Questions: Counting significant digits when measurements are multiplied or divided Delena Multiply or divide the following measurements. Be sure each answer you enter contains the correct number of significant digits. - 784.14 g / 0.80 mL = □ g/mL - 93.4 mol/L * 53 L = □ mol - 704.66 m / 64.12 s = □ m/s

Solution Steps

1. For $784.14 \mathrm{~g}$ and $0.80 \mathrm{~mL}$:

   • $784.14 \mathrm{~g}$ has 5 significant digits.
   • $0.80 \mathrm{~mL}$ has 2 significant digits.

2. For $93.4 \frac{\mathrm{~mol}}{\mathrm{~L}}$ and $53 \mathrm{~L}$:

   • $93.4 \frac{\mathrm{~mol}}{\mathrm{~L}}$ has 3 significant digits.
   • $53 \mathrm{~L}$ has 2 significant digits.

3. For $704.66 \mathrm{~m}$ and $64.12 \mathrm{~s}$:

   • $704.66 \mathrm{~m}$ has 5 significant digits.
   • $64.12 \mathrm{~s}$ has 4 significant digits.

1. $784.14 \mathrm{~g} \div 0.80 \mathrm{~mL}$: $$\frac{784.14 \mathrm{~g}}{0.80 \mathrm{~mL}} = 980.175 \frac{\mathrm{g}}{\mathrm{~mL}}$$

2. $93.4 \frac{\mathrm{~mol}}{\mathrm{~L}} \times 53 \mathrm{~L}$: $$93.4 \frac{\mathrm{~mol}}{\mathrm{~L}} \times 53 \mathrm{~L} = 4950.2 \mathrm{mol}$$

3. $704.66 \mathrm{~m} \div 64.12 \mathrm{~s}$: $$\frac{704.66 \mathrm{~m}}{64.12 \mathrm{~s}} = 10.987 \frac{\mathrm{m}}{\mathrm{~s}}$$

1. $784.14 \mathrm{~g} \div 0.80 \mathrm{~mL}$:

   • The result should have 2 significant digits (the smallest number of significant digits in the measurements). $$980.175 \rightarrow 980 \frac{\mathrm{g}}{\mathrm{~mL}}$$

2. $93.4 \frac{\mathrm{~mol}}{\mathrm{~L}} \times 53 \mathrm{~L}$:

   • The result should have 2 significant digits. $$4950.2 \rightarrow 5000 \mathrm{mol}$$

3. $704.66 \mathrm{~m} \div 64.12 \mathrm{~s}$:

   • The result should have 4 significant digits. $$10.987 \rightarrow 10.99 \frac{\mathrm{m}}{\mathrm{~s}}$$

Final Answer