To find the area of a Canadian football field, we start with the area of the American football field, which is given as \( 6.4 \times 10^3 \) square yards.
The Canadian football field is 3,350 square yards larger, so we need to add this amount to the area of the American football field:
\[ \text{Area of Canadian football field} = 6.4 \times 10^3 + 3,350 \]
First, we need to express 3,350 in scientific notation.
\[ 3,350 = 3.35 \times 10^3 \]
Now, we can rewrite the equation:
\[ \text{Area of Canadian football field} = 6.4 \times 10^3 + 3.35 \times 10^3 \]
Since the bases are the same (both are powers of \( 10^3 \)), we can add the coefficients:
\[ = (6.4 + 3.35) \times 10^3 \]
First, calculate \( 6.4 + 3.35 \):
\[ 6.4 + 3.35 = 9.75 \]
So, the area of the Canadian football field is:
\[ 9.75 \times 10^3 \text{ square yards} \]
This is already in scientific notation and to two decimal places.
Thus, the final answer is:
\[ \boxed{9.75 \times 10^3} \text{ square yards} \]