Questions: A student sets up the following equation to convert a measurement (The ? stands for a number the student is going to calculate.) Fill in the missing part of this equation. (0.020 mL) * ? = ? dL

A student sets up the following equation to convert a measurement (The ? stands for a number the student is going to calculate.) Fill in the missing part of this equation. (0.020 mL) * ? = ? dL
Transcript text: A student sets up the following equation to convert a measurement (The ? stands for a number the student is going to calculate.) Fill in the missing part of this equation. \[ (0.020 \mathrm{~mL}) \cdot \square=? \mathrm{dL} \]
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Solution

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Solution Steps

Step 1: Understanding the Conversion

To convert from milliliters (mL) to deciliters (dL), we need to understand the relationship between these units.

1 milliliter (mL) is equal to 10310^{-3} liters (L). 1 deciliter (dL) is equal to 10110^{-1} liters (L).

Step 2: Setting Up the Conversion Factor

We need to convert from milliliters to deciliters. First, convert milliliters to liters, then convert liters to deciliters.

1 mL=103 L 1 \text{ mL} = 10^{-3} \text{ L} 1 dL=101 L 1 \text{ dL} = 10^{-1} \text{ L}

Step 3: Calculating the Conversion Factor

To convert from mL to dL, we combine the two conversion factors:

1 mL=103 L 1 \text{ mL} = 10^{-3} \text{ L} 1 L=10 dL 1 \text{ L} = 10 \text{ dL}

Thus,

1 mL=103 L×10 dL/L=102 dL 1 \text{ mL} = 10^{-3} \text{ L} \times 10 \text{ dL/L} = 10^{-2} \text{ dL}

Step 4: Applying the Conversion Factor

Now, we apply this conversion factor to the given measurement:

(0.020 mL)(102 dL/mL)=0.020×102 dL (0.020 \text{ mL}) \cdot (10^{-2} \text{ dL/mL}) = 0.020 \times 10^{-2} \text{ dL}

Final Answer

(0.020 mL)102=0.0002 dL (0.020 \text{ mL}) \cdot 10^{-2} = 0.0002 \text{ dL}

(0.020 mL)102=0.0002 dL \boxed{(0.020 \text{ mL}) \cdot 10^{-2} = 0.0002 \text{ dL}}

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