Post on 14-Dec-2015
Steps in the Scientific Method
1. Observations- quantitative- qualitative
2. Formulating hypotheses- possible explanation for
the observation3. Performing experiments
- gathering new information to decide
whether the hypothesis is valid
Outcomes Over the Long-Term
Theory (Model)- A set of tested hypotheses that give an overall explanation of some natural phenomenon.
Natural Law- The same observation applies to many different systems
Law vs. Theory
A law summarizes what happens
A theory (model) is an attempt to explain why it happens.
Einstein's theory of gravity describes gravitational forces in terms of the curvature of spacetime caused by the presence of mass
Nature of Measurement
Part 1 - numberPart 2 - scale (unit)
Examples:20 grams
6.63 x 10-34 Joule·seconds
A measurement is a quantitative observation consisting of 2 parts:
The Fundamental SI Units (le Système International, SI)
Physical Quantity Name Abbreviation
Mass kilogram kg
Length meter m
Time second s
Temperature Kelvin K
Electric Current Ampere A
Amount of Substance mole mol
Luminous Intensity candela cd
SI Units
Celsius & Kelvin
SI Prefixes Common to Chemistry
Prefix Unit Abbr. ExponentMega M 106
Kilo k 103
Deci d 10-1
Centi c 10-2
Milli m 10-3
Micro 10-6
Nano n 10-9
Pico p 10-12
Uncertainty in Measurement
A digit that must be estimated is called uncertain. A measurement always has some degree of uncertainty. Measurements are performed
with instruments No instrument can read to an infinite number of decimal places
Precision and AccuracyAccuracy refers to the agreement of a particular value with the true value.
Precision refers to the degree of agreement among several measurements made in the same manner.
Neither accurate
nor precise
Precise but not accurate
Precise AND
accurate
Types of Error
Random Error (Indeterminate Error) - measurement has an equal probability of being high or low.
Systematic Error (Determinate Error) - Occurs in the same direction each time (high or low), often resulting from poor technique or incorrect calibration. This can result in measurements that are precise, but not accurate.
Rules for Counting Significant Figures - Details
Nonzero integers always count as significant figures.
3456 has 4 sig figs.
Rules for Counting Significant Figures - Details
Zeros- Leading zeros do not count as significant figures.
0.0486 has3 sig figs.
Rules for Counting Significant Figures - Details
Zeros- Captive
zeros always count as significant figures.
16.07 has4 sig figs.
Rules for Counting Significant Figures - Details
ZerosTrailing zeros are significant only if the number contains a decimal point.
9.300 has4 sig figs.
Rules for Counting Significant Figures - Details
Exact numbers have an infinite number of significant figures.
1 inch = 2.54 cm, exactly
Sig Fig Practice #1How many significant figures in each of the following?
1.0070 m 5 sig figs
17.10 kg 4 sig figs
100,890 L 5 sig figs
3.29 x 103 s 3 sig figs
0.0054 cm 2 sig figs
3,200,000 2 sig figs
Rules for Significant Figures in Mathematical Operations
Multiplication and Division: # sig figs in the result equals
the number in the least precise measurement used in the calculation.
6.38 x 2.0 =12.76 13 (2 sig figs)
Sig Fig Practice #2
3.24 m x 7.0 m
Calculation Calculator says: Answer
22.68 m2 23 m2
100.0 g ÷ 23.7 cm3 4.219409283 g/cm3 4.22 g/cm3
0.02 cm x 2.371 cm 0.04742 cm2 0.05 cm2
710 m ÷ 3.0 s 236.6666667 m/s 240 m/s
1818.2 lb x 3.23 ft 5872.786 lb·ft 5870 lb·ft
1.030 g ÷ 2.87 mL 2.9561 g/mL 2.96 g/mL
Rules for Significant Figures in Mathematical Operations
Addition and Subtraction: The number of decimal places in the result equals the number of decimal places in the least precise measurement.
6.8 + 11.934 =18.734 18.7 (3 sig figs)
Sig Fig Practice #3
3.24 m + 7.0 m
Calculation Calculator says: Answer
10.24 m 10.2 m
100.0 g - 23.73 g 76.27 g 76.3 g
0.02 cm + 2.371 cm 2.391 cm 2.39 cm
713.1 L - 3.872 L 709.228 L 709.2 L
1818.2 lb + 3.37 lb 1821.57 lb 1821.6 lb
2.030 mL - 1.870 mL 0.16 mL 0.160 mL
Metric PrefixesKilo- means 1000 of that unit
»1 kilometer (km) =
1000 meters (m)Centi- means 1/100 of that unit
»1 meter (m) = 100
centimeters (cm)
»1 dollar = 100 centsMilli- means 1/1000 of that unit
»1 Liter (L) = 1000
milliliters (mL)
Metric Prefixes
Metric Prefixes
1. 1000 m = 1 ___ a) mm b) km c) dm
2. 0.001 g = 1 ___ a) mg b) kg c) dg
3. 0.1 L = 1 ___ a) mL b) cL c) dL
4. 0.01 m = 1 ___ a) mm b) cm c) dm
Learning Check
Units of Length
? kilometer (km) = 500 meters
(m)
2.5 meter (m) = ? centimeters
(cm)
1 centimeter (cm) = ? millimeter
(mm)
1 nanometer (nm) = 1.0 x 10-9
meter
O—H distance =9.4 x 10-11 m9.4 x 10-9 cm0.094 nm
O—H distance =9.4 x 10-11 m9.4 x 10-9 cm0.094 nm
Learning Check Select the unit you would use to measure 1. Your height
a) millimeters b) meters c) kilometers
2. Your mass a) milligrams b) grams c)
kilograms
3. The distance between two cities a) millimeters b) meters
c) kilometers
4. The width of an arterya) millimeters b) meters
c) kilometers
Conversion Factors
Fractions in which the numerator and denominator are EQUAL quantities expressed in different units
Example: 1 in. = 2.54 cm
Factors: 1 in. and 2.54 cm 2.54 cm 1 in.
Learning Check
Write conversion factors that relate each of the following pairs of units:
1. Liters and mL
2. Hours and minutes
3. Meters and kilometers
How many minutes are in 2.5 hours?
Conversion factor
2.5 hr x 60 min = 150 min 1 hr
cancel
By using dimensional analysis / factor-label method, the UNITS ensure that you have the conversion right side up, and the UNITS are calculated as well as the
numbers!
Steps to Problem SolvingWrite down the given amount. Don’t forget the
units!Multiply by a fraction.Use the fraction as a conversion factor.
Determine if the top or the bottom should be the same unit as the given so that it will cancel.
Put a unit on the opposite side that will be the new unit. If you don’t know a conversion between those units directly, use one that you do know that is a step toward the one you want at the end.
Insert the numbers on the conversion so that the top and the bottom amounts are EQUAL, but in different units.
Multiply and divide the units (Cancel).If the units are not the ones you want for your
answer, make more conversions until you reach that point.
Multiply and divide the numbers. Don’t forget “Please Excuse My Dear Aunt Sally”! (order of operations)
Sample Problem
You have $7.25 in your pocket in quarters. How many quarters do you have?
7.25 dollars 4 quarters 1 dollar
X = 29 quarters
You Try This One!
If Jacob stands on Spencer’s shoulders, they are two and a half yards high. How many feet is that?
Learning Check
A rattlesnake is 2.44 m long. How long is the snake in cm?
a) 2440 cmb) 244 cmc) 24.4 cm
Solution
A rattlesnake is 2.44 m long. How long is the snake in cm?b) 244 cm
2.44 m x 100 cm = 244 cm1 m
Learning Check
How many seconds are in 1.4 days?
Unit plan: days hr min seconds
1.4 days x 24 hr x ?? 1 day
Wait a minute!
What is wrong with the following setup?
1.4 day x 1 day x 60 min x 60 sec 24 hr 1 hr 1 min
English and Metric Conversions
If you know ONE conversion for each type of measurement, you can convert anything!
»Mass: 454 grams = 1 pound
»Length: 2.54 cm = 1 inch
»Volume: 0.946 L = 1 quart
Learning Check
An adult human has 4.65 L of blood. How many gallons of blood is that?
Unit plan: L qt gallon
Equalities:1 quart = 0.946 L 1 gallon = 4 quarts
Your Setup:
Equalities
State the same measurement in two different units
length
10.0 in.
25.4 cm
Steps to Problem Solving
Read problem Identify data Make a unit plan from the initial unit
to the desired unit Select conversion factors Change initial unit to desired unit Cancel units and check Do math on calculator Give an answer using significant
figures
Dealing with Two Units
If your pace on a treadmill is 65 meters per minute, how many seconds will it take for you to walk a distance of 8450 feet?
What about Square and Cubic units? –
Use the conversion factors you already know, but when you square or cube the unit, don’t forget to cube the number also!
Best way: Square or cube the ENITRE conversion factor
Example: Convert 4.3 cm3 to mm3
4.3 cm3 10 mm 3
1 cm ( ) = 4.3 cm3 103 mm3
13 cm3
= 4300 mm3
Learning Check
A Nalgene water bottle holds 1000 cm3 of dihydrogen monoxide (DHMO). How many cubic decimeters is that?
Solution
1000 cm3 1 dm 3
10 cm( ) = 1 dm3
So, a dm3 is the same as a Liter !
A cm3 is the same as a milliliter.