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
6.2×106
6.2 times 10 superscript 6 baseline
0.62×107
0.62 times 10 superscript 7 baseline
6.2×10−7
6.2 times 10 superscript negative 7 baseline
6.2×108
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
6.2×106
6.2 times 10 superscript 6 baseline
0.62×107
0.62 times 10 superscript 7 baseline
6.2×10−7
6.2 times 10 superscript negative 7 baseline
6.2×108
Answers
GPT-4o mini
To find out how many pennies are 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.
To calculate the number of pennies, we divide the total weight by the weight of one penny:
\[
\text{Number of pennies} = \frac{\text{Total weight}}{\text{Weight of one penny}} = \frac{3.596 \times 10^4 \text{ lb}}{5.8 \times 10^{-3} \text{ lb}}
\]
Performing the division:
\[
\text{Number of pennies} = \left( \frac{3.596}{5.8} \right) \times \left( \frac{10^4}{10^{-3}} \right)
\]
Calculating \( \frac{3.596}{5.8} \):
\[
\frac{3.596}{5.8} \approx 0.6196551724 \approx 0.62
\]
Next, for the powers of ten:
\[
\frac{10^4}{10^{-3}} = 10^{4 - (-3)} = 10^{4 + 3} = 10^7
\]
Now combine the two results:
\[
\text{Number of pennies} \approx 0.62 \times 10^7
\]
To express this in scientific notation, we can rewrite \( 0.62 \) as \( 6.2 \times 10^{-1} \):
\[
0.62 \times 10^7 = 6.2 \times 10^{-1} \times 10^7 = 6.2 \times 10^{7 - 1} = 6.2 \times 10^6
\]
Thus, the number of pennies in the pile is:
\[
\boxed{6.2 \times 10^6}
\]
To calculate the number of pennies, we divide the total weight by the weight of one penny:
\[
\text{Number of pennies} = \frac{\text{Total weight}}{\text{Weight of one penny}} = \frac{3.596 \times 10^4 \text{ lb}}{5.8 \times 10^{-3} \text{ lb}}
\]
Performing the division:
\[
\text{Number of pennies} = \left( \frac{3.596}{5.8} \right) \times \left( \frac{10^4}{10^{-3}} \right)
\]
Calculating \( \frac{3.596}{5.8} \):
\[
\frac{3.596}{5.8} \approx 0.6196551724 \approx 0.62
\]
Next, for the powers of ten:
\[
\frac{10^4}{10^{-3}} = 10^{4 - (-3)} = 10^{4 + 3} = 10^7
\]
Now combine the two results:
\[
\text{Number of pennies} \approx 0.62 \times 10^7
\]
To express this in scientific notation, we can rewrite \( 0.62 \) as \( 6.2 \times 10^{-1} \):
\[
0.62 \times 10^7 = 6.2 \times 10^{-1} \times 10^7 = 6.2 \times 10^{7 - 1} = 6.2 \times 10^6
\]
Thus, the number of pennies in the pile is:
\[
\boxed{6.2 \times 10^6}
\]