To convert the fraction \( \frac{15}{8} \) to a decimal, you can divide 15 by 8:
\[ 15 \div 8 = 1.875 \]
The decimal representation of \( \frac{15}{8} \) is 1.875. Since this value is already to the nearest thousandth, the final answer is:
\[ \boxed{1.875} \]