Chapter 1: Measurements

Introduction

Accurate and reliable measurements are fundamental to chemistry. This chapter introduces the concepts of observations, scientific notation, significant figures, units, and conversions, which are essential for quantitative work in chemistry.

Observations

Types of Observations

Observations are the foundation of scientific inquiry. They can be classified into two main types:

• Qualitative Observations: Describe the quality or character of a substance, such as its physical state, color, or smell. Examples: Liquid vs. solid; metal vs. nonmetal; blue color; pungent odor.

• Quantitative Observations: Involve measurements and deal with the quantity or amount of a substance. Examples: Mass, volume, temperature.

By definition, a quantitative observation is a measurement.

Scientific Notation

Purpose and Format

Scientific notation is used to express very large or very small numbers efficiently, using powers of ten.

• Format: , where a is a number between 1 and 10, and n is an integer (the exponent).

• Examples:

• Moving the Decimal Point: If the decimal point is moved to the left, the exponent is positive. If the decimal point is moved to the right, the exponent is negative. Examples:

Calculations with Scientific Notation

• Addition & Subtraction: Exponents must be the same before performing the operation.

• Multiplication & Division: Exponents are added (for multiplication) or subtracted (for division). Example:

Calculators can perform these operations automatically.

Measurements

Parts of a Measurement

Every measurement consists of three parts:

• Value: The magnitude of the measurement.

• Unit: Specifies the scale (e.g., grams, meters).

• Uncertainty: Indicates the reliability of the measurement.

Example: 35.621 g (where 35.621 is the measured value, g is the unit, and the last digit indicates uncertainty).

Significant Figures

Definition and Rules

Significant figures (sig figs) reflect the precision of a measurement and indicate which digits are meaningful.

• All nonzero digits are significant.

• Interior zeros (zeros between nonzero digits) are significant.

• Trailing zeros (zeros to the right of a nonzero digit) are significant if there is a decimal point.

• Leading zeros (zeros to the left of the first nonzero digit) are not significant; they only locate the decimal point.

• Trailing zeros at the end of a number, but before an implied decimal point, are ambiguous and should be avoided.

Exact Numbers

Definition

Exact numbers are values that are defined or counted, not measured, and have no uncertainty. Significant figures do not apply to exact numbers.

• Examples: 1 foot = 12 inches; 1 hour = 60 minutes; counted items (e.g., 12 eggs).

• Exact numbers have an infinite number of significant figures.

Determining Significant Figures

Examples

Significant Figures in Calculations

Addition and Subtraction Rule

For addition or subtraction, the result should have the same number of decimal places as the measurement with the fewest decimal places.

Multiplication and Division Rule

For multiplication or division, the result should have the same number of significant figures as the measurement with the fewest significant figures.

Rounding

Rules for Rounding

• After completing a calculation, round the final digit to reflect the correct number of significant figures.

• If the digit to be dropped is 1–4, round down.

• If the digit to be dropped is 5–9, round up.

Units of Measurement

SI Units

The International System of Units (SI) is used in science and is based on powers of ten.

Prefix Multipliers

SI units use prefixes to indicate multiples or fractions of base units.

Example: g = 1500 g

Mass and Weight

Definitions

• Mass: The amount of material in an object, independent of location.

• Weight: The force exerted by gravity on an object; depends on location.

• Unit of mass: Kilogram (kg), Gram (g), Milligram (mg)

Length

Definition and Units

• Length: How long an object is.

• SI unit: Meter (m)

• Conversions: 1 m = 100 cm; 1 m = 1000 mm; 1 km = 1000 m

Unit Conversion Factors

Purpose and Use

Unit conversion factors relate different units and are used to convert measurements from one unit to another.

• Exact conversions: No uncertainty; sig figs do not apply. Examples: 12 in = 1 ft; 60 min = 1 hr

• Measured conversions: Have uncertainty; sig figs apply. Examples: 1.09 yd = 1 m (3 sig figs); 1.056 qt = 1 L (4 sig figs)

Conversion factors always come in pairs (e.g., 1 ft/12 in and 12 in/1 ft) but are not interchangeable unless the physical context allows.

Setting Up Conversions

• Start with the known value and units.

• Choose a conversion factor so that units cancel appropriately.

• Multiply by successive conversion factors as needed.

• Cancel units and perform the calculation.

Example: How many inches are in 3.45 yd? (3 sig figs)

Density

Definition and Formula

Density is a physical property defined as mass per unit volume.

• Formula:

• Units: g/cm3, g/mL, kg/m3

• Density can be used as a conversion factor between mass and volume.

Example: A block of aluminum with a volume of 370.146 cm3 and mass of 1000 g has a density: (3 sig figs)

Table: Densities of Common Substances

Additional info: Some density values and conversion factor examples were inferred and clarified for completeness and academic context.