Question

Express the following dosages as ratios. Be sure to include the units of measure and numerical value. An injectable solution that contains \(1,000 \mathrm{mcg}\) in each \(2 \mathrm{~mL}\) ______

Short answer

500 mcg:1 mL

Step-by-step solution

Identify the Given Quantities

The problem provides two quantities: 1000 micrograms ( mmcg) of medication and 2 milliliters ( mmL) of solution. These need to be compared as a ratio.

Write the Ratio with Units

To express the wanted ratio, write the two quantities in the format of a fraction with the first quantity as the numerator and the second as the denominator: \( \frac{1000\ \mathrm{mcg}}{2\ \mathrm{mL}} \).

Simplify the Ratio

Simplify the fraction by dividing both the numerator and the denominator by the greatest common divisor (GCD) of the two numbers. Here, the GCD is 500. Thus, \( \frac{1000\ \mathrm{mcg}}{2\ \mathrm{mL}} = \frac{500\ \mathrm{mcg}}{1\ \mathrm{mL}} \).

Express the Final Ratio

The simplified ratio is written as \( 500 \mathrm{mcg} : 1 \mathrm{mL} \), which indicates that there are 500 micrograms of the drug per 1 milliliter of solution.

Key concepts

Ratios in Medication

Understanding how to express dosages as ratios is crucial in medical practices. Dosage ratios help to clearly communicate the concentration of medication within a solution. When given a problem of expressing an injectable solution ratio, the first step is identifying the quantities involved. For example, in a solution that contains 1000 micrograms (mcg) of medication in 2 milliliters (mL) of solution, you want to determine how these numbers relate as a ratio.
To form a ratio, think of it as creating a relationship between two numbers using a fraction. The first quantity, which is usually the dose (1000 mcg), becomes the numerator, and the second quantity (2 mL) becomes the denominator, written as:

• \( \frac{1000\ mcg}{2\ ml} \).

This clear representation helps ensure medications are administered safely and effectively by accurately conveying the strength of the solution.

Dimensional Analysis

Dimensional analysis is an essential technique to ensure the units of measurements are consistent and logical in calculations involving medications. This method often uses a series of conversions that make calculations clear and accurate.
For example, you start by writing the ratio with units, as we've established:

• \( \frac{1000\ mcg}{2\ ml} \).

Check the units to confirm that they match the desired outcome of the calculation.Conversion factors are based on equivalences, such as 1 mg = 1000 mcg, which can be used to convert micrograms to milligrams if necessary. This ensures clarity and accuracy in medication dosage preparations.
Dimensional analysis helps cross-check calculations, reducing the risk of dosage errors, which is vital in healthcare settings.

Mathematical Simplification

Mathematical simplification in dosage calculation involves reducing fractions to their simplest form. This helps to easily comprehend the concentration levels of medicine in a solution.
In our example, we simplify the given ratio \( \frac{1000\ mcg}{2\ ml} \). You need to find the greatest common divisor (GCD) to simplify both numbers. Here, the GCD is 500:

• Divide 1000 mcg by 500 = 500 mcg.
• Divide 2 mL by 500 = 1 mL.

Hence, the simplified ratio becomes \( 500\ mcg : 1\ ml \). This simplification ensures clarity by expressing the dose more conveniently as 500 mcg per 1 mL. Simplifying ratios ensures that medication dosages are easily understandable and that healthcare professionals can administer them effectively.