NurseSavvy Cheat SheetProcedure
Ratio, Proportion & Dimensional Analysis
Overview
Ratio-proportion and dimensional analysis organize the same dosage relationships in different ways. A proportion equates two ratios, keeps like units aligned, and solves the unknown by cross-multiplication. Dimensional analysis multiplies the ordered amount by one or more equivalence factors, turning each factor so unwanted units cancel. Proportion is compact for a one-step dose. Dimensional analysis makes a multi-conversion chain visible from start to finish and supplies a built-in unit check. Both methods are safe only when the remaining unit matches the requested answer.
Interpretation
A proportion states that two ratios are equal Hallmark
Like units stay in the same positions Hallmark
mg over mL on one side means mg over mL on the otherCross-products of a correct proportion are equal
A conversion factor is an equivalence equal to 1 Hallmark
its direction is chosen by which unit must cancelThe requested unit is the only unit left uncancelled Hallmark
One step favors proportion; multiple conversions favor dimensional analysis
Technique
Worked example: 750 mg ordered, 250 mg per 5 mL available
- Align like units250 mg / 5 mL = 750 mg / x mL
- Cross-multiply250x = 750 × 5
- Solvex = 3,750 ÷ 250 = 15 mL
- Check by dimensional analysis750 mg × 5 mL / 250 mg = 15 mL
- Confirm the unitmg cancels and mL remains
During — Monitoring
Check that like units occupy matching positions in a proportion Hallmark
Strike through every cancelled unit in a dimensional-analysis chain Hallmark
Stop if more than the requested unit remains
the setup is incomplete or a factor is reversedCompare the result with the available quantity before administering Hallmark
Have a second nurse verify high-alert calculations
Patient Teaching
Use the measuring device marked in the unit on the label Hallmark
Read both the number and unit before measuring a dose Hallmark
Ask the pharmacist when prescription and label units differ
Do not substitute a household utensil for a calibrated device
Report Nowescalate immediately
Unit mismatch Hallmark
Like units were not aligned, or the chain ended in a unit the question did not request.Inverted D/H Hallmark
The available strength was placed over the ordered dose, reversing the relationship.Wrong quantity
The container size replaced the quantity tied to the labelled strength.Stopped one step early
An intermediate mass or conversion was reported instead of the requested dose unit.Rounding violation
The chain was rounded before all conversion factors were applied.Unreasonable-magnitude blindness Hallmark
The setup produced an implausible amount, but the result was accepted without comparing it with the supply.Clinical Pearl
Let the units choose the setup: cancel every unit except the one the question asks for.