Certainly! Here is a detailed, step-by-step solution to the question:
### Problem 1: Division of Measurements
[tex]\( \frac{484.00 \, m}{84.83 \, s} = \square \frac{m}{s} \)[/tex]
1. Identify significant figures:
- 484.00 has 5 significant figures.
- 84.83 has 4 significant figures.
2. Perform the division:
[tex]\[
\frac{484.00 \, m}{84.83 \, s} \approx 5.7055 \frac{m}{s}
\][/tex]
3. Determine the significant figures for the result:
- The result should have the same number of significant figures as the measurement with the fewest significant figures, which is 4 significant figures.
Therefore, the result is:
[tex]\[
5.7055 \frac{m}{s}
\][/tex]
### Problem 2: Division of Measurements
[tex]\( \frac{552.2 \, g}{32.87 \, mL} = \square \frac{g}{mL} \)[/tex]
1. Identify significant figures:
- 552.2 has 4 significant figures.
- 32.87 has 4 significant figures.
2. Perform the division:
[tex]\[
\frac{552.2 \, g}{32.87 \, mL} \approx 16.7995 \frac{g}{mL}
\][/tex]
3. Determine the significant figures for the result:
- The result should have the same number of significant figures as the measurement with the fewest significant figures, which is 4 significant figures.
Therefore, the result is:
[tex]\[
16.7995 \frac{g}{mL}
\][/tex]
### Problem 3: Multiplication of Measurements
[tex]\( 20.9476 \frac{mol}{L} \times 26 \, L = \square \, mol \)[/tex]
1. Identify significant figures:
- 20.9476 has 6 significant figures.
- 26 has 2 significant figures.
2. Perform the multiplication:
[tex]\[
20.9476 \frac{mol}{L} \times 26 \, L \approx 544.64 \, mol
\][/tex]
3. Determine the significant figures for the result:
- The result should have the same number of significant figures as the measurement with the fewest significant figures, which is 2 significant figures.
Therefore, the result is:
[tex]\[
544.64 \, mol
\][/tex]
