To find out how many feathers you would need to weigh 4.1 × 10³ g, you can use the following formula:
\[ \text{Number of feathers} = \frac{\text{Total weight}}{\text{Weight of one feather}} \]
Given that the weight of one feather is 0.0082 g, you can substitute the values into the formula:
\[ \text{Number of feathers} = \frac{4.1 \times 10^3 , \text{g}}{0.0082 , \text{g}} \]
Now, perform the division:
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First, convert 0.0082 g to scientific notation: \[ 0.0082 , \text{g} = 8.2 \times 10^{-3} , \text{g} \]
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Now, substitute this back into the equation: \[ \text{Number of feathers} = \frac{4.1 \times 10^3}{8.2 \times 10^{-3}} \]
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Perform the division: \[ \text{Number of feathers} = \frac{4.1}{8.2} \times \frac{10^3}{10^{-3}} = 0.5 \times 10^6 \]
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Convert \(0.5 \times 10^6\) to proper scientific notation: \[ 0.5 \times 10^6 = 5.0 \times 10^5 \]
Thus, you would need approximately \(5.0 \times 10^5\) feathers to weigh 4.1 × 10³ g.
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