metric system measurements significant figures relationships factor label method
TRANSCRIPT
Metric systemMeasurements Significant figuresRelationships Factor Label Method
SYSTEM OF MEASUREMENTS (SI)
SI Base Units
Derived SI Units
• Combinations of SI base units form derived units.• pressure is measured in kg/m•s2, or pascals
Temperature can be measured using three different units
Conversion between T units
°F = 9/5 °C + 32
OR
°F = 1.8 °C + 32
K = °C + 273.15
T _ _ G _ _ M _ _ K H D _ d c m _ _ μ _ _ n _ _ p _ _ f
1 kg = 1000 g
e i e i e e e e i i a i er g g l c k c n l c n c ma a a o t a i t l r o o t o i i o o
1 cL = 10000 μL or 1x104 μL
1 dm = 1x108 nm1 kJ = 1x105 cJ
Accuracy and Precision
Three students perform the same experiment:
The density of the metal is 4.2845 g/mL
Density values (g/mL)
Joy Taylor Simon
Trial 1 2.4563 2.2846 4.2867
Trial 2 1.6798 2.2798 4.2904
Trial 3 4.7893 2.2901 4.2896
Accuracy and Precision, continuedPercentage Error• Percentage error is calculated by subtracting the
accepted value from the experimental value, dividing the difference by the accepted value, and then multiplying by 100.
Percentage error = Value
experimental-Value
accepted
Valueaccepted
100
• Sample Problem • A student measures the mass and volume of a
substance and calculates its density as 1.40 g/mL. The correct, or accepted, value of the density is 1.30 g/mL. What is the percentage error of the student’s measurement?
Use of Numbers
• Exact numbers– 1 dozen = 12 things for example
• Accuracy – how closely measured values agree with
the correct value• Precision
– how closely individual measurements agree with each other
Use of Numbers• Significant figures
– digits believed to be correct by the person making the measurement
• Exact numbers have an infinite number of significant figures12.000000000000000 = 1 dozenbecause it is an exact number!!!!
Use of NumbersSignificant Figures - Rules
• Leading zeroes are never significant0.000357 has three significant figures
• Trailing zeroes only significant if after decimal point.2.7800 has five significant figures
• Use scientific notation to remove doubt2.40 x 103 has 3 significant figures
2.400x103 has 4 significant figures
2400 has only two significant figures.
Use of Numbers• Imbedded zeroes are always
significant3.0604 has five significant figures
Use of Numbers
• Multiplication & Division rule Easier of the two rules
Product has the smallest number of significant figures of multipliers
5.22 tooff round
21766.5
31.2x
224.4
3.9 tooff round
89648.3
41.x
2783.2
Sample Problem. Calculate the density of a substance with a mass of 14.78 g and a volume of 10.3 mL
Use of Numbers• Addition & Subtraction rule
More subtle than the multiplication rule
Answer contains smallest decimal place of the addends.
6.95 tooff round
9463.6
20.2
423.1
3692.3
6.671 tooff round
6707.6
312.2
7793.8
Sample problem Determine the perimeter of a piece of paper of 27.94 cm long and 6.92 cm wide.
• Sample Problem • How many significant figures are in each of
the following measurements?
• a. 28.6 g• b. 34.40 cm• c. 910 m• d. 0.046 04 L• e. 0.006 700 0 kg
Chapter 2
•Two quantities are directly proportional to each other if dividing one by the other gives a constant value.
Direct Proportion
Chapter 2Direct Proportion
Two quantities are inversely proportional to each other if multiplying one by the other gives a constant value.
Inverse Proportion
Chapter 2Inverse Proportion
The Unit Factor Method
• Simple but important method to get correct answers in word problems.
• Method to change from one set of units to another.
The Unit Factor Method• fractions represent unit factors
1 ft = 12 in becomes or
in 12
ft 1ft 1
in 12
The Unit Factor Method• Example: Express 9.32 meters in micrometers.
The Unit Factor Method• Example: Express 627 milliliters in L.
The Unit Factor Method• Example: Express 45.8 kg in mg.
Density conversions• Example: A 20.0 g irregular solid is introduced
in a graduated cylinder. The level of water inside the graduated cylinder when from 20.0 mL to 23.3 mL. Calculate the density of the solid.
Density conversions• Example: What volume will occupy a liquid
with a mass of 15.7 g and a density of 1.34g/mL?
Density conversions• Example: Calculate the mass of a gas that
occupies 1.5 L and it has a density of 0.00143g/mL?