To find how many pennies are in a pile that weighs \( 3.596 \times 10^4 \) pounds, we need to divide the total weight of the pile by the weight of one penny.
The weight of one penny is \( 5.8 \times 10^{-3} \) pounds.
Now, we can set up the calculation:
\[ \text{Number of pennies} = \frac{3.596 \times 10^4 \text{ pounds}}{5.8 \times 10^{-3} \text{ pounds}} \]
To perform the division, we can divide the coefficients and subtract the exponents (according to the laws of exponents):
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Divide the coefficients: \[ \frac{3.596}{5.8} \approx 0.620 \quad (using a calculator) \]
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Subtract the exponents: \[ 10^{4 - (-3)} = 10^{4 + 3} = 10^{7} \]
Now, putting it all together:
\[ \text{Number of pennies} \approx 0.620 \times 10^{7} \]
To express this in proper scientific notation, we want the coefficient to be between 1 and 10. So we can write:
\[ 0.620 \times 10^{7} = 6.20 \times 10^{6} \]
Thus, the number of pennies in the pile is
\[ \boxed{6.20 \times 10^{6}} \]