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

0.62×107
0.62 times 10 superscript 7 baseline

6.2×108
6.2 times 10 superscript 8 baseline

6.2×106

Answer 1

To find the number of pennies in a pile that weighs \( 3.596 \times 10^4 \) lb., we can use the weight of a single penny, which is \( 5.8 \times 10^{-3} \) lb. The number of pennies can be calculated by dividing the total weight of the pennies 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, let's perform the division:

1. Calculate the coefficients:

\[
\frac{3.596}{5.8} \approx 0.620
\]

2. Now, perform the division for the powers of ten:

\[
\frac{10^4}{10^{-3}} = 10^{4 - (-3)} = 10^{4 + 3} = 10^7
\]

3. Combine the results:

\[
\text{Number of pennies} \approx 0.620 \times 10^7
\]

4. Convert \( 0.620 \) into scientific notation:

\[
0.620 \equiv 6.2 \times 10^{-1}
\]

Thus:

\[
0.620 \times 10^7 = 6.2 \times 10^{-1} \times 10^7 = 6.2 \times 10^{7 - 1} = 6.2 \times 10^6
\]

The final answer is:

\[
\boxed{6.2 \times 10^6}
\]