A penny weighs 5.8×10−3

Question

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
0.62 times 10 superscript 7 baseline

6.2×108
6.2 times 10 superscript 8 baseline

6.2×106
6.2 times 10 superscript 6 baseline

6.2×10−7

Answer 1

To find the number of pennies in a pile that weighs \(3.596 \times 10^4\) lb, we need to divide the total weight of the pennies by the weight of a single penny.

First, we calculate the number of pennies:

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

Now, perform the division:

1. Divide the coefficients: \[ \frac{3.596}{5.8} \approx 0.620 \]

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

Now combine the results:

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

In proper scientific notation, we express \(0.620\) as \(6.2\) and decrease the exponent by 1 to maintain equivalence:

\[ 0.620 \times 10^7 = 6.2 \times 10^6 \]

Thus, the final answer in scientific notation is:

6.2 × 10⁶.