Sure, let's solve each measurement operation step by step, ensuring to express the results with the correct number of significant digits.
### 1. [tex]\( 93.4 \frac{ \text{mol} }{ \text{L} } \times 35 \text{ L} \)[/tex]
First, identify the significant digits in each measurement:
- [tex]\( 93.4 \frac{ \text{mol} }{ \text{L} } \)[/tex] has 3 significant digits.
- [tex]\( 35 \text{ L} \)[/tex] has 2 significant digits.
When multiplying, the result should be expressed in the least number of significant digits present in the operands:
[tex]\[
93.4 \times 35 = 3269.0 \text{ mol}
\][/tex]
But since we need to honor the lowest number of significant digits:
[tex]\[
93.4 \times 35 = 3300 \text{ mol}
\][/tex]
### 2. [tex]\( 103.0 \text{ m} \div 0.38 \text{ s} \)[/tex]
First, identify the significant digits in each measurement:
- [tex]\( 103.0 \text{ m} \)[/tex] has 4 significant digits.
- [tex]\( 0.38 \text{ s} \)[/tex] has 2 significant digits.
When dividing, the result should be expressed in the least number of significant digits present in the operands:
[tex]\[
103.0 \div 0.38 = 271.052631578947368421... \text{ m/s}
\][/tex]
But rounding to 2 significant digits:
[tex]\[
103.0 \div 0.38 = 270 \text{ m/s}
\][/tex]
### 3. [tex]\( 0.934 \frac{ \text{mol} }{ \text{L} } \times 3.525 \text{ L} \)[/tex]
First, identify the significant digits in each measurement:
- [tex]\( 0.934 \frac{ \text{mol} }{ \text{L} } \)[/tex] has 3 significant digits.
- [tex]\( 3.525 \text{ L} \)[/tex] has 4 significant digits.
When multiplying, the result should be expressed in the least number of significant digits present in the operands:
[tex]\[
0.934 \times 3.525 = 3.29235 \text{ mol}
\][/tex]
But rounding to 3 significant digits:
[tex]\[
0.934 \times 3.525 = 3.29 \text{ mol}
\][/tex]
To summarize:
[tex]\[
\begin{aligned}
93.4 \frac{ \text{mol} }{ \text{L} } \times 35 \text{ L} & = 3300 \text{ mol} \\
103.0 \text{ m} \div 0.38 \text{ s} & = 271.1 \frac{ \text{m} }{ \text{s} } \\
0.934 \frac{ \text{mol} }{ \text{L} } \times 3.525 \text{ L} & = 3.29 \text{ mol}
\end{aligned}
\][/tex]
