Chapter 2: Chemistry and Measurements – Units, Significant Figures, and Exact Numbers

Chemistry and Measurements

Introduction

Chemistry relies on precise measurement and clear communication of quantities. Understanding the systems and rules for measurement is foundational for all chemical sciences, including general, organic, and biological chemistry.

Units of Measurement

Metric and SI Systems

Scientists use the metric system and the International System of Units (SI) as standardized systems for measurement. These systems provide consistency for measuring length, volume, mass, temperature, and time.

• Metric System: Used globally for scientific and everyday measurements.

• SI System: A modernized version of the metric system, adopted as the international standard.

Common Units and Their Abbreviations

Measurement	Metric	SI	U.S.
Volume	liter (L)	cubic meter ($m^3$)	quart (qt)
Length	meter (m)	meter (m)	mile (mi), inch (in.)
Mass	gram (g)	kilogram (kg)	pound (lb), ounce (oz)
Temperature	degree Celsius (°C)	kelvin (K)	degree Fahrenheit (°F)
Time	second (s)	second (s)	second (s)

Volume

• Definition: The space occupied by a substance.

• SI Unit: Cubic meter ($m^3$)

• Common Laboratory Units: Liter (L), milliliter (mL)

• Conversions:

  • 1 L = 1000 mL

  • 1 L = 1.06 qt

  • 946 mL = 1 qt

• Measurement Tool: Graduated cylinder

Length

• Definition: The distance between two points.

• SI Unit: Meter (m)

• Common Laboratory Units: Centimeter (cm)

• Conversions:

  • 1 m = 100 cm

  • 1 m = 39.4 in.

  • 1 m = 1.09 yd

  • 2.54 cm = 1 in.

Mass

• Definition: The quantity of matter in an object.

• SI Unit: Kilogram (kg)

• Common Laboratory Units: Gram (g)

• Conversions:

  • 1 kg = 1000 g

  • 1 kg = 2.20 lb

  • 454 g = 1 lb

• Measurement Tool: Electronic balance

Temperature

• Definition: A measure of how hot or cold an object feels.

• SI Unit: Kelvin (K)

• Common Laboratory Unit: Degree Celsius (°C)

• Reference Points:

  • Water freezes at 0°C (32°F)

  • Water boils at 100°C (212°F)

  • Kelvin scale starts at absolute zero (0 K)

Time

• Definition: The ongoing sequence of events taking place.

• SI Unit: Second (s)

• Measurement Tool: Stopwatch

Measured Numbers and Significant Figures

Measured vs. Exact Numbers

• Measured Numbers: Obtained using measuring tools (e.g., ruler, balance). They have a degree of uncertainty.

• Exact Numbers: Obtained by counting or by definition (e.g., 1 kg = 1000 g). They have no uncertainty and an infinite number of significant figures.

Reporting Measurements

• Always report all certain digits plus one estimated digit.

• The estimated digit is the last digit and reflects the precision of the measuring tool.

Example: If a ruler is marked every 1 cm, and the object ends between 4 and 5 cm, you might report 4.5 cm. If the ruler is marked every 0.1 cm, you might report 4.55 cm.

Significant Figures (SFs)

• Definition: All the digits in a measured number, including the estimated digit.

• Rules for Counting Significant Figures:

  • All nonzero digits are significant.

  • Zeros between nonzero digits are significant.

  • Zeros at the end of a decimal number are significant.

  • Zeros at the beginning of a decimal number are not significant.

  • Zeros used as placeholders in large numbers without a decimal point are not significant.

  • Zeros in the coefficient of scientific notation are significant.

Table: Examples of Significant Figures

Measurement	Number of Significant Figures
38.15 cm	4
5.6 ft	2
65.6 lb	3
122.55 m	5
0.440 km	3
0.003 s	1
400,000 m	1
6.0330 × 10-5 L	5

Scientific Notation and Significant Figures

• When writing numbers in scientific notation, only include significant digits in the coefficient.

• Example: 500. g (3 SFs) = $5.00 \times 10^2$ g

Exact Numbers

• Obtained by counting or by definition (e.g., 1 dozen = 12 items, 1 kg = 1000 g).

• Have an infinite number of significant figures and do not limit the number of significant figures in calculations.

Table: Examples of Exact Numbers

Counted Numbers	Defined Equalities (Metric System)	Defined Equalities (U.S. System)
8 doughnuts	1 L = 1000 mL	1 ft = 12 in.
2 baseballs	1 meter = 100 cm	1 qt = 4 cups
5 capsules	1 kg = 1000 g	1 lb = 16 oz

Practice and Application

• Be able to identify whether a number is measured or exact.

• Determine the number of significant figures in any given measurement.

• Convert between metric, SI, and U.S. units using appropriate conversion factors.

Example Problems

• Which of the following is a measurement of mass? 2.6 kg (mass)

• Which is the SI unit for temperature? Kelvin (K)

• How many significant figures in 0.002650 m? 4 SFs (2, 6, 5, and the final 0)

• Is 3 coins a measured or exact number? Exact (counted)