To find the time it takes 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 these values into the formula:
\[ \text{Time} = \frac{3.311 \times 10^8 \text{ miles}}{7.7 \times 10^4 \text{ miles per hour}} \]
Now, we can calculate this step by step.
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Dividing the numeric parts: \[ \frac{3.311}{7.7} = 0.4301 \text{ (approximately)} \]
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Dividing the powers of \(10\): \[ 10^8 \div 10^4 = 10^{8 - 4} = 10^4 \]
Putting both parts together, we have:
\[ \text{Time} = 0.4301 \times 10^4 \text{ hours} \]
We can convert \(0.4301 \times 10^4\) into proper scientific notation:
\[ 0.4301 \times 10^4 = 4.301 \times 10^3 \text{ hours} \]
Thus, the time before the asteroid hits Mars, expressed in scientific notation, is:
\[ \boxed{4.301 \times 10^3} \] hours.