To determine the approximate value of the gold in Earth's crust, we need to perform the following steps:
1. Identify the given values:
- The amount of gold in Earth's crust is approximately 120 trillion metric tons. In scientific notation, this can be written as 120 × 10^12 metric tons.
- Each metric ton of gold is worth $9 million. In scientific notation, this is 9 × 10^6 dollars.
2. Calculate the total value:
- The total value (V) of the gold can be calculated by multiplying the amount of gold by the worth per metric ton.
- Using the formula:
[tex]\[
V = (\text{amount of gold}) \times (\text{worth per metric ton})
\][/tex]
Thus,
[tex]\[
V = (120 \times 10^{12}) \times (9 \times 10^6)
\][/tex]
3. Perform the multiplication:
- First, multiply the coefficients (120 and 9):
[tex]\[
120 \times 9 = 1080
\][/tex]
- Next, add the exponents of 10 (since the bases are the same):
[tex]\[
10^{12} \times 10^6 = 10^{18}
\][/tex]
- Combine these results:
[tex]\[
V = 1080 \times 10^{18}
\][/tex]
4. Convert to proper scientific notation:
- Move the decimal point three places to the left in the coefficient to get it between 1 and 10:
[tex]\[
1080 = 1.08 \times 10^3
\][/tex]
- Incorporate this back with the exponent on 10:
[tex]\[
V = 1.08 \times 10^3 \times 10^{18} = 1.08 \times 10^{21}
\][/tex]
So, the approximate value of the gold in Earth's crust is:
[tex]\[
1.08 \times 10^{21} \text{ dollars}
\][/tex]
The correct answer is:
C. 1.08 x 10^21 dollars
