To find the thickness of a fingernail, we start with the diameter of a human hair, which is approximately \(4 \times 10^{-3}\) inches, and then we need to add the thickness of the fingernail, which is given as \(0.011\) inches thicker than the hair.
First, let's convert \(4 \times 10^{-3}\) inches to a decimal:
\[ 4 \times 10^{-3} = 0.004 \text{ inches} \]
Now, we add \(0.011\) inches to \(0.004\) inches to find the thickness of the fingernail:
\[ \text{Thickness of fingernail} = 0.004 + 0.011 = 0.015 \text{ inches} \]
Now, rounding to three decimal places, the thickness of the fingernail is:
\[ \boxed{0.015} \text{ inches} \]