https://file.aiquickdraw.com/mathbot/file/1726114171300xcn1zxaa.jpg

Let's break down the problem from the image and find the missing part of the equation.

We are given the equation:
\[
-3.0 \times 10^4 \, \frac{\mu g}{dL} \cdot \text{(Missing Value)} = ? \, \frac{g}{mL}
\]

### Understanding the units:

1. **\(\mu g\) to \(g\)** conversion:
   - \(1 \, g = 10^6 \, \mu g\), meaning we need to multiply by \(10^{-6}\) to convert micrograms to grams.
   
2. **\(dL\) to \(mL\)** conversion:
   - \(1 \, dL = 100 \, mL\), so we need to divide by 100 (i.e., multiply by \(10^{-1}\)) to convert deciliters to milliliters.

### The missing factor in the equation:
To convert from \(\frac{\mu g}{dL}\) to \(\frac{g}{mL}\), the missing value must combine both unit conversions. Therefore, the missing factor is:
\[
\left( \frac{1 \, g}{10^6 \, \mu g} \right) \cdot \left( \frac{10 \, dL}{1 \, mL} \right)
\]
Simplifying this, the missing value becomes:
\[
\frac{10^{-5}}{1} = 10^{-5}
\]

Thus, the missing part of the equation is \(10^{-5}\).

Would you like further details or have any questions?

Here are 5 related questions:
1. What is the relation between micrograms and grams in scientific notation?
2. How do we convert deciliters to milliliters?
3. What role does unit conversion play in solving this type of problem?
4. Can this method be applied to other conversions, like kilograms to milligrams?
5. How can we handle complex conversions involving multiple units?

**Tip:** Always keep track of unit conversions when multiplying or dividing quantities to avoid errors.

A student sets up the following equation to convert a measurement: -3.0 × 10^4 (μg/dL) = ? (g/mL). What is the missing part of this equation?

Learn how to convert micrograms per deciliter (μg/dL) to grams per milliliter (g/mL) using scientific notation and unit conversion principles. This problem involves understanding unit conversions and handling scientific notation. Ideal for students in Grades 9-12.

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