Question

It has been estimated that \(8.0 \times 10^{4}\) tons of gold \((\mathrm{Au})\) have been mined. Assume gold costs $$ 1350\( per troy ounce. What is the total worth of this quantity of gold? \)(1\( troy ounce \)=31.103 \mathrm{~g})$.

Short answer

The total worth is approximately $3.471 trillion.

Step-by-step solution

Convert Tons to Grams

First, we need to convert the total mass of gold from tons to grams. We know that 1 ton is equal to 1,000,000 grams. Therefore, for 80,000 tons of gold, the conversion to grams is calculated as follows: \[ 8.0 \times 10^{4} \text{ tons} \times 1,000,000 \frac{\text{grams}}{\text{ton}} = 8.0 \times 10^{10} \text{ grams} \]

Convert Grams to Troy Ounces

Next, using the fact that 1 troy ounce is equivalent to 31.103 grams, we convert the total grams of gold to troy ounces: \[ \frac{8.0 \times 10^{10} \, \text{grams}}{31.103 \, \text{grams/troy ounce}} \approx 2.571 \times 10^{9} \, \text{troy ounces} \]

Calculate Total Value of Gold

Now we calculate the total financial worth by multiplying the total troy ounces of gold by the price per troy ounce (\(1,350): \[ 2.571 \times 10^{9} \, \text{troy ounces} \times \\)1,350 \/ \text{troy ounce} \approx \$3.471 \times 10^{12} \]

Conclusion

The calculated total worth of all the mined gold, considering its weight and current price, is approximately $3.471 trillion.

Key concepts

Mass Conversion

When dealing with large quantities of gold, it is often necessary to convert between different units of measurement to accurately assess value. One of the primary conversions we need to understand is converting tons to grams. This step is crucial because we generally begin with a mass measured in tons due to the massive scales involved with mined materials.

• 1 ton is equal to 1,000,000 grams.
• For example, if you have 80,000 tons, you multiply by 1,000,000 to get a result of \( 8.0 \times 10^{10} \) grams.

This conversion ensures that we can then proceed to other necessary measurements, such as calculating the troy ounces, which is a standard in the precious metals industry.

Troy Ounce

The troy ounce is the unit of measure most commonly used for precious metals like gold. Unlike the avoirdupois ounce, which is more familiar in daily use, the troy ounce is heavier. In fact, 1 troy ounce equals approximately 31.103 grams rather than the 28.349 grams of an avoirdupois ounce.

• This means when you have a total mass in grams, you need to divide by 31.103 to convert to troy ounces.
• For our example, \( 8.0 \times 10^{10} \) grams of gold is equivalent to roughly \( 2.571 \times 10^{9} \) troy ounces.

This specific unit helps in maintaining consistency and standardization in the valuation process of gold and other precious metals worldwide.

Price Calculation

Once we have the total number of troy ounces, the next step is determining the monetary value of the gold. This is where price calculation comes into play. Gold prices are often quoted per troy ounce, which provides a standard pricing point for transactions.

• In the given problem, gold is priced at $1350 per troy ounce.
• To find the total worth, you multiply the number of troy ounces by the price per troy ounce.

For example, multiplying the \( 2.571 \times 10^{9} \) troy ounces by \( 1350 \) gives you a nice glimpse into the vast financial worth, totaling around \( 3.471 \times 10^{12} \) dollars. This step is crucial for anyone looking to assess the economic value of a substantial gold reserve.

Total Value Estimation

Estimating the total value of a large amount of gold involves combining all previous steps. By calculating both the mass and the value per unit weight, we can generate an estimation of the total worth.

• First, determine the total mass in troy ounces.
• Then, multiply the entire quantity by the current market value per troy ounce.

In our example, the final step would bring us to an estimated worth of approximately \( 3.471 \times 10^{12} \) dollars or $3.471 trillion. This thorough process of converting mass and estimating value is fundamental, especially in industries like jewelry and finance, where accurate portrayal of value is essential.