MEASUREMENT1.4 - Dimensional Analysis
MEASUREMENT
1.4 - Dimensional Analysis
Problem: Express 0.5 mg in µg.
Answer: The process which Inspect the units of the quantities of the calculation.
Step I: Identify the units in the given quantity of measurement.
information given - the units in the given quantity of measurement is in milligram.
Step II: Identify the units that you need to present the answer.
information sought.- the units that is required in the answer is microgram.
Step III: Figure out the conversion factor between milligram, mg, to microgram, µg.
To do that, we go back to the base unit of grams.
1 gram = 1000 milligram .................................
equation (1.4.1)
1 gram = 1,000,000 microgram ......................... equation (1.4.2)
Since both 1000 milligram and 1,000,000 microgram
equal to 1 gram, it follows that
1000 milligram = 1,000,000 microgram ...................
equation (1.4.3)
which reduces to
the conversion factor
1 milligram = 1000 microgram ...............................
equation (1.4.4)
Equation (1.4.4) is the conversion factor for milligram to microgram. We can set up the conversion factor as a fraction. We can either express the fraction with milligram as the numerator and microgram as the denominator (as in (a)) OR express the fraction with microgram as the numerator and milligram as the denominator (as in (b)).
Step IV: Apply the conversion factor to the problem. Follow the basic setup for problem solving.
| information given | 0.5 mg |
| conversion factor | |
| information sought (answer) | ? µg |
(information given) x (conversion factor(s)) = information
sought
We are given a quantity of measurement in units of mg. The answer (or information sought) must have units of µg. In solving for this problem, we need to multiply 0.5 mg with the conversion factor to obtain an answer in microgram. Although there are two ways to express the conversion factor between mg to µg, we must select the conversion factor expressed as in (b) and multiply it with 0.5 milligram.
In the above calculation, the units of milligram cancel and the answer is in microgram. Therefore, 0.5 mg = 500 µg.
What would happen if we selected the conversion factor expressed as in (a)? Notice that the units do not cancel out each other. The answer no longer has units of µg, instead the answer has a unit that does not have any physical sense, mg2/µg. The units alone should send you the signal that the calculation shown below is incorrect!
