Problem Solving
in
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:






 250.0100 m
207 ft
 627,005 g
0.025 g
610. liters
0.0350 cm
0.07050 milliliters
72,000 L
Significant Digits
Special Cases:

Counted quantities have an
unlimited number of significant
digits
Examples:



10 cars
5,500 apples
1 dozen pencils
Significant Digits
Special Cases:

Exact Conversions have an
unlimited number of
significant digits
Examples:



1 km = 1000 m
1 m = 100 cm
1 ft = 12 in
How are Significant
Digits used in problems?
Significant Digits
in 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.
Significant Digits
in 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
Significant Digits
in 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 =
Significant Digits
in 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.
Significant Digits
in 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
Significant Digits
in 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 =
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 crosscancellation 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?
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?
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?
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?
Dimensional Analysis
Examples:

You are driving in Canada.
Your speed reads 55 mi/hr.
Their speed limit is 70 km/hr.
Are you speeding?
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.)