Transcript Significant Figures

• most scientific advances result from carefully planned
investigation.
Scientific Method
• a logical approach to solving problems.
Observing
• collecting data
• measuring
Testing
• experimenting
• collecting data
Formulating Hypotheses
• analyzing data
• predicting
If data does
not support
hypothesis
Publish Results
• communicating
Theorizing
• constructing models
• predicting
1. Observing
• Making measurements and/or collecting data.
• Data can be either qualitative (descriptive/words) or
quantitative (numerical).
2. Formulating Hypotheses
• A testable statement that serves as the basis for
making predictions.
3. Testing Hypotheses
• Experiments are performed that provide data to
support or refute a hypothesis.
4. Theorizing
• When predictions of the hypothesis are successful,
scientists use models (explanations of how
phenomena occur and how events are related).
• Theories: a generalization that explains body of
facts and phenomena.
Units of Measurement
•
a measurement represents a quantity that has
magnitude, size or amount.
• scientists use SI units to describe measurements.
• there are seven base SI units.
Common SI Prefixes
• prefixes are used to represent quantities that are
larger or smaller than the base unit.
Density
• the ratio of the mass to volume
What is the density of a sample of ore that has a mass of
74.0 g and occupies 20.3 cm3?
Answer: 3.65 g/cm3
Find the volume of a sample of wood that has a mass of
95.1 g and a density of 0.857 g/cm3.
Answer: 111 cm3
Diamond has a density of 3.26 g/cm3. What is the mass
of a diamond that has a volume of 0.35cm3?
Answer: 1.14 g
Using Scientific Measurements
• accuracy: the closeness of
measurements to the correct or
accepted value.
• precision: closeness of a set of
measurements of the same
quantity made in the same way.
Percent Error
• a calculation used to see how accurate your
measurements are.
Error in Measurement
• some error or uncertainty always exists in
any measurement.
due to:
1. Skill of the measurer.
2. Precision of the measuring instruments.
Conversion Factors
• a ratio derived from the equality
between two different units that can
be used to convert from one unit to
the other.
Ex: Convert 0.014 mg to grams.
0.014 mg X (1 g / 1000mg) =
0.000014 g
Ex: Convert 6.2 km to m.
6.2 km X (1000m/1km) = 6200 m
Ex: How many cg are there in 6.25 kg?
6.25 kg X (1000g/1kg) X (100cg/1g)
=
625000 cg
Do Now!!!!!!!!!!!!!!!!!!!!!!!!!!!
Conversion Practice!
Mark McGuire hit 70 homeruns
in the 1998 season. Given that
there are 4 bases with 90 feet
between each base, how many
miles did he run last season from
homeruns? (5,280 feet per mile).
According to current records, Kamato Hongo
of Japan lived to the ripe old age of 116 yrs old!
How old is this women in seconds?
Significant Figures
“Atlantic-Pacific Rule”
1. “P” is for Pacific: meaning the decimal point is PRESENT.
• Count significant figures starting with the first non-zero
digit on the left.
Ex:
0.004703
 4 significant figures
18.00
 4 significant figures
0.0205
 3 significant figures
2. “A” is for Atlantic: meaning the decimal point is
ABSENT.
• Count significant figures starting with the first non-zero
digit on the right.
Ex:
140,000
 2 significant figures
20060
 4 significant figures
1,000,000
 1 significant figures
Rules for Rounding
1. If the number being examined is less than 5, drop it
and all the figures to the right of it.
2. If the number being examined is more than 5, increase
the number to be rounded by 1.
3. If the number being examined is 5, round the number
so that it will be even.
Ex: Round 62.5347 to four significant figures.
Answer: 62.53
Round 3.78721 to three significant figures.
Answer: 3.79
Round 726.835 to five significant figures.
Answer: 726.84
Round 24.8514 to three significant figures.
Answer: 24.8 (since the “8” is even it stays as “8”)
Scientific Notation
•
used to express very large and very small numbers.
•
follows the format:
M x 10n
where 1≤M<10
n is any integer.
Using Significant Figures in Calculations
1. Addition and Subtraction
• Your answer must have the same number of decimals as
the value with the fewest number of decimals.
Ex: 25.1g + 2.03g = ?
Answer: 27.1 g
Ex: 5.44m – 2.6103m = ?
Answer: 2.83m
Ex: 87.3cm – 1.655cm = ?
Answer: 85.6cm
2. Multiplication and Division
• Your answer can have no more significant figures than
are in the measurement with the fewest number of
significant figures.
Ex: 3.05g / 8.47mL = ?
Answer: 0.360 g/mL
Ex: 51.4g / .71cm3 = ?
Answer: 72 g/cm3
Ex: 21.100cm x 0.500cm x 2.90cm = ?
Answer: 30.6 cm3
Chapter 3 Exam will Cover:
 Scientific Method
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Units of Measurement
Density
Conversion Factors
Accuracy and Precision (10% error = good accuracy!)
Significant Figures
Calculating Percent Error
Rounding