Questions: Multiply or divide the following measurements. Be sure each answer you enter contains the correct number of significant digits. 93 cm × 48 cm = cm^2 688.72 mol ÷ 83.81 L = mol/L 207.6 mol ÷ 61.14 L = mol/L

Multiply or divide the following measurements. Be sure each answer you enter contains the correct number of significant digits. 93 cm × 48 cm = cm^2 688.72 mol ÷ 83.81 L = mol/L 207.6 mol ÷ 61.14 L = mol/L
Transcript text: Multiply or divide the following measurements. Be sure each answer you enter contains the correct number of significant digits. \[ \begin{aligned} 93 . \mathrm{cm} \times 48 . \mathrm{cm} & =\square \mathrm{cm}^{2} \\ 688.72 \mathrm{~mol} \div 83.81 \mathrm{~L} & =\square \frac{\mathrm{mol}}{\mathrm{~L}} \\ 207.6 \mathrm{~mol} \div 61.14 \mathrm{~L} & =\square \frac{\mathrm{mol}}{\mathrm{~L}} \end{aligned} \]
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Solution

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Solution Steps

Step 1: Multiplying Measurements and Counting Significant Digits

For the multiplication \(93 \, \text{cm} \times 48 \, \text{cm}\), we need to determine the number of significant digits in each measurement:

  • \(93 \, \text{cm}\) has 2 significant digits.
  • \(48 \, \text{cm}\) has 2 significant digits.

The result should have the same number of significant digits as the measurement with the fewest significant digits, which is 2.

Calculate the product:

\[ 93 \times 48 = 4464 \]

Round to 2 significant digits:

\[ 4464 \approx 4500 \]

Thus, the result is \(4500 \, \text{cm}^2\).

Step 2: Dividing Measurements and Counting Significant Digits

For the division \(688.72 \, \text{mol} \div 83.81 \, \text{L}\), we determine the number of significant digits:

  • \(688.72 \, \text{mol}\) has 5 significant digits.
  • \(83.81 \, \text{L}\) has 4 significant digits.

The result should have 4 significant digits.

Calculate the quotient:

\[ \frac{688.72}{83.81} \approx 8.2169 \]

Round to 4 significant digits:

\[ 8.2169 \approx 8.217 \]

Thus, the result is \(8.217 \, \frac{\text{mol}}{\text{L}}\).

Step 3: Dividing Measurements and Counting Significant Digits

For the division \(207.6 \, \text{mol} \div 61.14 \, \text{L}\), we determine the number of significant digits:

  • \(207.6 \, \text{mol}\) has 4 significant digits.
  • \(61.14 \, \text{L}\) has 4 significant digits.

The result should have 4 significant digits.

Calculate the quotient:

\[ \frac{207.6}{61.14} \approx 3.3958 \]

Round to 4 significant digits:

\[ 3.3958 \approx 3.396 \]

Thus, the result is \(3.396 \, \frac{\text{mol}}{\text{L}}\).

Final Answer

\[ \begin{aligned} 93 \, \text{cm} \times 48 \, \text{cm} & = \boxed{4500 \, \text{cm}^2} \\ 688.72 \, \text{mol} \div 83.81 \, \text{L} & = \boxed{8.217 \, \frac{\text{mol}}{\text{L}}} \\ 207.6 \, \text{mol} \div 61.14 \, \text{L} & = \boxed{3.396 \, \frac{\text{mol}}{\text{L}}} \end{aligned} \]

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