Questions: A chemical engineer must report the average volume of a certain pollutant produced by the plants under her supervision. Here are the data she has been given by each plant: plant volume of pollutant Cross Creek 49.1 L South Fork 3.050 L New Salem 0.703 L What average volume should the chemical engineer report? Be sure your answer has the correct number of significant digits. L

A chemical engineer must report the average volume of a certain pollutant produced by the plants under her supervision. Here are the data she has been given by each plant: plant volume of pollutant Cross Creek 49.1 L South Fork 3.050 L New Salem 0.703 L What average volume should the chemical engineer report? Be sure your answer has the correct number of significant digits. L
Transcript text: A chemical engineer must report the average volume of a certain pollutant produced by the plants under her supervision. Here are the data she has been given by each plant: \begin{tabular}{|c|r|} \hline plant & \begin{tabular}{c} volume of \\ pollutant \end{tabular} \\ \hline Cross Creek & 49.1 L \\ \hline South Fork & 3.050 L \\ \hline New Salem & 0.703 L \\ \hline \end{tabular} What average volume should the chemical engineer report? Be sure your answer has the correct number of significant digits. $\square$ L $\square$ $\times 10$
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Solution

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Solution Steps

Step 1: Summarize the Given Data

The volumes of pollutants from each plant are:

  • Cross Creek: 49.1 L
  • South Fork: 3.050 L
  • New Salem: 0.703 L
Step 2: Calculate the Total Volume

Add the volumes together: \[ 49.1 + 3.050 + 0.703 = 52.853 \text{ L} \]

Step 3: Calculate the Average Volume

Divide the total volume by the number of plants (3): \[ \frac{52.853}{3} = 17.6177 \text{ L} \]

Step 4: Determine the Correct Number of Significant Digits

The number with the least significant digits in the original data is 49.1 L, which has 3 significant digits. Therefore, the average should also be reported with 3 significant digits.

Step 5: Round the Average Volume

Round 17.6177 to 3 significant digits: \[ 17.6177 \approx 17.6 \text{ L} \]

Final Answer

\[ \boxed{17.6 \text{ L}} \]

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