In this review, I will demonstrate three different methods to solve dosage calculation problems: dimensional analysis, the desired over have method, and ratio and proportion. After reviewing this information, don’t forget to access the free series on nursing school dosage calculations.
Let’s start by examining the practice problem that we will utilize to implement these three methods:
The provider orders 2,000 milligrams (mg) to be administered intravenously (IV) daily. You have a vial containing 4 grams (g) per 2 milliliters (ml). The question is, how many milliliters per dose should you administer?
To solve this, you need to determine how many milliliters (mL) correspond to the 2,000 mg dose ordered. Let’s explore how to solve this using each method:
Dimensional Analysis
This method uses conversion factors to adjust units and eliminate any unwanted units until the desired unit is achieved, which in this case is milliliters per dose. Typically, conversion factors are presented as fractions, and you perform a continuous calculation to arrive at the answer.
Begin with the ordered dose of 2,000 mg, which represents one dose. Convert milligrams to grams using the conversion factor: 1 gram = 1,000 milligrams. Thus, 2,000 mg converts to 2 grams. Next, refer to the vial information where 4 grams is equivalent to 2 milliliters. Cancel out grams to find the milliliters per dose. By multiplying across the top and bottom of your fractions and dividing, you find that the result is 1 milliliter per dose.
Desired Over Have Method
This method requires using the formula: (Desired Dose / Have Dose) x Quantity = X (dose to be given). Substitute the given values into the formula: the desired dose is 2,000 mg, the have dose is 4 grams, and the volume is 2 ml.
To ensure unit consistency so you can solve the problem (remember the desired dose and have dose measurement units must match in order to solve), convert 2,000 mg to grams (which is 2 grams). Perform the division (2/4), then multiply by the quantity (2 ml) to reach the answer: 1 milliliter per dose.
Ratio and Proportion
With this method, you’re going to set up an equation with ratios and solve for a particular part of the ratio that you don’t know. In the end, once you calculate your answer, these ratios will be equal and proportionate to each other.
Ratios are often expressed as fractions. We want to combine a known ratio and an unknown ratio, and this information will come from your problem.
For your known ratio, you create it by putting the dosage you have on hand over the volume you have on hand. This should be equal to the dose ordered, which is the dose that the provider has ordered, over X, which is what you’re solving for. This should be the amount to give.
There are some things I want you to remember about ratio and proportion that you must ensure before you solve the problems. First, make sure that the units of measurement are in the same order and match before cross-multiplying, as that’s how you solve these problems. For instance, if you have milligrams for the top unit of measurement for the known ratio but grams for the top unit of measurement for the unknown ratio, you must do some converting BEFORE you cross-multiply.
The known ratio is based on the vial: 4 grams per 2 ml. The unknown ratio is the ordered dose over X (the unknown milliliters).
To ensure units are consistent, convert 4 grams to 4,000 mg. Set up the proportion: (4,000 mg / 2 ml) = (2,000 mg / X ml). Cross-multiply to solve for X. You will get 4000x = 4000. Then isolate x by itself. To do this, divide each side by 4000, which causes X to equal 1 milliliter per dose.
In conclusion, all three methods—dimensional analysis, desired over have, and ratio and proportion—yield the same answer: 1 milliliter per dose. Each method requires careful attention to unit conversion and consistency to ensure accurate results.
Lecture on Solving Dosage Calculations
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