Math
Master the quantitative skills used in science and healthcare: significant figures, unit conversions, proportions, functions, exponents, logarithms, statistics, and introductory calculus.
Dimensional Analysis & Unit Conversion
Sign in to track progressDimensional analysis (also called the factor-label method) is a systematic way to convert one unit to another by multiplying by conversion factors. It is one of the most useful skills in chemistry, physics, and the life sciences.
Purpose of Dimensional Analysis Dimensional analysis ensures units cancel correctly and helps set up complex conversions without memorizing formulas. Every conversion factor is a ratio equal to 1.
Conversion Factors A conversion factor relates two equivalent quantities. For example:
- 1 km = 1000 m, so 1000 m / 1 km = 1
- 1 hour = 60 min, so 60 min / 1 h = 1
Metric System Conversions The metric system uses prefixes based on powers of 10:
kilo (k) = 10³
hecto (h) = 10²
deka (da) = 10¹
base unit = 10⁰
deci (d) = 10⁻¹
centi (c) = 10⁻²
milli (m) = 10⁻³
micro (μ) = 10⁻⁶
nano (n) = 10⁻⁹
Unit Cancellation Write the starting value with its unit, then multiply by conversion factors arranged so unwanted units cancel and the desired unit remains.
Speed Conversions Convert speed units by handling distance and time separately.
Setting Up Dimensional Analysis Correctly
- Identify the given quantity and the desired unit.
- Find conversion factors that connect the units.
- Arrange factors so units cancel.
- Multiply the numerators and divide by the denominators.
- Check that the final unit matches what you need.
Key Points
- Dimensional analysis converts units using ratios equal to 1
- Metric prefixes are powers of 10; move the decimal to convert
- Arrange conversion factors so unwanted units cancel
- Convert speed units by handling distance and time separately
- Always verify the final unit is the one requested