Question

Nelly owns farm land that has an area of 4.2 × 10^2 acres. Each year, the farm produces 6.72 × 10^4 bushels of corn. What is the average amount of corn produced per acre represented in scientific notation?


A.
2.82 × 10^7 bushels per acre
B.
1.6 × 10^2 bushels per acre
C.
1.6 × 10^3 bushels per acre
D.
2.82 × 10^6 bushels per acre
E.
1.6 × 10^1 bushels per acre

Answer 1

So to get the average of corn per acre, you divide the amount of corn by the number of acres (in this case, \(\sf{\dfrac{6.72}{4.2}}\)).

Now, it has it to a power, which means that you'll have to figure out what the difference of the two is, and using the rule of exponents on division (which states this)

\(\sf\color{gray}{\text{If an exponent with the same base variable is divided by a similar variable,}\\\text{the exponent of the numerator is subtracted by the exponent of the denominator.}}\)

That given, the power of the amount of corn (4), is subtracted by the amount of acres' power (2)

That makes your power of the equality to 2 (because [4-2] is 2, obviously)

So, that given, you find what corn divided by acres is, and then add your \(\sf{\times 10 ^ x}\) to the end of it.

\(\sf{\dfrac{6.72\times 10^4}{4.2\times 10^2}\color{tomato}{=}\dfrac{6.72}{4.2}\times10^2 \color{tomato}{=}1.6 \times 10^2}\)

Answer 2

tyvm!