Let's break down the problem step by step: **Given:** \[ \left(32 \frac{\mu\text{g}}{dL}\right) \times \left[\text{?}\right] = \frac{g}{mL} \] We need to convert \(32 \frac{\mu\text{g}}{dL}\) to \(\frac{g}{mL}\). --- ### Step 1: Convert micrograms (\(\mu g\)) to grams (g) \[ 1\, \mu g = 1 \times 10^{-6}\, g \] So, \[ \frac{\mu g}{dL} \times \frac{1\, g}{1 \times 10^6\, \mu g} \] --- ### Step 2: Convert deciliters (dL) to milliliters (mL) \[ 1\, dL = 100\, mL \] So, \[ \frac{1\, dL}{100\, mL} \] But since dL is in the denominator, you invert it to multiply: \[ \frac{1\, dL}{100\, mL} = \frac{100\, mL}{1\, dL} \] --- ### Step 3: Combine the conversions Multiply the original value by both conversion factors: \[ \left(32 \frac{\mu g}{dL}\right) \times \left(\frac{1\, g}{1 \times 10^6\, \mu g}\right) \times \left(\frac{1\, dL}{100\, mL}\right) \] --- ### Step 4: Write the final answer The missing part (what you fill in) is: \[ \boxed{ \frac{1\, g}{1 \times 10^6\, \mu g} \times \frac{1\, dL}{100\, mL} } \] --- ### Step 5: Simplify (optional) If you multiply everything together you get: \[ \left(32 \frac{\mu g}{dL}\right) \times \frac{1}{1 \times 10^6} \frac{g}{\mu g} \times \frac{1}{100} \frac{dL}{mL} \] Units cancel to leave \(g/mL\). --- ## **Final Answer** \[ \boxed{ \frac{1\, g}{1 \times 10^6\, \mu g} \times \frac{1\, dL}{100\, mL} } \] This is the fraction (or product of fractions) you multiply by to convert \(32\, \frac{\mu g}{dL}\) to \(\frac{g}{mL}\).