Chapter 6.1, Problem 55E

To determine

To find: how many pounds of potatoes on average were produced for each acre harvested

Answer to Problem 55E

About $4.113\times {10}^4\text{ lb/acre}$ or $\text{41,130 lb/acre}$

Explanation of Solution

Given:

Total potatoes produced= $9.46\times {10}^{-1}\text{ lb}$

Total area harvested = $2.3\times {10}^5\text{ acre}$

Formula Used:

  $\frac{a^m}{a^n}=a^{m-n}$

Calculation:

The pound of potatoes produced per acre is given by the ratio of total potatoes produced to the total area harvested.

  $\begin{array}{c}\frac{9.46\times {10}^{-1}}{2.3\times {10}^{-5}}=\frac{9.46}{2.3}\times \frac{{10}^{-1}}{{10}^{-5}}\\ \approx 4.113\times {10}^{-1-\left(-5\right)}\\ \approx 4.113\times {10}^{-1+5}\\ \approx 4.113\times {10}^4\end{array}$

Conclusion:

The pound of potatoes produced per acre is about $4.113\times {10}^4\text{ lb/acre}$ (scientific notation) or about $\text{41,130 lb/acre}$ ( standard form).