To find out how many senior lunches the grant can provide, we start with the total grant amount of \( 1.925 \times 10^6 \) dollars and divide it by the cost per lunch, which is \( 2.75 \) dollars.
\[ \text{Number of lunches} = \frac{1.925 \times 10^6}{2.75} \]
Calculating the division:
\[ \frac{1.925}{2.75} = 0.7 \]
Now, we can write \( 0.7 \) in scientific notation, which is \( 7 \times 10^{-1} \).
Now multiplying by \( 10^6 \):
\[ 0.7 \times 10^6 = 7 \times 10^{5} \]
So the total number of lunches the grant can provide is:
\[ 7 \times 10^5 \]
Therefore, the correct answer is \( 7 \times 10^5 \).