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INTOCHEMISTRY · GENERAL CHEMISTRY

Dimensional Analysis & Unit Conversions

Convert quantities by canceling units instead of memorizing isolated formulas.

Step-by-step lessonWorked exampleInteractive practiceFree PDF + Word worksheet
Foundations

Learn the concept, then practice it

Convert quantities by canceling units instead of memorizing isolated formulas. Start with the illustrated overview, follow the calculation, and try the questions.

Instructional diagram for Dimensional Analysis & Unit Conversions
Original IntoChemistry teaching diagram · Editable SVG also included in the package
Key relationship

given quantity × (desired unit / given unit) = converted quantity

01

Start with units

A conversion factor is a ratio equal to one. Write the given unit first; place that unit in the denominator of your factor so it cancels.

02

Multiply across the chain

Combine more than one factor when moving between metric prefixes, moles and mass, or length and volume. Unit cancellation should leave only the requested unit.

03

Check the answer

Ask if the size is reasonable. Converting from meters to centimeters should increase the numerical value by 100, not decrease it.

WORKED EXAMPLE

Convert 2.50 km to meters.

2.50 km × (1000 m / 1 km) = 2.50 × 10³ m. The km units cancel and three significant figures are retained.

Final answer: 2.50 × 10³ m
!

Common mistake

A unit conversion changes the numerical value and the unit; it does not change the actual physical amount.

Practice with feedback

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