To find the time in hours before the asteroid hits Mars, we can use the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
Given:
- Distance to Mars \( = 3.311 \times 10^8 \) miles
- Speed of the asteroid \( = 7.7 \times 10^4 \) miles/hour
Let's calculate the time:
\[ \text{Time} = \frac{3.311 \times 10^8 \text{ miles}}{7.7 \times 10^4 \text{ miles/hour}} \]
To perform the division, we will divide the coefficients and then subtract the exponents:
\[ \text{Time} = \frac{3.311}{7.7} \times \frac{10^8}{10^4} \]
Calculating the coefficients:
\[ \frac{3.311}{7.7} \approx 0.4301 \]
Calculating the powers of ten:
\[ \frac{10^8}{10^4} = 10^{8-4} = 10^4 \]
Now, we combine the two results:
\[ \text{Time} \approx 0.4301 \times 10^4 \]
To express this in proper scientific notation, we adjust it:
\[ 0.4301 \times 10^4 = 4.301 \times 10^3 \]
Thus, the time until the asteroid hits Mars is:
\[ \boxed{4.301 \times 10^3} \text{ hours} \]
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