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 0.62×107 0 point 6 2 times 10 to the 7th power 6.2×108 6 point 2 times 10 to the 8th power 6.2×10−7 6 point 2 times 10 to the negative 7 power 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 one penny, which is \( 5.8 \times 10^{-3} \) lb. The number of pennies can be calculated by dividing the total weight of the pile 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, perform the division:

1. **Dividing the coefficients**:
\[
\frac{3.596}{5.8} \approx 0.619
\]

2. **Dividing the powers of ten**:
\[
\frac{10^4}{10^{-3}} = 10^{4 - (-3)} = 10^{4 + 3} = 10^7
\]

Now combine the results:

\[
\text{Number of pennies} \approx 0.619 \times 10^7
\]

To express \( 0.619 \) in proper scientific notation, we can write it as \( 6.19 \times 10^{-1} \), so:

\[
0.619 \times 10^7 = 6.19 \times 10^6
\]

Thus, multiplying these gives:

\[
6.19 \times 10^6
\]

Now we can round this to one decimal place, getting \( 6.2 \times 10^6 \).

Thus, the number of pennies in the pile, in scientific notation, is:

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