To find out how much greater the diameter of a human hair is than the diameter of a spider's silk, we need to subtract the diameter of the spider's silk from the diameter of the human hair.
The diameter of a human hair is: \[ d_{\text{hair}} = 9 \cdot 10^{-5} \text{ meters} \] The diameter of a spider's silk is: \[ d_{\text{silk}} = 3 \cdot 10^{-6} \text{ meters} \]
We need to perform the subtraction: \[ d_{\text{difference}} = d_{\text{hair}} - d_{\text{silk}} \] Substituting the values: \[ d_{\text{difference}} = 9 \cdot 10^{-5} - 3 \cdot 10^{-6} \]
To perform this subtraction, we should express both numbers in terms of the same exponent. We can rewrite \(9 \cdot 10^{-5}\) as: \[ 9 \cdot 10^{-5} = 9 \cdot 10^{-5} \quad \text{(remains the same)} \] And convert \(3 \cdot 10^{-6}\) to the same exponent: \[ 3 \cdot 10^{-6} = 0.3 \cdot 10^{-5} \] Now we can rewrite the subtraction as: \[ d_{\text{difference}} = 9 \cdot 10^{-5} - 0.3 \cdot 10^{-5} \]
Now performing the subtraction, we have: \[ d_{\text{difference}} = (9 - 0.3) \cdot 10^{-5} = 8.7 \cdot 10^{-5} \]
Thus, the diameter of a human hair is: \[ \boxed{8.7 \cdot 10^{-5}} \text{ meters} \] greater than the diameter of a spider's silk.
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