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Scientific Method
• Observation
» Qualitative vs. quantitative data
• Hypothesis
• Experimentation
» Control - standard used for comparison
» Independent variable - what the researcher changes
» Dependent variable – measured result
• Conclusion
• Theory – supported by many experiments
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What is Scientific Notation?
• Scientific notation is a way of expressing really big numbers or really small numbers.
• It is most often used in “scientific” calculations where the analysis must be very precise.
• For very large and very small numbers, scientific notation is more concise.
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Scientific notation consists of two parts:
• A number between 1 and 10
• A power of 10
N x 1 0 x
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Measurements
Number followed by a Unit from a measuring device
SI Units (Le Système international d'unités) – based on the metric system
Time second (s)
Length meter (m)
Mass kilogram (kg)
Temperature Kelvin (K)
Amount of a substance Mole (mol)
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Metric Prefixes
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Conversion factors
• Fractions in which the numerator and denominator are EQUAL quantities expressed in different units
• Dimensional Analysis (Factor-label method)
• A way of solving problems using conversion factors
• By using dimensional analysis the UNITS ensure that you have the conversion factor in the proper arrangement
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Significant Figures
The numbers reported in a measurement are limited by the measuring tool
Significant figures in a measurement include all; the known digits plus one estimated digit
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Which of the two clocks below has the
potential to be the most accurate? Why?
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Comparing Rulers
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Zero as a Measured Number
. l3. . . . I . . . . I4 . . . . I . . . . I5. . cm
What is the length of the line?
First digit 5.?? cm
Second digit 5.0? cm
Last (estimated) digit is 5.00 cm
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Reading a Meterstick
. l2. . . . I . . . . I3 . . . .I . . . . I4. . cm
First digit (known) = 2 2.?? cm
Second digit (known) = 0.7 2.7? cm
Third digit (estimated) between 0.05- 0.07
Length reported = 2.75 cm
or 2.74 cm
or 2.76 cm
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Rules for Significant Figures adapted from Russo's Reliable Rules for Significant Figures
1. All non-zero digits are significant
2. Zeroes between non-zero digits are significant
3. In measurements containing an expressed decimal,
zeros to the right of NON-ZERO digits are significant.
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“Atlantic - Pacific Rule”
Count from the ocean towards the coast starting with the first
nonzero digit, and include all the digits that follow.
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Significant Numbers in Calculations
A calculated answer cannot be more precise than the measuring tool.
A calculated answer must match the least precise measurement.
Significant figures are needed for final answers from
1) adding or subtracting
2) multiplying or dividing
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Adding and Subtracting
The answer has the same number of decimal places as the measurement with the fewest decimal places.
Practice:
a) 2.45 cm + 6.382 cm + 5.8 cm
b) 18.92 mL - 10.42 mL
c) 22.100 g -13 g + 2.93g
14.6 cm
8.50 mL
12 g
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Multiplying and Dividing
Round (or add zeros) to the calculated answer until you have the same number of significant figures as the measurement with the fewest significant figures.
Practice:
a) 4.20 m x 3.21 m x 0.16 m
b) 100.35 g / 90.2 mL
c) (3.28 x 10-5 km) / (4 x 102 s)
2.2 m3
1.11 g/mL
8 x 10-8 km/s
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Temperature Scales
• Fahrenheit
• Celsius
• Kelvin
Anders Celsius
1701-1744
Lord Kelvin
(William Thomson)
1824-1907
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Temperature Scales
Notice that 1 kelvin = 1 degree Celsius
Boiling point
of water
Freezing point
of water
Celsius
100 ˚C
0 ˚C
100˚C
Kelvin
373 K
273 K
100 K
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Calculations Using Temperature
• Generally require temp’s in Kelvin
•K = ˚C + 273
• Body temp = 37 ˚C + 273 = 310 K
• Liquid nitrogen = -196 ˚C + 273 = 77 K
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Temperature Demonstration
1. Obtain three cups of water. One with hot water, one
with ice cold water and one with room temperature
water.
2. Place one hand in the hot water and the other in the
cold water at the same time. Keep hands in the water
for 30-60 minutes.
3. Simultaneously, remove both hands and place them
both in the cup of room temperature water.
What did you observe? Why do you think this happened?
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Derived Units – a combination of 2 or more base units
• Area (length x length)
• Speed (length per time)
• V olume (length x length x length)
• Density (mass per volume)
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DENSITY
Density mass (g)
volume (cm3)
13.6 g/cm3 21.5 g/cm3
Aluminum
2.7 g/cm3
Platinum Mercury
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Learning Check
Osmium is a very dense metal. What is its
density in g/cm3 if 50.00 g of the metal occupies
a volume of 2.22cm3?
1) 2.25 g/cm3
2) 22.5 g/cm3
3) 111 g/cm3
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Solution
2) Placing the mass and volume of the osmium metal into the density setup, we obtain
D = mass = 50.00 g =
volume 2.22 cm3
= 22.522522 g/cm3 = 22.5 g/cm3
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Volume Displacement
A solid displaces a matching volume of water when the solid is placed in water.
33 mL
25 mL
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Learning Check
What is the density (g/cm3) of 48 g of a metal if the metal raises the level of water in a graduated cylinder from 25 mL to 33 mL?
1) 0.2 g/ cm3 2) 6 g/cm3 3) 252 g/cm3
33 mL
25 mL
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Solution
Volume (mL) of water displaced
= 33 mL - 25 mL = 8 mL
Volume of metal (cm3)
= 8 mL x 1 cm3 = 8 cm3
1 mL Density of metal =
mass = 48 g = 6 g/cm3
volume 8 cm3
The answer is: 2) 6 g/cm3
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Three targets with three arrows each to shoot.
Can you hit the bull's-eye?
Both accurate and precise
Precise but not accurate
Neither accurate nor precise
How do they compare?
Can you define accuracy and precision?
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How can someone show the accurate the
measurement?
Calculation of percent error
(Value accepted - Value experimental)
Value accepted
x 100 Percent Error (%) =
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Graphing Data
1. Bar graphs
2. Circle graphs
3. Line graphs
Directly proportional
Inverse proportional