The thin outer layer of Earth, called the crust, contains only 0.50 percent of the Earth's total mass and yet is the source of almost all the elements (the atmosphere provides elements such as oxygen, nitrogen, and a few other gases). Silicon ( Si ) is the second most abundant element in the Earth's crust ( 27.2 percent by mass). Calculate the mass of silicon in kilograms in Earth's crust. Round your answer to 2 significant digits. (The mass of Earth is \( 5.9 \times 10^{21} \) tons. 1 ton \( =2000 \mathrm{lb}, 1 \mathrm{lb}=453.6 \mathrm{~g} \) )

To find the mass of silicon in the Earth's crust, we first need the mass of the Earth's crust itself. Since the crust makes up 0.50 percent of the total mass of Earth, we start by calculating this mass. Given the mass of Earth is \( 5.9 \times 10^{21} \) tons, let's convert that into kilograms: 1. Convert tons to pounds: \[ 5.9 \times 10^{21} \text{ tons} \times 2000 \text{ lb/ton} = 1.18 \times 10^{24} \text{ lb} \] 2. Convert pounds to grams: \[ 1.18 \times 10^{24} \text{ lb} \times 453.6 \text{ g/lb} = 5.35 \times 10^{26} \text{ g} \] 3. Convert grams to kilograms: \[ 5.35 \times 10^{26} \text{ g} \div 1000 = 5.35 \times 10^{23} \text{ kg} \] Next, calculate the mass of the crust: \[ \text{Mass of the crust} = 0.005 \times 5.35 \times 10^{23} \text{ kg} = 2.675 \times 10^{21} \text{ kg} \] Now, let's find the mass of silicon in the Earth's crust: \[ \text{Mass of silicon} = 0.272 \times 2.675 \times 10^{21} \text{ kg} \approx 7.27 \times 10^{20} \text{ kg} \] Rounding to two significant digits gives us: \[ \text{Mass of silicon} \approx 7.3 \times 10^{20} \text{ kg} \]