Engineering strain (\( \epsilon \)) is defined as the change in length (\( \Delta L \)) divided by the original length (\( L_0 \)):
\[
\epsilon = \frac{\Delta L}{L_0}
\]
Given that \( \Delta L = 0.2 \, {mm} \) and \( L_0 = 50 \, {mm} \), we can substitute the values into the equation:
\[
\epsilon = \frac{0.2}{50} = 0.004
\]
Thus, the engineering strain is \( 0.004 \).