Question

In 2012, on average, about $9.46\times10^{-1}$ pound of potatoes was produced for every $2.3\times10^{-5}$ acre harvested. How many pounds of potatoes on average were produced for each acre harvested? Write your answer in scientific notation and in standard form. Round to the nearest pound per acre.

Answer 1

On average, approximately 41,043 pounds of potatoes are produced for each acre harvested.

Step-by-step explanation:

To find the average number of pounds of potatoes produced for each acre harvested, we need to divide the total pounds of potatoes produced by the total acres harvested.

Given that there is an average of

`$9.46 *10^(-1)$`

pound of potatoes produced for every

`$2.3 *10^(-5)$`

acre harvested, we can set up the following proportion:

`$9.46 *10^(-1)$ pound of potatoes / $2.3 *10^(-5)$ acre = x`

pounds of potatoes / 1 acre

To solve for x, we can cross multiply:

`$9.46 *10^(-1) * 1 = 2.3*10^(-5) * x$`

Simplifying, we get:

`$0.946 = 0.000023x$`

Dividing both sides by 0.000023, we get:

`$x \approx 41,043$`

This means that, on average, approximately 41,043 pounds of potatoes are produced for each acre harvested. In scientific notation, this is approximately

`$4.1043*10^(4)$`

pounds per acre.

Answer 2

4.113 × 10⁴ pounds per acre = 41,130 pounds per acre to the nearest pounds per acre

Step-by-step explanation:

9.46 × 10⁻¹ pounds of potatoes were produced for every 2.3 × 10⁻⁵ acre harvested. The average pounds of potatoes harvested per acre would be pounds of potatoes/acres harvested = 9.46 × 10⁻¹ pounds/2.3 × 10⁻⁵ acre = 4.113 × 10 ⁻¹⁻⁻⁵ = 4.113 × 10⁵⁻¹ = 4.113 × 10⁴ pounds per acre = 41,130 pounds per acre to the nearest pounds per acre.