An asteroid is heading toward Mars at the rate of 7.7×104

Question

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.

Answer 1

To find 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:

• Distance = \(3.311 \times 10^8\) miles
• Speed = \(7.7 \times 10^4\) miles per hour

Now, substituting the 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 can first divide the coefficients and then the powers of ten:

1. Divide the coefficients:

\[ \frac{3.311}{7.7} \approx 0.430 \]

2. Divide the powers of ten:

\[ 10^8 / 10^4 = 10^{8-4} = 10^4 \]

Now, combine the results:

\[ \text{Time} \approx 0.430 \times 10^4 \]

To express \(0.430 \times 10^4\) in proper scientific notation, we adjust it to \(4.30 \times 10^3\) (moving the decimal point one place to the right).

Thus, the time it will take for the asteroid to hit Mars is:

\[ \boxed{4.30 \times 10^3} \text{ hours} \]