An American football field has an area of 6.4 × 103 square yards. A Canadian football field is 3,350 square yards larger. What is the area of a Canadian football field? Write your answer in scientific notation to 2 decimal places.

1 answer

To find the area of a Canadian football field, we start with the area of an American football field, which is given as:

\[ 6.4 \times 10^3 \text{ square yards} \]

Next, we know that a Canadian football field is 3,350 square yards larger than an American football field. Therefore, we need to add 3,350 square yards to the area of the American football field:

\[ \text{Area of Canadian football field} = 6.4 \times 10^3 + 3350 \]

Next, we need to express 3,350 in scientific notation to combine it better with the area of the American football field. To convert 3,350 to scientific notation:

\[ 3350 = 3.35 \times 10^3 \]

Now we can add the two areas together. Note that both numbers are in terms of \(10^3\):

\[ \text{Area of Canadian football field} = (6.4 \times 10^3 + 3.35 \times 10^3) \]

Combining the coefficients (since they have the same power of ten):

\[ = (6.4 + 3.35) \times 10^3 \]

Calculating the sum of the coefficients:

\[ 6.4 + 3.35 = 9.75 \]

Thus, we have:

\[ \text{Area of Canadian football field} = 9.75 \times 10^3 \]

Finally, in scientific notation rounded to two decimal places, the area of the Canadian football field is:

\[ \boxed{9.75 \times 10^3} \]