To find the number of pennies in a pile that weighs \( 3.596 \times 10^4 \) lb, we can use the weight of one penny, which is \( 5.8 \times 10^{-3} \) lb. The number of pennies can be calculated by dividing the total weight of the pile by the weight of one penny:
\[ \text{Number of pennies} = \frac{\text{Total weight}}{\text{Weight of one penny}} = \frac{3.596 \times 10^4 , \text{lb}}{5.8 \times 10^{-3} , \text{lb}} \]
Now, perform the division:
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Dividing the coefficients: \[ \frac{3.596}{5.8} \approx 0.619 \]
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Dividing the powers of ten: \[ \frac{10^4}{10^{-3}} = 10^{4 - (-3)} = 10^{4 + 3} = 10^7 \]
Now combine the results:
\[ \text{Number of pennies} \approx 0.619 \times 10^7 \]
To express \( 0.619 \) in proper scientific notation, we can write it as \( 6.19 \times 10^{-1} \), so:
\[ 0.619 \times 10^7 = 6.19 \times 10^6 \]
Thus, multiplying these gives:
\[ 6.19 \times 10^6 \]
Now we can round this to one decimal place, getting \( 6.2 \times 10^6 \).
Thus, the number of pennies in the pile, in scientific notation, is:
\[ \boxed{6.2 \times 10^6} \]
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