Question

A penny weighs 5.8×10^-3 pounds. How many pennies are in a pile of pennies that weighs 3.596×10^4 pounds. Write the answer in scientific notation.

A. 6.2×10^6
B. 0.62×10^7
C. 6.2×10^8
D. 6.2×10-7

Answer 1

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

Given:
- Weight of one penny = \(5.8 \times 10^{-3}\) pounds
- Total weight of the pile = \(3.596 \times 10^4\) pounds

The number of pennies \(N\) can be calculated as follows:

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

We can simplify this division step-by-step. First, divide the coefficients:

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

Next, divide the powers of ten:

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

Now combine the results:

\[
N \approx 0.620 \times 10^7
\]

To express \(0.620\) in scientific notation, we can write it as \(6.2 \times 10^{-1}\). Therefore, we can multiply this with \(10^7\):

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

Thus, the answer in scientific notation is:

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

This corresponds to option A.