To find the number of hours it will take for the asteroid to hit Mars, we can use the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Rate}} \]
In this case, the distance to Mars is \(3.311 \times 10^8\) miles and the rate at which the asteroid is traveling is \(7.7 \times 10^4\) miles per hour. We can substitute these values into the formula:
\[ \text{Time} = \frac{3.311 \times 10^8 \text{ miles}}{7.7 \times 10^4 \text{ miles/hour}} \]
To perform the division, we divide the coefficients and then subtract the exponents:
\[ \text{Time} = \frac{3.311}{7.7} \times 10^{8 - 4} \]
Calculating the coefficient:
\[ \frac{3.311}{7.7} \approx 0.4309 \]
And subtracting the powers of ten:
\[ 10^{8 - 4} = 10^4 \]
Combining these gives:
\[ \text{Time} \approx 0.4309 \times 10^4 \]
Now, converting \(0.4309 \times 10^4\) into proper scientific notation:
\[ 0.4309 \times 10^4 = 4.309 \times 10^3 \]
Thus, the time until the asteroid hits Mars is:
\[ \boxed{4.309 \times 10^3} \text{ hours} \]