To find the thickness of a fingernail, we add the thickness of a human hair to its additional thickness.
The thickness of a human hair is given as:
\[ 4 \times 10^{-3} \text{ inches} = 0.004 \text{ inches} \]
The fingernail is about \( 0.011 \) inches thicker than the hair. Therefore:
\[ \text{Thickness of a fingernail} = 0.004 \text{ inches} + 0.011 \text{ inches} = 0.015 \text{ inches} \]
Thus, the thickness of a fingernail is:
\[ \boxed{0.015} \] inches (to 3 decimal places).