\(\sin \dfrac{{\pi x}}{3} = 0,5\,\,\,\, \Leftrightarrow \,\,\,\,\left[ {\begin{array}{*{20}{c}}{\dfrac{{\pi x}}{3} = \dfrac{\pi }{6} + 2\pi n\left| { \cdot 3\,} \right.}\\{\dfrac{{\pi x}}{3} = \dfrac{{5\pi }}{6} + 2\pi n\left| { \cdot 3} \right.}\end{array}} \right.\,\,\,\,\, \Leftrightarrow \,\,\,\,\left[ {\begin{array}{*{20}{c}}{\pi x = \dfrac{\pi }{2} + 6\pi n\left| {:\pi } \right.}\\{\pi x = \dfrac{{5\pi }}{2} + 6\pi n\left| {:\pi } \right.}\end{array}} \right.\,\,\,\, \Leftrightarrow \,\,\,\,\left[ {\begin{array}{*{20}{c}}{x = \dfrac{1}{2} + 6n;\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}\\{x = \dfrac{5}{2} + 6n,\,\,\,n\, \in \,Z.}\end{array}} \right.\)
Рассмотрим \(x = \dfrac{1}{2} + 6n,\,\,n\, \in \,Z\). Если \(n = 0\), то \(x = 0,5\); если \(n = -1\), то \(x = -5,5\).
Рассмотрим \(x = \dfrac{5}{2} + 6n,\,\,n\, \in \,Z\). Если \(n = 0\), то \(x = 2,5\); если \(n = -1\), то \(x = -3,5\).
Следовательно, наименьший положительный корень \(x = 0,5\).
Ответ: 0,5.