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Chapter 8: Problem 57

Solve each of the following. (None of these medications should be taken without consulting your own physician.) Cephalexin is an antibiotic that frequently is prescribed in a 500 -mg tablet form. A physician prescribes \(2 \mathrm{~g}\) of cephalexin per day for a patient with a skin sore. How many 500 -mg tablets would have to be taken in order to achieve this daily dosage?

Short Answer

Expert verified
4 tablets

Step by step solution

01

Convert grams to milligrams

First, convert the prescribed dosage from grams to milligrams. Since 1 gram (g) is equal to 1000 milligrams (mg), calculate the dosage in milligrams: \( 2 \text{ g} \times 1000 \frac{\text{mg}}{\text{g}} = 2000 \text{ mg} \)
02

Determine the number of tablets

Each tablet contains 500 mg of cephalexin. To find out how many 500-mg tablets are needed to equal the total daily dosage of 2000 mg, divide the total milligrams required by the amount per tablet: \( \frac{2000 \text{ mg}}{500 \text{ mg/tablet}} = 4 \text{ tablets} \)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

unit conversion
Understanding unit conversion is essential in many fields, especially in medicine where precise dosages are crucial. When given a prescription in units that differ from what you have on hand, you will need to convert those units.

For example, if a patient needs a medication in grams but the tablets available are measured in milligrams, you'll need to convert grams to milligrams:
  • 1 gram (g) equals 1000 milligrams (mg).
  • This is a standard conversion factor used in metric measurements. It's permanent and always the same.

So, to convert grams to milligrams, you multiply the number of grams by 1000.

It's straightforward, but it's a crucial step. Mistakes in this step can lead to incorrect dosages, which could be dangerous.
milligrams to grams
Converting milligrams to grams involves the same principles but in reverse. You need to divide the number of milligrams by 1000 to get the number of grams.

So, if you have a dosage instruction in milligrams but you need to understand it in grams, this conversion is necessary.
  • For example, 2000 mg is converted to grams by dividing by 1000, leading to a result of 2 grams.
  • This is useful for interpreting medical prescriptions and other similar contexts.

The key thing to remember is that 1000 milligrams make up 1 gram. So, no matter the quantity, just apply this rule for conversion.
division
Once you've got your values in the same units, the next main concept is division. This is especially important for determining the number of doses or tablets required.

For instance, after converting 2 grams to 2000 milligrams, you need to understand how many 500-mg tablets will make up 2000 mg. To do this, you divide the total milligrams by the milligrams per tablet:

\[\frac{2000 \text{ mg}}{500 \text{ mg/tablet}}\]
This will equal the number of tablets needed.

In our example, \[\frac{2000 \text{ mg}}{500 \text{ mg/tablet}} = 4 \text{ tablets}. \]
  • Dividing helps us figure out how many parts of a certain size make up a whole.
  • This step ensures you give the correct quantity medicine.

So, be sure to use this concept to determine the number of units required in practical situations.

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