Chemistry · General chemistry I · Concept
Dimensional analysis and unit conversion
Use units to choose conversion factors, organize a calculation and check whether the answer makes sense.
Let the requested unit guide the calculation
Before reaching for a formula, write down what you have and what you need. If you have a volume in milliliters and want a mass in grams, you need a relationship that connects those units. Density provides that relationship.
Distinguish a unit conversion from a physical relationship
A unit conversion changes how you express the same quantity: 1 L and 1000 mL are the same volume, so their ratio is equal to one. Density connects two different quantities, mass and volume, for a particular substance under stated conditions. Both can be arranged as factors, but their meanings differ.
Choose the orientation that cancels the unwanted unit
A factor can be written in either direction. Put the unit you want to remove opposite the matching unit already present. Read the units before doing the arithmetic; they often reveal a reversed factor immediately.
What would dividing by density do here?
Volume divided by density would have units mL²/g, not grams. That unit mismatch tells us the arrangement cannot answer this mass question. For a different question—finding volume from a known mass—dividing by density would be appropriate.
Treat exact relationships and measurements differently
The metric relationship 1 L = 1000 mL is exact. A measured density such as 1.20 g/mL has limited precision. In multiplication and division, the least precise measured input determines the significant figures in the reported result; exact conversion numbers do not limit them.
Why write 30.0 instead of 30?
The trailing zero after the decimal point communicates three significant figures. It tells the reader how precisely the measured inputs support the result. Keep extra digits during the calculation and round when reporting the final answer.
Check the units and the size of the answer
Correct units are necessary, but a calculation can have correct units and still contain a wrong number. Estimate as well: at roughly 1 g/mL, 25 mL should have a mass near 25 g. A density of 1.20 g/mL makes 30.0 g reasonable. A result of 30,000 g would call for another look.
Common mistakes
- Multiplying by a factor that repeats the unwanted unit instead of canceling it.
- Rounding intermediate results unnecessarily.
- Treating an exact metric conversion as a measured value.
Key terms
- Dimensional analysis
- Solving a problem by multiplying by conversion factors so the units cancel, such as grams → moles → grams. Checking that the units come out right also catches setup mistakes.
- Significant figures
- The digits in a measurement that are known reliably, plus one final estimated digit. Exact counts and defined conversions, such as 1 m = 100 cm, never limit the significant figures of an answer.
Work through an example
A sample occupies 25.0 mL and has density 1.20 g/mL. What is its mass?
Find mass from volume and density →Sources and scope
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Try in the workspace
Open the example inputs, change a value and keep a useful result on your board.
Build the factor chain Open the calculation in Math Open worked example on a board Conversion factorsYour existing work stays on this device. Examples open as editable copies.