# Chapter 2: Measurement and Calculations

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Chapter 2: Measurement and Calculations
Key concepts: Differentiate between accuracy and precision Apply principles of measurement and significant figures Identify and use the 7 base SI units Name and apply units of measure Perform unit conversions Calculate density Calculate percent error

A. Accuracy vs. Precision
__________ - How close you are to the correct measurement or calculation based on the standard value. PRECISION __________ - How close your measurements are to EACH OTHER The density of aluminum is 2.78 g/cm3. Bob calculates the density three times and gets 2.75, 2.79 and 2.77. AVG: 2.77 Mary calculates the density three times and gets 4.66, 4.67, and 4.65 AVG: 4.66 Holden calculates the density three times and gets 10.25, 6.87, and 1.25 AVG: 6.12 Franz calculates the density three times and gets 2.90, 1.95, 3.44 AVG: 2.76 ACCURATE AND PRECISE PRECISE BUT NOT ACCURATE NIETHER ACCURATE NOR PRECISE ACCURATE BUT NOT PRECISE

B. Measurement Measurement
___________ Something with magnitude, size or amount. Unit ________ - Compares what is measured to a defined size. Metric ________ - Standard system of measure using base 10. SI ________ - The international system of measure that uses only BASE metric units

B. Measurement Quantitative
___________ - Measurements having numbers or size. Qualitative ___________ - Measurement having subjective descriptions Examples: 20 ml of water The reaction bubbles Uma Thurman is blonde 17 g/ml Bulldogs are #1 QUANTITATIVE QUALITATIVE QUALITATIVE QUANTITATIVE QUALITATIVE

C. Significant figures Significant figures indicate the accuracy of the measuring instrument. 2.35 cm Last digit is ESTIMATED Not possible to estimate ; can only estimate between graduations

C. Significant figures Consider the following: What’s the estimate?
This ruler isn’t as accurate as the previous.

C. Significant figures RULE EXAMPLE NO. OF SIG FIGS All nonzero digits and zeros between those digits are significant 1 458 g 40.7 m mm Leading zeros with decimal points are NOT significant; Ending zeros ARE significant with decimal kg m L m Ending zeros left of the decimal point may or may not be significant. Indication needed. kg kg 1.50E4 kg 1.500E4 kg 4 3 7 1 4 6 6 2 5 3 4 Scientific notation is always in sig fig form

C. Significant figures ADDITION AND SUBTRACTION
Answer has as many DECIMAL POINTS as the part with the LEAST decimals. 5.44 – = – = = = 2.83 2.8294 -13.4 -13.42 2.156 0.4 0.358

C. Significant figures MULTIPLICATION AND DIVISION
Answer can only contain as many SIG FIGS as the part with the LEAST sig figs 8.15 x 6 = / 0.87 = 1.2 x 1010 = / 1.50 = 48.9 50 0.29 1200 1212 11.4

Scientific researchers use ONLY these units!
D. SI base units Quantity Unit Abb. Meter m Length Mass Kilogram kg Time Second s Temperature Kelvin K Amount of substance Mole mol E. Current Ampere A Luminous intensity candela cd We won’t Scientific researchers use ONLY these units!

D. SI Base units cont. Derived units – Made up of the base units
Quantity SI Unit Other Units Area Volume Density Speed Energy acres, cm2, ft2 m2 m3 L, gal, cm3 mi/hr, ft/s Calorie, kWhr

E. Unit Conversions – metric prefixes
kilo hecto deca unit deci centi milli king hector Doesn't Usually Drink Chocolate milk EXAMPLES 1 000g = ________ Kg dam = _______ mm 0.23 Kg =________ dg cL = ________ HL 345 DaL = _____ Km Km = ___________ mm

F. Metric conversions – conversion factors
All conversions start with an EQUALITY 1 inch is the same as 2.54 cm 1 inch = 2.54 cm Equalities are turned into conversion factors: Notice the top and bottom are same length!

F. Metric conversions – conversion factors
Convert 34 inches to centimeters 2.54 cm 34 in 86.36 cm 1 in Conversion factor goes here

F. Metric conversions – conversion factors
MULTI- STEP The Bulldogs need 550 cm for a first down. How many yards is that? Plan: cm  inch  feet  yards yd 1 in 1 ft 1 550 cm 6 yards 2.54 cm 12 in 3 ft

F. Metric conversions – conversion factors
A baseball is thrown 60 ft/s. How fast is this in miles/hour? Two things to convert. Do one at a time. 1. ft  miles 2. s  min  hours 1 mi 60 s 60 min 40.91 mi/hr 5280 ft 1 min 1 hr

F. Metric conversions – powered units
Misconception: 1 m = 100 cm but 1m3 ≠ 100 cm3 So, 100x100x100 = 1,000,000 cm3 1 m3 cube 1 m 100 cm If the unit is cubed, you cube the numbers too 1 m (1 m)3 = (100 cm)3 100 cm 1 m 1 m3 = 1,000,000 cm3 100 cm

F. Metric conversions – Volumes
1 ml = 1 cm3 Critical equality: How many liters of fuel does a 300 m3 tank hold? 1 1,000,000 cm3 1 ml L 300 m3 300,000 L 1 1 ml m3 cm3 1,000 Or you could do King Hector

F. Metric conversions - Temperature
180 Fo = ? K Thou shalt use: Work:

G. Density Measure of how tightly packed matter is. More dense

Floating Boat on SF6

Inhaling SF6

G. Density, cont. Units: When measuring LxWxH When measuring
Volume w/ cylinder

G. Density, cont. A liquid has a density of 0.87 g/mL. What volume is occupied by 25 g of the liquid? Given: Work: D = 0.87 g/mL V = ? M = 25 g

H. Percent Error %E = Percent error Va = Accepted value
Ve = Experimental value Example: A student measures the density of a solid as 3.42 g/cc. The solid really has a density of 3.76 g/cc. Calculate the percent error. cc = cubic centimeter Va = 3.76 g/cc Ve = 3.42 g/cc

Watch parentheses here!!!
H. Percent Error, cont Given: Work: Va = 3.76 g/cc Ve = 3.42 g/cc Watch parentheses here!!! %E = %E = 9.04% (sig figs) You can ignore negative signs. A positive percent means the accepted value is higher than your value. A negative means it’s lower.