To find out how many senior lunches the grant can provide, we need to divide the total grant amount by the cost per lunch.
Grant amount: \( 1.925 \times 10^6 \) dollars
Cost per lunch: \( 2.75 \) dollars
Now, we perform the division:
\[ \text{Number of lunches} = \frac{1.925 \times 10^6}{2.75} \]
First, calculate \( \frac{1.925}{2.75} \):
\[ \frac{1.925}{2.75} \approx 0.7 \]
Next, we keep the exponent \( 10^6 \):
\[ \text{Number of lunches} \approx 0.7 \times 10^6 \]
To express it in proper scientific notation, we can rewrite \( 0.7 \times 10^6 \) as:
\[ 7 \times 10^5 \]
So, the answer in scientific notation is:
\[ \boxed{7 \times 10^5} \]