To find the thickness of a fingernail, we need to add the thickness of the hair and the additional thickness of the fingernail.
The diameter of a human hair is given as \(4 \times 10^{-3}\) inches, which is equivalent to 0.004 inches.
A fingernail is about 0.011 inches thicker than the hair, so we can calculate the thickness of the fingernail as follows:
\[ \text{Thickness of fingernail} = \text{Thickness of hair} + 0.011 \text{ inches} \]
\[ \text{Thickness of fingernail} = 0.004 \text{ inches} + 0.011 \text{ inches} \]
\[ \text{Thickness of fingernail} = 0.015 \text{ inches} \]
Now, writing this as a decimal to three places:
\[ \text{Thickness of fingernail} = 0.015 \text{ inches} \]
Thus, the thickness of a fingernail is \( \boxed{0.015} \) inches.