To find the value of \( q \) that makes the addition sentence true, we can start by simplifying the right side of the equation:
\[ 657.2 + (q + 284) = (657.2 + 996.8) + 284 \]
First, calculate \( 657.2 + 996.8 \):
\[ 657.2 + 996.8 = 1654 \]
Now substitute this back into the equation:
\[ 657.2 + (q + 284) = 1654 + 284 \]
Next, calculate \( 1654 + 284 \):
\[ 1654 + 284 = 1938 \]
Now our equation simplifies to:
\[ 657.2 + (q + 284) = 1938 \]
Next, simplify the left side:
\[ 657.2 + q + 284 = 1938 \]
Combine \( 657.2 \) and \( 284 \):
\[ 941.2 + q = 1938 \]
To isolate \( q \), subtract \( 941.2 \) from both sides:
\[ q = 1938 - 941.2 \]
Now perform the subtraction:
\[ q = 996.8 \]
Thus, the value of \( q \) that makes the addition sentence true is:
\[ \boxed{996.8} \]