Problem Solving in Chemistry 2.2 & 2.3. What are Significant Digits?

Problem Solvingin

Chemistry

2.2 & 2.3

What are Significant Digits?

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

Significant Digits Can easily be determined using the Atlantic-Pacific rules

Significant Digits

Atlantic-Pacific rules: Decimal Present – count

from the Pacific

Significant Digits

Atlantic-Pacific rules: Decimal Present – count

from the Pacific Find the first non-zero digit Everything to the right is significant

Significant Digits

Atlantic-Pacific rules: Decimal Absent– count

from the Atlantic

Significant Digits

Atlantic-Pacific rules: Decimal Absent– count from

the Atlantic Find the first non-zero digit Everything to the left is significant

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

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

Significant Digits

Special Cases: Counted quantities have an

unlimited number of significant digitsExamples: 10 cars 5,500 apples 1 dozen pencils

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

How are Significant Digits used in problems?

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.


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


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 =


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.


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


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 =

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

Significant Digits

Review:Round the following number to

the specified number of sig. digs.

468,399.172 2 5 8

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

What is Dimensional Analysis?

Dimensional Analysis is a method that uses

cross-cancellation and equality statements to convert from one unit to another.

How is Dimensional Analysis used?

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?


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?


Examples: There are 21 peanut

M&Ms in a 1.74 oz bag. How many would be in a 2.00 lb bag?


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?


Examples: You are driving in Canada.

Your speed reads 55 mi/hr. Their speed limit is 70 km/hr. Are you speeding?


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.)

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Problem Solving in Chemistry 2.2 & 2.3. What are Significant Digits?