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