A feather weighs 0.0082 g. How many feathers would you need to make a weight of 4.1×10^3 g? Write the answer in scientific notation.(1

1 answer

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.