At Sandra's clinic, the medications in a. to d. are used. Write the equality and two conversion factors, and identify the numbers as exact or give the number of significant figures for each:
a. The label on a bottle reads 10 mg of furosemide per 1 mL.

Verified step by step guidance

1. Step 1: Write the equality based on the information provided. The label states that there are 10 mg of furosemide per 1 mL. Therefore, the equality is: $10 \mathrm{mg} = 1 \mathrm{mL}$.
2. Step 2: Create the first conversion factor using the equality. The first conversion factor is: $\frac{10 \mathrm{mg}}{1 \mathrm{mL}}$. This means 10 mg of furosemide is equivalent to 1 mL.
3. Step 3: Create the second conversion factor by inverting the equality. The second conversion factor is: $\frac{1 \mathrm{mL}}{10 \mathrm{mg}}$. This means 1 mL contains 10 mg of furosemide.
4. Step 4: Identify the numbers in the equality and conversion factors as exact or approximate. The number '1' in 1 mL is exact because it is defined, while '10' in 10 mg has 2 significant figures because it is a measured quantity.
5. Step 5: Summarize the equality and conversion factors. The equality is $10 \mathrm{mg} = 1 \mathrm{mL}$, the first conversion factor is $\frac{10 \mathrm{mg}}{1 \mathrm{mL}}$, and the second conversion factor is $\frac{1 \mathrm{mL}}{10 \mathrm{mg}}$. The number '1' is exact, and '10' has 2 significant figures.

Key Concepts

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one set of units to another. In this context, it involves converting milligrams (mg) to milliliters (mL) using the information provided on the medication label. Understanding how to perform these conversions is essential for accurate dosing and medication administration.

Significant Figures

Significant figures are the digits in a number that contribute to its precision. This includes all non-zero digits, any zeros between significant digits, and trailing zeros in the decimal portion. In the context of the question, identifying the significant figures in the measurements provided (10 mg and 1 mL) is crucial for ensuring that calculations maintain the appropriate level of precision.

Exact Numbers

Exact numbers are values that are counted or defined and have no uncertainty, such as the number of items in a dozen or defined conversion factors. In this case, the relationship between milligrams and milliliters as stated on the medication label can be considered an exact number, which is important for calculations as it does not limit the number of significant figures in the final result.