Question

A penny weighs 5.8×10^−3
lb. How many pennies are in a pile of pennies that weighs 3.596×10^4
lb.? Write the answer in scientific notation.(1 point)
Responses

6.2×108
6 point 2 times 10 to the 8th power - no response given

6.2×106
6 point 2 times 10 to the 6th power - no response given

0.62×10^7

Answer 1

To find out how many pennies are in a pile that weighs \( 3.596 \times 10^4 \) lb, we can use the formula:

\[
\text{Number of pennies} = \frac{\text{Total weight of pennies}}{\text{Weight of one penny}}
\]

Plugging in the values:

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

Now, we perform the division:

1. Divide the coefficients:
\[
\frac{3.596}{5.8} \approx 0.62068966 \approx 0.62 \, (\text{rounded to two decimal places})
\]

2. Subtract the exponents:
\[
10^{4 - (-3)} = 10^{4 + 3} = 10^{7}
\]

Combining these, we get:
\[
\text{Number of pennies} \approx 0.62 \times 10^{7}
\]

To express \( 0.62 \times 10^{7} \) in standard scientific notation, we move the decimal point one place to the right, which increases the exponent by 1:

\[
0.62 \times 10^{7} = 6.2 \times 10^{6}
\]

Thus, the final answer is:

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