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 point 6 2 times 10 to the 7th power

6.2×108
6 point 2 times 10 to the 8th power

6.2×106
6 point 2 times 10 to the 6th power

6.2×10−7

Answer 1

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

1. Weight of one penny: \( 5.8 \times 10^{-3} \) lb
2. Total weight of the pile: \( 3.596 \times 10^4 \) lb

Now, perform the division:

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

To simplify that calculation:

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

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

So, combining the results, we have: \[ \text{Number of pennies} = 0.620 \times 10^7 \]

In scientific notation: \[ 6.2 \times 10^6 \]

Therefore, the correct answer is: \[ \boxed{6.2 \times 10^6} \]