An asteroid is heading toward Mars at the rate of 7.7×104 mi./hr. If the asteroid is 3.311×108 miles away from Mars, how many hours will it be before it hits Mars? Write the answer in scientific notation, expressed to the exact decimal place.(1 point)

__hours

1 answer

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:

\[ \boxed{4.309 \times 10^3} \text{ hours} \]