Chapter 2, Problem 81A

Interpretation Introduction

Interpretation:

The cost of $\text{1}\text{g}$ gold needs to be determined, if the cost of gold is $\$560$ per troy ounce.

Concept introduction:

Unit conversion is defined as a multi-step process involving division or multiplication by a numerical factor, rounding and selection of correct number of significant digits.

Answer to Problem 81A

The cost of $\text{1}\text{gram}$ gold is $\text{\$18/g}$.

Explanation of Solution

Given information:

In 1 troy ounce of gold there are $480$ grains also, $1$ grain is equal to $\text{64}\text{.8}\text{milligrams}$.

Calculation: Convert the troy of ounce to grams to determine the cost of gold in $\text{1}\text{g}$. In one troy ounce there are $480$ grains. There are $\text{64}\text{.8}\text{milligrams}$ in 1 grain and there are $\text{1000}\text{milligrams}$ in $\text{1}\text{gram}$. Cost of 1 gram gold can be calculated using the following equation:

$\begin{array}{c}\text{Cost}\text{of}\text{1}\text{g}\text{of}\text{gold}\text{=}\frac{\text{\$560}}{\text{1}\text{troy}\text{ounce}}\text{×}\frac{\text{1}\text{troy}\text{ounce}}{\text{480}\text{grains}}\text{×}\frac{\text{1}\text{grain}}{\text{64}\text{.8}\text{mg}}\text{×}\frac{\text{1000}\text{mg}}{\text{1}\text{g}}\\ =\text{\$18/g}\end{array}$

Hence, the cost of $\text{1}\text{gram}$ gold is $\text{\$18/g}$.

Conclusion

The cost of $\text{1}\text{gram}$ gold is $\text{\$18/g}$.