To find out how many senior lunches can be provided by the grant, we divide the total grant amount by the cost per lunch.
The total grant amount is: \[ 1.925 \times 10^6 \text{ dollars} \]
The cost per lunch is: \[ 2.75 \text{ dollars} \]
Now, we perform the division:
\[ \frac{1.925 \times 10^6}{2.75} \]
First, let's divide the coefficients:
\[ \frac{1.925}{2.75} \approx 0.700 \quad (\text{using a calculator}) \]
Next, we keep the power of ten the same:
\[ 10^6 \]
Now we can combine the results:
\[ 0.700 \times 10^6 \]
However, we need to express this in proper scientific notation. Scientific notation requires a coefficient between 1 and 10. So we adjust \(0.700\) to \(7.00\) (which is valid in scientific notation), and we need to decrease the exponent by 1 to account for the shift:
\[ 7.00 \times 10^5 \]
Thus, the total number of senior lunches that the grant can provide is:
\[ \boxed{7.00 \times 10^5} \]