Question
a feather way, 0.0082 g how many feathers would you need to make a weight of 4.1×10 power of three write the answer in scientific notation
Answers
GPT-4o mini
To determine how many feathers you need to make a weight of \( 4.1 \times 10^3 \) grams, we can use the weight of a single feather, which is \( 0.0082 \) grams.
1. First, we need to find out how many feathers are required to reach \( 4.1 \times 10^3 \) grams. We can do this by dividing the total weight desired by the weight of one feather:
\[
\text{Number of feathers} = \frac{4.1 \times 10^3 \text{ g}}{0.0082 \text{ g/feather}}
\]
2. Performing the calculation:
\[
\text{Number of feathers} = \frac{4.1 \times 10^3}{0.0082}
\]
3. Calculating \( \frac{4.1}{0.0082} \):
- First, calculate \( 4.1 \div 0.0082 \) which is approximately \( 500 \).
4. Then, include the power of ten:
\[
\text{Number of feathers} \approx 500 \times 10^3
\]
5. To write it in scientific notation:
\[
500 = 5.0 \times 10^2
\]
So:
\[
500 \times 10^3 = 5.0 \times 10^{2 + 3} = 5.0 \times 10^5
\]
Thus, the number of feathers needed is approximately:
\[
\text{Number of feathers} \approx 5.0 \times 10^5
\]
1. First, we need to find out how many feathers are required to reach \( 4.1 \times 10^3 \) grams. We can do this by dividing the total weight desired by the weight of one feather:
\[
\text{Number of feathers} = \frac{4.1 \times 10^3 \text{ g}}{0.0082 \text{ g/feather}}
\]
2. Performing the calculation:
\[
\text{Number of feathers} = \frac{4.1 \times 10^3}{0.0082}
\]
3. Calculating \( \frac{4.1}{0.0082} \):
- First, calculate \( 4.1 \div 0.0082 \) which is approximately \( 500 \).
4. Then, include the power of ten:
\[
\text{Number of feathers} \approx 500 \times 10^3
\]
5. To write it in scientific notation:
\[
500 = 5.0 \times 10^2
\]
So:
\[
500 \times 10^3 = 5.0 \times 10^{2 + 3} = 5.0 \times 10^5
\]
Thus, the number of feathers needed is approximately:
\[
\text{Number of feathers} \approx 5.0 \times 10^5
\]