Measurement and Problem 2
Solving
Chapter Overview
Chapter 2 introduces the student to a cornerstone of the chemical sciences, the
manipulation of numbers and their associated units. These concepts are very important for the
Lecture Outline
2.1 Measuring Global Temperatures
A. Units are important
B. How many digits do I report?
2.2 Scientific Notation: Writing Large and Small Numbers
Learning Objective: Express very large and very small numbers using scientific notation.
2.3 Scientific Figures: Writing Numbers to Reflect Precision
Learning Objective: Report measured quantities to the right number of digits.
A. How many digits can I report? How many should I report?
B. Certain digits and estimated digits
C. Counting significant figures
2. Interior zeros are significant
4. Trailing zeros before a decimal point are significant
6. Zeros at the end of a number, but to the left of a decimal point, are ambiguous
D. Exact numbers
2.4 Significant Figures in Calculations
Learning Objective: Round numbers to the correct number of significant figures.
Learning Objective: Determine the correct number of significant figures in the results of
1. Result carries as many significant digits as the factor with the fewest significant
digits.
B. Rounding
2. If leftmost dropped digit is 5 or higher, round up
C. Addition and Subtraction
1. Result carries as many decimal places as the quantity with the fewest
decimal places
D. Calculations Involving Both Multiplication/Division and Addition/Subtraction
2. Determine the number of significant figures in intermediate answer
2.5 The Basic Units of Measurement
Learning Objective: Recognize and work with the SI base units of measurement, prefix
multipliers, and derived units.
A. English, metric, SI
B. SI Units
1. Length – m
3. Time – s
C. Prefix Multipliers
2. centi (c) 0.01
4. Mega (M) 1,000,000
D. Derived Units
2. Volume – cm3 or L
2.6 Problem Solving and Unit Conversions
Learning Objective: Convert between units.
2.7 Solving Multistep Conversion Problems
2.8 Units Raised to a Power
2.9 Density
Learning Objective: Calculate the density of a substance.
A. Mass per unit volume
B. Derived unit
C. Can be used as a conversion factor between mass and volume
2.10 Numerical Problem-Solving Strategies and the Solution Map
Chemical Principle Teaching Ideas
Uncertainty
Students generally have a hard time understanding this concept. One method is to refer to
everyday objects that they recognize. For example, you can talk about a coffee cup containing
about 200 mL of coffee. You then ask the students what the new volume would be if you were to
add a drop of water with a volume of 0.05 mL.
Units
Units are very important, and should always be used. Consider giving the students a
measured value in many different units and having them guess what the unit is. Report the
volume of your mug in barrels. What is the volume of the room measured in teaspoons?
Density
Most students understand the concept of density, or how much stuff is packed into a
Skill Builder Solutions
2.2. All the leading zeros are not significant, so we move the decimal over 5 places to give
2.3. Each of the markings on the thermometer represents 1 degree Fahrenheit. We can
2.4. a. 4
b. 3, as leading zeros do not count, but trailing zeros after the decimal do
1.10 0.512 1.301 0.005 0.001
2.6. a. 2.18 + 5.621 + 1.5870 – 1.8 = 7.6. Only one digit past the decimal place is quoted
2.7. a.
3.897 (782.3 451.88) 3.897 330.42 1288− = =
. Four digits are quoted because the
5280 ft
1 lap
3
1 cm
Suggested Demonstrations
Density and Miscibility of Liquids, Chemical Demonstrations 3:233, Shakhashiri, B.Z.
University of Wisconsin Press, 1989.
Guided Inquiry Ideas
Below are a few example questions that students answer in the guided inquiry activities provided
in the Guided Activity Workbook.
How many significant figures are there in the number 0.0051? Underline it/them.
How many significant figures are there in the number 5.00? Underline it/them.