There are circumstances where laboratorians must convert a test result or known concentration of a standard from one set of units to another. This process is called dimensional analysis and capitalizes on the concept that any variable like a number or unit can be multiplied or divided by the number 1 without changing the result. This allows for a visual representation of unit conversions in which numerators and denominators can cancel each other out, thus removing original units and replacing them with new ones based on their individual conversions.
Using the top image and the steps below, we will work through an example of converting mg/dL to mmol/L.
- Step 1. 8.2 mg/dL of calcium can be written so that 8.2 mg is the numerator and 1 dL is the denominator.
- Step 2. Since we want to convert mg to mmol and mg is currently a numerator in step 1, and we know that 40.08 mg of calcium is equal to 1 mmol of calcium based on the periodic table provided, we must cancel out the mg of calcium by placing the conversion in the denominator and 1 mmol of calcium in the numerator. This allows for mg to cancel themselves, placing mmol in the numerator position.
- Note: 40.08 g Ca = 1 mole Ca; 1 g = 1000 mg; 1 mole = 1000 mmol.
- Step 3. Since we want to convert deciliters (dL) to Liters (L) and dL is currently a denominator in step 1, and we know that 10 dL equals 1 L, we must cancel out the dL placing the conversion in the numerator and 1 1 L in the denominator. This allows for dL to cancel themselves, placing L in the denominator position.
- Step 4. With mmol being in the numerator and L being in the denominator with no other uncanceled units remaining, the last step is to multiply all numerator values and divide by denominator values. Because multiplying and dividing by 1 does not change the final value, the calculation would look like:
8.2 x 10 / 40.08 = 2.04 mmol/L calcium
Conversion factors such as 1 cm = 10 mm are considered exact and have an infinite number of significant figures. This effectively prevents conversion factors from ever being considered for the number of significant figures when calculating a final value.
