Question

multiply or divide the following measurements. be sure each answer you enter contains the correct number of significant digits.
$\frac{20.9476 \text{mol}}{\text{l}} \times 33. \text{l} = \square \text{mol}$
$\frac{2.09476 \text{g}}{\text{ml}} \times 3.75 \text{ml} = \square \text{g}$
$472.32 \text{m} \div 0.87 \text{s} = \square \frac{\text{m}}{\text{s}}$

Explanation:

First Calculation: $\boldsymbol{\frac{20.9476\ \text{mol}}{L} \times 33.\ L}$

Step1: Multiply the values

Multiply the numerical part and the units. The $L$ in the denominator and the $L$ in the multiplier will cancel out, leaving $\text{mol}$.
$20.9476 \times 33. = 691.2708$

Step2: Consider significant figures

The number $33.$ has two significant figures, and $20.9476$ has five. When multiplying, the result should have two significant figures (from $33.$). Rounding $691.2708$ to two significant figures gives $690$ (or $6.9 \times 10^2$). But wait, $33.$ could be considered as two significant figures (the decimal indicates that the trailing zero is significant? Wait, no, $33.$ is two significant figures (the dot is maybe a typo, but assuming $33.$ is two sig figs). Wait, actually, $33.$ might be intended to have two significant figures. So $20.9476 \times 33. = 20.9476 \times 33 = 691.2708$. Rounding to two significant figures: $6.9 \times 10^2$ or $690$. But maybe the $33.$ is three significant figures? Wait, the original problem: $33.\ L$ – the decimal after 33 might mean that it's two significant figures (the 3 and 3, with the decimal indicating that the zero is not present, so two sig figs). So $20.9476 \times 33. = 691.2708 \approx 690$ (two sig figs) or if $33.$ is three sig figs (3,3, and the decimal is a typo, and it's 33.0), then three sig figs. But the problem says "correct number of significant digits". Let's check the original numbers: $20.9476$ has five, $33.$ has two (the decimal is maybe to show that it's exact? No, in measurements, $33.$ is two sig figs). So $20.9476 \times 33. = 691.2708 \approx 690$ (two sig figs) or $6.9 \times 10^2$. But maybe the problem expects us to just multiply without worrying about sig figs first. Wait, maybe the $33.$ is 33.0 (three sig figs). Let's recalculate: $20.9476 \times 33. = 20.9476 \times 33 = 691.2708$. If we take 33. as two sig figs, then 690 (or 6.9×10²). If 33. is three, then 691. But the problem says "each answer you enter contains the correct number of significant digits". Let's see the other problems: the second one has 3.75 (three sig figs), the third has 472.32 (five) and 0.87 (two). So maybe 33. is two sig figs. So first answer: $\boldsymbol{690\ \text{mol}}$ (or $6.9 \times 10^2\ \text{mol}$)

Second Calculation: $\boldsymbol{\frac{2.09476\ \text{g}}{mL} \times 3.75\ \text{mL}}$

Step1: Multiply the values

The $mL$ in the denominator and the $mL$ in the multiplier cancel out, leaving $\text{g}$. Multiply the numerical part: $2.09476 \times 3.75$.
$2.09476 \times 3.75 = 7.85535$

Step2: Consider significant figures

$3.75$ has three significant figures, $2.09476$ has six. The result should have three significant figures. Rounding $7.85535$ to three significant figures gives $7.86$.
So the answer is $\boldsymbol{7.86\ \text{g}}$

Third Calculation: $\boldsymbol{472.32\ \text{m} \div 0.87\ \text{s}}$

Step1: Divide the values

Divide the numerical part: $472.32 \div 0.87$.
$472.32 \div 0.87 = 542.8965517...$

Step2: Consider significant figures

$0.87$ has two significant figures, $472.32$ has five. The result should have two significant figures. Rounding $542.8965517$ to two significant figures gives $540$ (or $5.4 \times 10^2$). Wait, $0.87$ is two sig figs, so $472.32 \div 0.87 \approx 540$ (two sig figs) or $5.4 \times 10^2$. But let's check the division: $472.32 \div 0.87 = 542.896...$ Rounding to two significant figures: $540$ (since the first two significant figures are 5 and 4, the next digit is 2, which is less than 5, so we keep 540). Alternatively, $5.4 \times 10^2$.
So the answer is $\boldsymbol{540\ \frac{\text{m}}{\text{s}}}$ (or $5.4 \times 10^2\ \frac{\text{m}}{\text{s}}$)

Answer:

s:

1. $\frac{20.9476\ \text{mol}}{L} \times 33.\ L = \boldsymbol{690\ \text{mol}}$ (or $6.9 \times 10^2\ \text{mol}$)
2. $\frac{2.09476\ \text{g}}{mL} \times 3.75\ \text{mL} = \boldsymbol{7.86\ \text{g}}$
3. $472.32\ \text{m} \div 0.87\ \text{s} = \boldsymbol{540\ \frac{\text{m}}{\text{s}}}$ (or $5.4 \times 10^2\ \frac{\text{m}}{\text{s}}$)

(Note: The significant figure handling might vary slightly depending on interpretation of the original numbers, but the above is a standard approach.)