Dimensional Analysis Notes

Dimensional Analysis

Dimensional Analysis Method

  • Dimensional Analysis (DA) is used in health care sciences, math, technology, and other sciences to solve mathematical equations.

  • It emphasizes the units of measurement to set up the equation.

  • It is solved using fraction multiplication.

  • It uses clinical ratios and equivalents.

  • It reduces multiple-step calculations into a single equation.

  • Example: mcg=1000 mcg1 mg x 0.5 mg1=500 mcgmcg = \frac{1000 \text{ mcg}}{1 \text{ mg}} \text{ x } \frac{0.5 \text{ mg}}{1} = 500 \text{ mcg}

Advantages of Dimensional Analysis

  • Organized.

  • Quick, simple problem set up.

  • All work is in a single equation.

  • Decreases errors.

  • Able to see all parts of a problem.

  • Early identification of incorrect setup.

  • Conversions are incorporated into the problem.

  • Used in any dosage calculation problem.

  • Utilizes critical thinking skills.

  • Allows recognition of incorrect set up before calculation is carried out.

Steps for Dimensional Analysis

  • Desired units (needed quantity).

  • Conversion factor (fraction form).

  • Given quantity (what is available).

  • Use algebraic formula style for equations.

  • First numerator unit matches the desired unit.

  • Next numerator unit matches previous denominator unit.

  • Cancel unwanted units (matching numerator and denominator).

  • Multiply numerators and denominators.

  • Only wanted units should remain.

  • Example: mL=51 x 21=10 mLmL = \frac{5}{1} \text{ x } \frac{2}{1} = 10 \text{ mL}

Dimensional Analysis Example

  • A medication comes in 0.7 mg tablets. How many mcg are in each tablet?

  • Desired units (mcg) left of equal sign.

  • First numerator unit matches the desired unit.

  • Conversion factor (mcg to mg).

  • Given Quantity: (0.7 mg tablet).

  • Next numerator unit matches previous denominator unit.

  • Cancel unwanted units (matching numerator and denominator).

  • Multiply numerators and denominators.

  • Only wanted units should remain.

  • Example: mcg=1000 mcg1 mg x 0.7 mg1=700 mcgmcg = \frac{1000 \text{ mcg}}{1 \text{ mg}} \text{ x } \frac{0.7 \text{ mg}}{1} = 700 \text{ mcg}

Conversion Factor

  • Conversion factor: A ratio in fraction form used to convert one unit of measurement to equivalent numerical amount in another unit of measurement.

  • Contains both quantity and a unit of measure.

  • Examples:

    • 3 ft1 yard\frac{3 \text{ ft}}{1 \text{ yard}}

    • 250 mg1 tablet\frac{250 \text{ mg}}{1 \text{ tablet}}

    • 1 g1000 mg\frac{1 \text{ g}}{1000 \text{ mg}}

    • 1000 mL1 L\frac{1000 \text{ mL}}{1 \text{ L}}

Estimation and Calculation

  • Estimate the answer before solving.

  • Recheck equation setup before doing math:

    • Are all components entered correctly?

    • Are conversion factors entered correctly?

  • Do the math

    • Diagonally cancel out unwanted units.

    • Multiply the numerators.

    • Then multiply the denominators.

    • Then divide numerator product by the denominator product.

  • Evaluate

    • Does the answer make sense?

  • Example: Tab=1325 x 6501=650325=2 tabsTab = \frac{1}{325} \text{ x } \frac{650}{1} = \frac{650}{325} = 2 \text{ tabs}

  • Faulty data entry and math errors are common sources of incorrect calculations in Dimensional Analysis.

Troubleshooting Tips

  • Avoid using · (dot) for multiplication function.

    • It may be misinterpreted as a decimal (example: 2 · 3 may be read as 2.3 in equation).

    • Use X for multiplication function (2 x 3).

  • Avoid box format.

    • Assumes multiplication function.

    • Missing some elements of DA format.

  • Algebraic format preferred with all components spelled out.

  • Example: The nurse practitioner ordered 0.15 g of a medication. What is the equivalent dose in mg?

    • Incorrect setup: mg=1000 mg1 g x 0.15 g1 dose x 1 mgmg = \frac{1000 \text{ mg}}{1 \text{ g}} \text{ x } \frac{0.15 \text{ g}}{1 \text{ dose}} \text{ x } \frac{1 \text{ mg}}{}

    • Correct setup: mg=1000 mg1 g x 0.15 g1=150 mgmg = \frac{1000 \text{ mg}}{1 \text{ g}} \text{ x } \frac{0.15 \text{ g}}{1} = 150 \text{ mg}

Multiple Conversion Factors

  • Place all individual conversion factors in equation.

    • How many seconds are in 5 hours?

    • seconds=60 seconds1 x 60 minutes1 h x 5 hours1=18,000 secondsseconds = \frac{60 \text{ seconds}}{1} \text{ x } \frac{60 \text{ minutes}}{1 \text{ h}} \text{ x } \frac{5 \text{ hours}}{1} = 18,000 \text{ seconds}

  • Avoid combining information before set up which increases possible error.

    • Example: Parents need to administer 5.5 mL of an oral medication to their child. The medication comes in a 16 oz bottle. How many full doses can be administered?

    • doses=1 dose5.5 mL x 30 mL1 x 161=4805.5=87.2727 (round to 87 doses)doses = \frac{1 \text{ dose}}{5.5 \text{ mL}} \text{ x } \frac{30 \text{ mL}}{1} \text{ x } \frac{16}{1} = \frac{480}{5.5} = 87.2727 \text{ (round to 87 doses)}