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Problem Solvingin
Chemistry
2.2 & 2.3
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What are Significant Digits?
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Significant Digits are all of the digits that you
know plus one final digit that is estimated or uncertain.
Example: 500.0 mL of liquid
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Significant Digits Can easily be determined using the Atlantic-Pacific rules
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Significant Digits
Atlantic-Pacific rules: Decimal Present – count
from the Pacific
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Significant Digits
Atlantic-Pacific rules: Decimal Present – count
from the Pacific Find the first non-zero digit Everything to the right is significant
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Significant Digits
Atlantic-Pacific rules: Decimal Absent– count
from the Atlantic
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Significant Digits
Atlantic-Pacific rules: Decimal Absent– count from
the Atlantic Find the first non-zero digit Everything to the left is significant
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Significant Digits
Examples: 115 volts 0.04700 amperes 7.009 grams 0.20 miles 69.72 meters 32.0070 g 4.0 10-3 g
3201 g 4100 mi 4100. mi 4100 mi 4.1 103
mi 200,001
cm 173.4 m
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Significant Digits
Examples: 207 ft 0.025 g 610. liters 0.0350 cm 0.07050 milliliters 72,000 L
250.0100 m 627,005 g
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Significant Digits
Special Cases: Counted quantities have an
unlimited number of significant digitsExamples: 10 cars 5,500 apples 1 dozen pencils
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Significant Digits
Special Cases: Exact Conversions have an
unlimited number of significant digitsExamples: 1 km = 1000 m 1 m = 100 cm 1 ft = 12 in
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How are Significant Digits used in problems?
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Significant Digitsin Math Problems
Multiplication/Division: General Rule: The product
or quotient contains the same number of significant figures as the measurement with the least amount of sig. digs.
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Significant Digitsin Math Problems
Multiplication/Division Rules:
count the sig digs in each number determine which number has the
smallest amount of sig digs do the calculation round off the answer so it has the same
amount of sig digs as the number with the least amount of sig digs
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Significant Digitsin Math Problems
Multiplication/Division Examples:
1.25 g × 8.6 C = 100.00 g 25.0 mL = 500.00 cm × 40.00 cm = 28.00 g 85.2 cm3 =
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Significant Digitsin Math Problems
Addition/Subtraction:General Rule: The sum or
difference contains the same number of decimal places as the measurement with the least number of decimal places.
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Significant Digitsin Math Problems
Addition/Subtraction Rules:
line up the decimal points do the calculation round off the answer so that the
final digit is in the same place as the leftmost uncertain digit
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Significant Digitsin Math Problems
Addition/Subtraction Examples:
38 cm + 5.100 cm + 4.13 cm =
716.55 g – 0.005 g = 8.000 km – 0.54 km = 23.18 m + 6.189 m =
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Significant Digits
Review:What is the number of
significant digits in each of the following?
54.0 kg 0.001 g 1,100 m 12 eggs
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Significant Digits
Review:Round the following number to
the specified number of sig. digs.
468,399.172 2 5 8
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Significant Digits
Review:Perform the following operations.
Express the answers with the correct number of sig. digs.
67.14 kg + 8.2 kg 5.44 m – 2.6103 m 6.9 g/mL × 15.82 mL 94.20 g / 3.16722 mL
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What is Dimensional Analysis?
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Dimensional Analysis is a method that uses
cross-cancellation and equality statements to convert from one unit to another.
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How is Dimensional Analysis used?
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Dimensional Analysis
Examples: In a 5-lb bag of apples,
there are about 20 Michigan apples. How many apples would there be in a 1-lb bag?
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Dimensional Analysis
Examples: Assume that there are 80
apples in a bushel and a tree could produce 32 bushels of apples. How many five-pound bags of apples did the tree produce?
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Dimensional Analysis
Examples: There are 21 peanut
M&Ms in a 1.74 oz bag. How many would be in a 2.00 lb bag?
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Dimensional Analysis
Examples: A production line at the
peanut M&M factory is able to produce 1325 2.00-lb bags every 35.50 minutes. How many M&Ms are produced in an hour?
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Dimensional Analysis
Examples: You are driving in Canada.
Your speed reads 55 mi/hr. Their speed limit is 70 km/hr. Are you speeding?
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Dimensional Analysis
Examples: A person claims to be able to
run at a speed of 3.5 meters per second. Convert this to miles per hour. Do you think the person is lying? (Show your work.)