Let's break this down step by step: --- ### **Step 1: Identify Units to Convert** - The given value is \( 32 \, \frac{\mu g}{dL} \). - We need to convert this to \( \frac{g}{mL} \). **Explanation:** We need to convert micrograms (\( \mu g \)) to grams (g), and deciliters (dL) to milliliters (mL). --- ### **Step 2: Write Conversion Factors** - **Micrograms to grams:** \( 1 \, g = 1,000,000 \, \mu g \) or \( 1 \, \mu g = 1 \times 10^{-6} \, g \) - **Deciliters to milliliters:** \( 1 \, dL = 100 \, mL \) So the conversion factors are: - \( \frac{1 \, g}{1,000,000 \, \mu g} \) - \( \frac{1 \, dL}{100 \, mL} \) (but since dL is in the denominator, we need the reciprocal: \( \frac{100 \, mL}{1 \, dL} \)) **Explanation:** Conversion factors are written so units cancel out correctly. --- ### **Step 3: Set Up the Conversion Equation** \[ 32 \, \frac{\mu g}{dL} \times \frac{1 \, g}{1,000,000 \, \mu g} \times \frac{100 \, mL}{1 \, dL} \] **Explanation:** - The \( \mu g \) cancels with \( \mu g \), and \( dL \) cancels with \( dL \), leaving \( g \) in the numerator and \( mL \) in the denominator. --- ## **Final Answer:** \[ 32 \, \frac{\mu g}{dL} \times \frac{1 \, g}{1,000,000 \, \mu g} \times \frac{100 \, mL}{1 \, dL} \] Or, the missing part in the equation box should be: \[ \boxed{\frac{1 \, g}{1,000,000 \, \mu g} \times \frac{100 \, mL}{1 \, dL}} \]

Let's proceed with the calculation step by step: --- ### **Step 1: Write the expression** Given: \[ 32 \, \frac{\mu g}{dL} \] Conversion factors: \[ \frac{1 \, g}{1,000,000 \, \mu g} \quad \text{and} \quad \frac{100 \, mL}{1 \, dL} \] So, the full calculation: \[ 32 \times \frac{1 \, g}{1,000,000 \, \mu g} \times \frac{100 \, mL}{1 \, dL} \] --- ### **Step 2: Perform the multiplication** First, multiply the numerical parts: \[ 32 \times 100 = 3,200 \] Now, combine the units: \[ \frac{\mu g}{dL} \times \frac{g}{1,000,000 \, \mu g} \times \frac{mL}{dL} \] which simplifies to: \[ 3,200 \times \frac{g \times mL}{1,000,000 \, \mu g \times dL \times dL} \] But since \(\mu g\) cancels with \(\mu g\) numerator, and \(dL\) cancels with \(dL\): \[ \Rightarrow \frac{3,200 \, g \times mL}{1,000,000} \] --- ### **Step 3: Final calculation** Dividing: \[ \frac{3,200}{1,000,000} = 0.0032 \] So, the final concentration in \( g/mL \): \[ 0.0032 \, g/mL \] --- ### **Final Answer:** \[ \boxed{0.0032 \, g/mL} \] This is the converted value from 32 μg/dL to g/mL.