Question

A penny weighs 5.8×10−3%0D%0A5.8%0D%0A×%0D%0A10%0D%0A−%0D%0A3%0D%0A lb. How many pennies are in a pile of pennies that weighs 3.596×104%0D%0A3.596%0D%0A×%0D%0A10%0D%0A4%0D%0A lb. ? Write the answer in scientific notation.(1 point)%0D%0AResponses%0D%0A%0D%0A6.2×106%0D%0A6.2%0D%0A×%0D%0A10%0D%0A6%0D%0A6 point 2 times 10 to the 6th power%0D%0A%0D%0A0.62×107%0D%0A0.62%0D%0A×%0D%0A10%0D%0A7%0D%0A0 point 6 2 times 10 to the 7th power%0D%0A%0D%0A6.2×10−7%0D%0A6.2%0D%0A×%0D%0A10%0D%0A−%0D%0A7%0D%0A6 point 2 times 10 to the negative 7 power%0D%0A%0D%0A6.2×108

Answer 1

To find out how many pennies are in a pile of pennies that weighs \(3.596 \times 10^4\) lb, we can follow these steps:

1. **Weight of a penny**:
The weight of one penny is given as \(5.8 \times 10^{-3}\) lb.

2. **Weight of the pile of pennies**:
The total weight of the pile is \(3.596 \times 10^4\) lb.

3. **Number of pennies**:
To find the number of pennies, we can divide the total weight by the weight of one penny:

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

4. **Calculating**:
First, divide the coefficients:

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

Then, divide the powers of ten:

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

5. **Combine the results**:
So we have:

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

To convert this to proper scientific notation, we can adjust:

\[
0.620 \times 10^7 = 6.20 \times 10^6
\]

Therefore, the number of pennies is \(6.2 \times 10^6\).

The correct response is:

**6.2 × 10^6**.