Measurements, Uncertainty, And Dimensional Analysis

Master the rules for significant figures, scientific notation, and factor-label conversions.

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Uncertainty in Measurement

Introduction to scientific notation and the definition of significant figures.

Uncertainty in Measurement

Chemistry involves measuring atoms that are incredibly small, and counting them in quantities that are unimaginably large. To handle these extremes, scientists use scientific notation.

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Diagram

Measurements, Uncertainty, and Dimensional Analysis Visual

Needs SI unit tables and a diagram of dimensional analysis.

Clean scientific diagram showing an analytical balance measuring a chemical sample, with a neat professional reference t…

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Arithmetic Rules for Sig Figs

Rules for addition/subtraction and multiplication/division with significant figures.

Arithmetic & Rounding Rules for Sig Figs

Addition & Subtraction

Rule: Match Least Decimal Places

The result cannot have more digits to the right of the decimal point than either of the original numbers.

12.11 + 18.0 = 30.1

Multiplication & Division

Rule: Match Least Sig Figs

The result must be reported with no more sig figs than the measurement with the fewest sig figs.

2.5 \times 1.25 = 3.1

Rounding Off

Rule: Removing trailing digits

If > 5: Increase preceding by 1.
If < 5: Preceding is unchanged.
If exactly 5: Preceding is unchanged if even, increased by 1 if odd.

6.35 \to 6.4

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Worked Example

Example: Sig Fig Operations

Worked example showing addition and multiplication with sig fig rounding.

Example: Sig Fig Operations

Let's apply the rules of significant figures to mathematical operations.

Problem 1. Add $6.65 \times 10^4$ and $8.95 \times 10^3$ .

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Quiz

Practice: Significant Figures

MCQ testing identification of significant figures.

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How many significant figures are present in $0.0025$ ?

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Dimensional Analysis

Introduction to the factor-label method.

Dimensional Analysis

Often in chemistry, you need to convert units from one system to another. The most reliable way to do this is using the factor label method, also known as dimensional analysis.

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Worked Example

Volume Conversion

Worked example converting Liters to cubic meters.

Example: Volume Conversion

Converting squared (area) or cubed (volume) units requires special attention in dimensional analysis.

Problem. A jug contains $2\text{ L}$ of milk. Calculate the volume of the milk in $\text{m}^3$ .

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Worked Example

Example: Sig Fig Operations

Worked example showing addition and multiplication with sig fig rounding.

Example: Sig Fig Operations

Let's apply the rules of significant figures to mathematical operations.

Problem 1. Add $6.65 \times 10^4$ and $8.95 \times 10^3$ .

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Quiz

Practice: Significant Figures

MCQ testing identification of significant figures.

1 / 5

How many significant figures are present in $0.0025$ ?

Worked Example

Volume Conversion

Worked example converting Liters to cubic meters.

Example: Volume Conversion

Converting squared (area) or cubed (volume) units requires special attention in dimensional analysis.

Problem. A jug contains $2\text{ L}$ of milk. Calculate the volume of the milk in $\text{m}^3$ .

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