Chemistry and Measurements: Units, Significant Figures, and Problem Solving

Chemistry and Measurements

Introduction

Chemistry relies on precise measurements to describe matter and its changes. Understanding units, significant figures, and conversion methods is essential for accurate scientific communication and calculations.

Units of Measurement

Metric and SI Units

The International System of Units (SI) is the global standard for scientific measurements. It is based on the metric system and includes units for length, volume, mass, temperature, and time.

• Length: meter (m)

• Volume: cubic meter (m3), commonly liter (L) and milliliter (mL) in chemistry

• Mass: kilogram (kg), commonly gram (g) in chemistry

• Temperature: kelvin (K), Celsius (°C) also widely used

• Time: second (s)

Volume

Volume is the space occupied by a substance. Common units include liters (L) and milliliters (mL). Graduated cylinders are used to measure small volumes in the laboratory.

• 1 L = 1000 mL

• 1 L = 1.06 qt

• 946 mL = 1 qt

Length

Length is measured in meters (m) in both the metric and SI systems. Chemists often use centimeters (cm) for smaller measurements.

• 1 m = 100 cm

• 1 m = 39.4 in.

• 1 m = 1.09 yd

• 2.54 cm = 1 in.

Mass

Mass is a measure of the quantity of material in an object. The SI unit is the kilogram (kg), but grams (g) are often used in chemistry. Mass is measured using an electronic balance.

• 1 kg = 1000 g

• 1 kg = 2.20 lb

• 454 g = 1 lb

Temperature

Temperature measures how hot or cold an object is. It is measured in degrees Celsius (°C) and kelvin (K). Water freezes at 0°C (32°F) and boils at 100°C (212°F). The Kelvin scale starts at absolute zero (0 K).

Time

Time is measured in seconds (s) in both the metric and SI systems. A stopwatch is commonly used to measure time intervals.

Measured Numbers and Significant Figures

Measured vs. Exact Numbers

Measured numbers are obtained using measuring tools and have a degree of uncertainty. Exact numbers are obtained by counting or by definition and have no uncertainty.

• Example of exact number: 2 baseballs

• Example of measured number: 1.9 meters (height)

Reporting Measurements

When reporting a measurement, include all certain digits plus one estimated digit. The estimated digit reflects the uncertainty in the measurement.

• Example: If a ruler is marked in 1 cm increments and the object ends halfway between 4 and 5 cm, report as 4.5 cm.

Significant Figures (SFs)

Significant figures are all the digits in a measured number, including the estimated digit. Rules for determining significant figures:

• All nonzero digits are significant.

• Zeros between nonzero digits are significant.

• Leading zeros in decimals are not significant.

• Trailing zeros in decimals are significant.

• Zeros in large numbers without a decimal are not significant.

Exact Numbers

Exact numbers do not affect the number of significant figures in a calculation. They are obtained by counting or by definition (e.g., 1 kg = 1000 g).

Significant Figures in Calculations

Rounding Off

When performing calculations, round the final answer to the correct number of significant figures:

• If the first digit to be dropped is 4 or less, drop it and all following digits.

• If the first digit to be dropped is 5 or greater, increase the last retained digit by 1.

Multiplication and Division

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

Addition and Subtraction

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

Prefixes and Equalities

Metric Prefixes

Prefixes are used to indicate multiples or fractions of units. Common prefixes include:

• kilo- (k): 1000 times the unit

• centi- (c): 0.01 times the unit

• milli- (m): 0.001 times the unit

• micro- (μ or mc): 0.000001 times the unit

Equalities

An equality shows the relationship between two units that measure the same quantity (e.g., 1 m = 100 cm).

Conversion Factors

Writing Conversion Factors

Any equality can be written as two conversion factors (fractions) that relate the two units. For example, from 1 h = 60 min, the conversion factors are:

• 60 min / 1 h

• 1 h / 60 min

Using Conversion Factors in Problem Solving

To convert from one unit to another, multiply by the appropriate conversion factor so that units cancel, leaving the desired unit.

Density

Definition and Formula

Density compares the mass of an object to its volume. It is calculated as:

$\text{Density} = \frac{\text{Mass}}{\text{Volume}}$

• Units for solids/liquids: g/cm3 or g/mL

• Units for gases: g/L

Applications of Density

Density is used to identify substances and to calculate mass or volume when one of these quantities and the density are known.

Density and Health

Bone density is an important health indicator. Low bone density can indicate osteoporosis, a condition where bones become weak and brittle.

Volume Displacement

The volume of an irregular solid can be determined by the amount of water it displaces in a graduated cylinder. The density can then be calculated using the measured mass and displaced volume.

Summary Table: Common Units and Relationships

Quantity	SI Unit	Common Metric Units	Relationships
Length	meter (m)	centimeter (cm), millimeter (mm)	1 m = 100 cm = 1000 mm
Mass	kilogram (kg)	gram (g), milligram (mg)	1 kg = 1000 g; 1 g = 1000 mg
Volume	cubic meter (m3)	liter (L), milliliter (mL)	1 L = 1000 mL
Time	second (s)	—	—
Temperature	kelvin (K)	degree Celsius (°C)	0°C = 273.15 K