Chapter 2
Standards of Measurement

Section 2.1 - Mass and Weight.

Know the difference between mass and weight. We will be dealing with mass, for the most part. What is the standard metric unit for mass? What is the more common American unit? Which is has more mass: one pound or one gram?

Section 2.2 - Measurement and Significant Figures.

• Know the difference between measured numbers and counted or defined numbers.
• Counted and defined numbers are exact values.
• Measured values are never exact. The precision of the measurement is shown by the number of significant figures (digits).
• More significant figures means greater precision.
• Remember, precision has very little to do with accuracy.
• The last significant digit is always estimated. The other digits are known from the measurement.
• Know the rules for significant figures!
• You should be able to look at any number and tell how many significant figures it has.
• Are zeroes in a number significant? What about the zeroes in these numbers: 201, 0.200, 0.201, 0.002, 0.00200, 200.001, 201.10
• How many significant figures are in the above numbers?

Practice determining the number of significant figures in Practice 2.1.

Section 2.3 - Rounding off numbers.

When you measure something, like mass, the instrument always determines the number of significant figures you should write in your result. Modern calculators often confuse the issue by showing you too many digits at the end of your calculation. You need to know how to round numbers that you obtain on your calculator to the appropriate number of significant figures. This section gives the rules for rounding. Important: Don't round off numbers in the middle of a calculation. Wait until the final answer is obtained, then round to the correct number of sig figs.

• If your last non-significant digit is 5 or greater, increase the last significant digit by one and drop the non-significant digits.
• If the last non-significant digit is less than 5, drop all of the non-significant digits.

Section 2.4 - Scientific Notation.

Scientific notation is writing a number as a power of 10. Do Practice 2.3. Think a little about the scales in atoms compared to the scales we normally see here on earth or the scales in the solar system or universe. What sort of exponents are used in each of these "worlds?"

Section 2.5 - Significant Figures in Calculations.

In terms of how it will affect your grade, this is one of the most important sections in the book. In every calculation that you do, every answer that you write on homework, labs, or tests, I'll be checking that you have the correct number of significant digits. Usually, I'll take off a point for "sig-figs" if you get them wrong. Each problem will be a few points in value, depending on its complexity, so that one point for sig-figs could really hurt. Significant figures are important in chemistry and any class or application science, engineering, statistics, or other quantifative endeavour in which you'll be involved. Chemistry teachers, including me, are especially picky about sig-figs, so learn the rules now, and don't plan on forgetting them. I'll remind you, often.

• For multiplication and division, count the sig-figs in each of the terms. The answer will have the same number of sig-figs as the term with the fewest number of sig-figs.
• The rule for addition and subtraction doesn't depend on the total number of sig-figs, but on the number of digits after the decimal point. And, this is important, if the numbers are in scientific notation, they all have to be the same power of 10. Now that answer must be only as precise as the least precise number that you added or subtracted. It can't go any further to the right than the number with the least precision.

Section 2.6 - The Metric System

You'll need to memorize the highlighted prefixes in Table 2.1. Also, you should know which units correspond to each type of measurement.

Section 2.7 - The Measurement of Length

Know at least one conversion between metric and American units for length. (I know this one: 1 inch = 2.54 centimeters.) Practice.

Section 2.8 - Problem Solving

Mastering the art of setting up and solving a word problem in numerical terms is essential to success in this course. Practice the systematic approach to problem solving in this section, even if you can do the problem in your head or get answer by another method.

Section 2.9 - Measurement of Mass

Know at least one conversion between metric and American units for mass. (I know this one: 1 pound = 453.6 grams.) Practice.

Section 2.10 - Measurement of Volume

Know at least one conversion between metric and American units for volume. (I know this one: 1 gallon = 3.785 liters. Another good one to know is the metric-metric conversion: 1 cubic centimeter = 1 milliliter.) Practice.

Section 2.11 - Measurement of Temperature

Know how to apply the conversion equations. Which units give absolute temperature? What does absolute mean? How does heat differ from temperature? (Remember, significant figures count in temperature conversions too.)

Section 2.12 - Density

Practice conversions among mass, volume, and density. What is density? What are the units for density? Remember at least one density unit. (I know this one: grams per milliliter.) What is specific gravity? How does temperature affect density?

Chapter 2 Homework

Chapter 2 Practice Problems and More Practice Problems
Chapter 2 Frequently Asked Questions (FAQ)

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