To find out how many feathers you would need to make a weight of \( 4.1 \times 10^3 \) g, you can use the following formula:
\[ \text{Number of feathers} = \frac{\text{Total weight desired}}{\text{Weight of one feather}} \]
Given:
- Weight of one feather = \( 0.0082 \) g
- Total weight desired = \( 4.1 \times 10^3 \) g
Substituting the values into the formula gives:
\[ \text{Number of feathers} = \frac{4.1 \times 10^3 \text{ g}}{0.0082 \text{ g}} \]
Calculating this:
\[ \text{Number of feathers} = \frac{4.1 \times 10^3}{0.0082} \]
This can also be written as:
\[ \text{Number of feathers} = 4.1 \times 10^3 \times \frac{1}{0.0082} \]
Calculating \( \frac{1}{0.0082} \):
\[ \frac{1}{0.0082} \approx 121.9512 \]
Now, calculate:
\[ \text{Number of feathers} \approx 4.1 \times 10^3 \times 121.9512 \approx 5.0009 \times 10^5 \]
In scientific notation, this rounds to:
\[ \text{Number of feathers} \approx 5.0 \times 10^5 \]
Thus, you would need approximately \( 5.0 \times 10^5 \) feathers to create a weight of \( 4.1 \times 10^3 \) g.