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

6.2×108
6.2 times 10 superscript 8 baseline

6.2×106
6.2 times 10 superscript 6 baseline

0.62×107
0.62 times 10 superscript 7 baseline

6.2×10−7

Answer 1

To find out how many pennies are in a pile that weighs \( 3.596 \times 10^4 \) lb, you can use the formula:

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

Now calculate the division step by step:

1. First, find the division of the coefficients:

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

2. Then, perform the division of the powers of ten:

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

3. Combine the two results:

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

To express this in proper scientific notation, we rewrite \( 0.620 \) as \( 6.2 \times 10^{-1} \):

\[ 0.620 \times 10^7 = 6.2 \times 10^{-1} \times 10^7 = 6.2 \times 10^{7 - 1} = 6.2 \times 10^6 \]

Therefore, the number of pennies in the pile is:

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