To determine how many hours it will take for the asteroid to hit Mars, we can use the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
Given that the distance to Mars is \( 3.311 \times 10^8 \) miles and the speed of the asteroid is \( 7.7 \times 10^4 \) miles per hour, we can plug in these values:
\[ \text{Time} = \frac{3.311 \times 10^8 \text{ miles}}{7.7 \times 10^4 \text{ mi/hr}} \]
Now, we can perform the division.
First, divide the coefficients:
\[ \frac{3.311}{7.7} \approx 0.4301 \]
Then, subtract the exponents in the scientific notation:
\[ 10^8 / 10^4 = 10^{8-4} = 10^4 \]
Now we combine the two results:
\[ \text{Time} \approx 0.4301 \times 10^4 \]
We can convert \(0.4301 \times 10^4\) to proper scientific notation by moving the decimal point one place to the right, which increases the exponent by one:
\[ 4.301 \times 10^3 \]
Thus, the time it will take for the asteroid to hit Mars is:
\[ \boxed{4.301 \times 10^3} \text{ hours} \]