Question
A penny weighs 5.8×10−3 lb. How many pennies are in a pile of pennies that weighs 3.596×104 lb.? Write the answer in scientific notation.(1 point)
Responses
6.2×10−7
6.2 times 10 superscript negative 7 baseline
6.2×108
6.2 times 10 superscript 8 baseline
6.2×106
6.2 times 10 superscript 6 baseline
0.62×107
Responses
6.2×10−7
6.2 times 10 superscript negative 7 baseline
6.2×108
6.2 times 10 superscript 8 baseline
6.2×106
6.2 times 10 superscript 6 baseline
0.62×107
Answers
GPT-4o mini
To find the number of pennies in a pile that weighs \(3.596 \times 10^4\) lb, we need to divide the total weight of the pile by the weight of a single penny.
1. **Weight of a penny**: \(5.8 \times 10^{-3}\) lb
2. **Weight of the pile**: \(3.596 \times 10^4\) lb
Now, we can use the formula:
\[
\text{Number of pennies} = \frac{\text{Weight of pile}}{\text{Weight of one penny}} = \frac{3.596 \times 10^4}{5.8 \times 10^{-3}}
\]
To perform the division, we can rewrite it as:
\[
\text{Number of pennies} = \frac{3.596}{5.8} \times \frac{10^4}{10^{-3}} = \frac{3.596}{5.8} \times 10^{4 - (-3)}
\]
Calculating the division of the coefficients:
\[
\frac{3.596}{5.8} \approx 0.619
\]
And adding the exponents:
\[
10^{4 - (-3)} = 10^{4 + 3} = 10^7
\]
Now we combine the two parts:
\[
\text{Number of pennies} \approx 0.619 \times 10^7
\]
To express this in proper scientific notation, we can adjust \(0.619\) to \(6.19\) and reduce the exponent by 1:
\[
0.619 \times 10^7 = 6.19 \times 10^6
\]
However, we need our answer to match one of the provided options. The closest representation while still being rounded would be \(6.2 \times 10^6\).
Thus, the number of pennies in the pile is:
\[
\boxed{6.2 \times 10^6}
\]
1. **Weight of a penny**: \(5.8 \times 10^{-3}\) lb
2. **Weight of the pile**: \(3.596 \times 10^4\) lb
Now, we can use the formula:
\[
\text{Number of pennies} = \frac{\text{Weight of pile}}{\text{Weight of one penny}} = \frac{3.596 \times 10^4}{5.8 \times 10^{-3}}
\]
To perform the division, we can rewrite it as:
\[
\text{Number of pennies} = \frac{3.596}{5.8} \times \frac{10^4}{10^{-3}} = \frac{3.596}{5.8} \times 10^{4 - (-3)}
\]
Calculating the division of the coefficients:
\[
\frac{3.596}{5.8} \approx 0.619
\]
And adding the exponents:
\[
10^{4 - (-3)} = 10^{4 + 3} = 10^7
\]
Now we combine the two parts:
\[
\text{Number of pennies} \approx 0.619 \times 10^7
\]
To express this in proper scientific notation, we can adjust \(0.619\) to \(6.19\) and reduce the exponent by 1:
\[
0.619 \times 10^7 = 6.19 \times 10^6
\]
However, we need our answer to match one of the provided options. The closest representation while still being rounded would be \(6.2 \times 10^6\).
Thus, the number of pennies in the pile is:
\[
\boxed{6.2 \times 10^6}
\]