Question

multiply or divide the following measurements. be sure each answer you enter contains the correct number of significant digits.
859.4 m ÷ 36.652 s = \boxed{\dfrac{m}{s}}
326.12 g ÷ 0.73 ml = \boxed{\dfrac{g}{ml}}
\dfrac{0.93 g}{ml} × 1.75 ml = \boxed{g}

Explanation:

First Calculation: \( 859.4 \, \text{m} \div 36.652 \, \text{s} \)

Step 1: Perform the division

We divide \( 859.4 \) by \( 36.652 \).
\( 859.4 \div 36.652 \approx 23.45 \)

Step 2: Determine significant figures

The number \( 859.4 \) has 4 significant figures, and \( 36.652 \) has 5 significant figures. When dividing, the result should have the same number of significant figures as the least precise measurement, which is 4. So we round \( 23.45 \) to 4 significant figures.
\( 23.45 \approx 23.45 \) (already 4 significant figures? Wait, \( 859.4 \) is 4 sig figs, \( 36.652 \) is 5. So the result should have 4 sig figs. Let's recalculate more accurately: \( 859.4 \div 36.652 = 23.4475... \). Rounding to 4 sig figs: \( 23.45 \)? Wait, no, 23.45 has 4 sig figs? Wait, 2 (1st), 3 (2nd), 4 (3rd), 5 (4th). Yes. Wait, but maybe I made a mistake. Wait, \( 859.4 \) is 4 sig figs, \( 36.652 \) is 5. So the result should have 4 sig figs. So \( 23.45 \) is 4 sig figs? Wait, 23.45: the first non - zero digit is 2, then 3, 4, 5. So four significant figures. So \( 859.4 \div 36.652\approx23.45 \, \frac{\text{m}}{\text{s}} \) (wait, actually, let's check the division again. \( 36.652\times23 = 842.996 \), \( 859.4 - 842.996 = 16.404 \), \( 16.404\div36.652\approx0.4475 \), so total is \( 23.4475 \), which is approximately \( 23.45 \) when rounded to four significant figures.

Second Calculation: \( 326.12 \, \text{g} \div 0.73 \, \text{mL} \)

Step 1: Perform the division

Divide \( 326.12 \) by \( 0.73 \).
\( 326.12\div0.73\approx446.74 \)

Step 2: Determine significant figures

The number \( 326.12 \) has 5 significant figures, and \( 0.73 \) has 2 significant figures. When dividing, the result should have 2 significant figures. So we round \( 446.74 \) to 2 significant figures.
\( 446.74\approx450 \) (or \( 4.5\times 10^{2} \))? Wait, no. Wait, \( 446.74 \) rounded to 2 significant figures: the first two significant figures are 4 and 4? Wait, no, \( 446.74 \): the first significant figure is 4, the second is 4, the third is 6. Since the third digit is 6 (greater than 5), we round up the second digit. So \( 446.74\approx450 \) (but in scientific notation, \( 4.5\times 10^{2} \)) with 2 significant figures. Wait, but maybe I made a mistake. Wait, \( 0.73 \) has two significant figures, \( 326.12 \) has five. So the result should have two significant figures. So \( 326.12\div0.73 = 446.7397\approx450 \) (or \( 4.5\times 10^{2} \)) \( \frac{\text{g}}{\text{mL}} \)

Third Calculation: \( \frac{0.93 \, \text{g}}{\text{mL}} \times 1.75 \, \text{mL} \)

Step 1: Perform the multiplication

Multiply \( 0.93 \) by \( 1.75 \).
\( 0.93\times1.75 = 1.6275 \)

Step 2: Determine significant figures

The number \( 0.93 \) has 2 significant figures, and \( 1.75 \) has 3 significant figures. When multiplying, the result should have the same number of significant figures as the least precise measurement, which is 2. So we round \( 1.6275 \) to 2 significant figures.
\( 1.6275\approx1.6 \, \text{g} \)

Final Answers:

• \( 859.4 \, \text{m} \div 36.652 \, \text{s} \approx \boldsymbol{23.45 \, \frac{\text{m}}{\text{s}}} \) (or if we consider 4 significant figures correctly, maybe my initial thought was wrong. Wait, \( 859.4 \) is 4 sig figs, \( 36.652 \) is 5. So the result should have 4 sig figs. \( 859.4\div36.652 = 23.4475\approx23.45 \) (4 sig figs).
• \( 326.12 \, \text{g} \div 0.73 \, \text{mL} \approx \boldsymbol{4.5\times 10^{2} \, \frac{\text{g}}{\text{mL}}} \) (2 sig figs)
• \( \frac{0.93 \, \text{g}}{\text{mL}} \times 1.75 \, \text{mL} \approx \boldsymbol{1.6 \, \text{g}} \) (2 sig figs)

(Note: There might be some differences in significant figure rounding depending on the exact rules followed, but the above is a standard approach.)

Answer:

Step 1: Perform the multiplication

Multiply \( 0.93 \) by \( 1.75 \).
\( 0.93\times1.75 = 1.6275 \)

Step 2: Determine significant figures

The number \( 0.93 \) has 2 significant figures, and \( 1.75 \) has 3 significant figures. When multiplying, the result should have the same number of significant figures as the least precise measurement, which is 2. So we round \( 1.6275 \) to 2 significant figures.
\( 1.6275\approx1.6 \, \text{g} \)

Final Answers:

• \( 859.4 \, \text{m} \div 36.652 \, \text{s} \approx \boldsymbol{23.45 \, \frac{\text{m}}{\text{s}}} \) (or if we consider 4 significant figures correctly, maybe my initial thought was wrong. Wait, \( 859.4 \) is 4 sig figs, \( 36.652 \) is 5. So the result should have 4 sig figs. \( 859.4\div36.652 = 23.4475\approx23.45 \) (4 sig figs).
• \( 326.12 \, \text{g} \div 0.73 \, \text{mL} \approx \boldsymbol{4.5\times 10^{2} \, \frac{\text{g}}{\text{mL}}} \) (2 sig figs)
• \( \frac{0.93 \, \text{g}}{\text{mL}} \times 1.75 \, \text{mL} \approx \boldsymbol{1.6 \, \text{g}} \) (2 sig figs)

(Note: There might be some differences in significant figure rounding depending on the exact rules followed, but the above is a standard approach.)