Question
a penny weighs 5.8×10 to the -3rd pound how many pennies are in a pile of pennies that way 3.596×10 to the fourth power pounds write the answer and scientific notation
Answers
GPT-4o mini
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):
1. Divide the coefficients:
\[
\frac{3.596}{5.8} \approx 0.620 \quad (using a calculator)
\]
2. 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
\[
\boxed{6.20 \times 10^{6}}
\]
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):
1. Divide the coefficients:
\[
\frac{3.596}{5.8} \approx 0.620 \quad (using a calculator)
\]
2. 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
\[
\boxed{6.20 \times 10^{6}}
\]