To find out how many senior lunches the grant can provide, you can divide the total grant amount by the cost per lunch.
The grant amount is \( 1.925 \times 10^6 \) dollars, and the cost per lunch is $2.75.
Now, perform the division:
\[ \text{Number of lunches} = \frac{1.925 \times 10^6}{2.75} \]
First, calculate the division of the coefficients:
\[ \frac{1.925}{2.75} \approx 0.7 \]
Next, combine that with the power of ten:
\[ \text{Number of lunches} = 0.7 \times 10^6 \]
To express this in scientific notation, we need to adjust the coefficient to be between 1 and 10. We can do this by changing \(0.7\) to \(7\) and decreasing the exponent by 1:
\[ 0.7 \times 10^6 = 7.0 \times 10^5 \]
Thus, the number of senior lunches the grant can provide, in scientific notation, is:
\[ \boxed{7.0 \times 10^5} \]