To find how many pennies are in a pile that weighs \(3.596 \times 10^4\) pounds, we can divide the total weight of the pile by the weight of one penny.
Given:
- Weight of one penny = \(5.8 \times 10^{-3}\) pounds
- Total weight of the pile = \(3.596 \times 10^4\) pounds
The number of pennies \(N\) can be calculated as follows:
\[ N = \frac{3.596 \times 10^4}{5.8 \times 10^{-3}} \]
We can simplify this division step-by-step. First, divide the coefficients:
\[ \frac{3.596}{5.8} \approx 0.620 \]
Next, divide the powers of ten:
\[ \frac{10^4}{10^{-3}} = 10^{4 - (-3)} = 10^{4 + 3} = 10^7 \]
Now combine the results:
\[ N \approx 0.620 \times 10^7 \]
To express \(0.620\) in scientific notation, we can write it as \(6.2 \times 10^{-1}\). Therefore, we can multiply this with \(10^7\):
\[ N = 6.2 \times 10^{-1} \times 10^{7} = 6.2 \times 10^{7 - 1} = 6.2 \times 10^6 \]
Thus, the answer in scientific notation is:
\[ \boxed{6.2 \times 10^6} \]
This corresponds to option A.
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