ) ) g / 4.13 cm 3 = 11) = 12) 2.0 * 4.35 = 13) ) ) 3500

Dimensional Analysis

Method of converting one unit to another Conversion factor—ratio relationship between 2 units Write units, BE SURE THEY CANCEL ! ! ! “Where are we starting? Where are we trying to go?”

KNOW 2.54 cm = 1 inch

Example 1: How fast do you have to run? A. Cheetah Speed 70 miles/hr ft/sec. How fast do you have to run? B. 1.95x10 -3 oz to μg

Example 2: Science fiction often uses nautical analogies to describe space travel. If the starship U.S.S. Enterprise is traveling at warp factor 1.71, what is its speed in knots? 1.71 Warp = 5.00 times the speed of light Speed of light = 3.00x10 8 m/s 1 knot = 2000 yd/h exactly

Example 3: Apothecaries use the following set of measures in the English system: 20 grains ap = 1 scruple 3 scruples = 1 dram ap 8 dram ap = 1 oz. ap 1 dram ap = 3.888g What is the mass of 1 scruple in grams?

Conversion Factors: In Detail = 1 value 12 inches = 1 ft cm = 1 inch 5280 ft. = 1 mile SO (12 inches = 1 ft.) 3 = 1 3 = 1 same conversion factor

In Detail Cont. Use same conversion factor but raise the factor to the correct power for conversion. Cubic inches to ft 3 (12 inches = 1 ft) 3 When converting between squared and cubic units (m 2 to cm 2 /m 3 to cm 3 )

Example 4: Volume of 2.56 cm 3 convert to m 3

Example 5: BMI is a measurement to determine if a person is obese. A BMI > 25 is considered overweight. Calculate the BMI for a 100 lb person with a height of 52 inches. Is this person overweight? Hint: Do conversion factors FIRST, then cancel units

Temperature Conversions °F = 1.8 (T °C ) + 32 °K = T °C

Homework Read pp Problems pp. 29 #37, 39-41, 42(b,c), 47, 49-50, 53