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 out how many pennies are in a pile that weighs \( 3.596 \times 10^4 \) lb, we can divide the total weight of the pile by the weight of one penny.

1. Weight of one penny = \( 5.8 \times 10^{-3} \) lb.
2. Total weight of the pile = \( 3.596 \times 10^4 \) lb.

Now, we perform the division:

\[
\text{Number of pennies} = \frac{\text{Total weight}}{\text{Weight of one penny}} = \frac{3.596 \times 10^4 \text{ lb}}{5.8 \times 10^{-3} \text{ lb}}
\]

We can first simplify the numbers:

\[
= \frac{3.596}{5.8} \times \frac{10^4}{10^{-3}}
\]

Calculating \( \frac{3.596}{5.8} \):

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

And for the powers of ten:

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

Combining both results:

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

Converting \( 0.620 \) to scientific notation gives us \( 6.2 \times 10^{-1} \). Therefore:

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

Thus, the number of pennies in the pile is:

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