Question

The diameter of a human hair is
\[9 \cdot 10^{-5}\] meters. The diameter of a spider's silk is
\[3 \cdot 10^{-6}\] meters.
How much greater is the diameter of a human hair than the diameter of a spider's silk?
Write your answer in scientific notation.
meters

Answer 1

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.