An asteroid is heading toward Mars at the rate of 7.7 × 10* 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 answer

To determine 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 to Mars = \(3.311 \times 10^8\) miles
  • Speed of the asteroid = \(7.7 \times 10^6\) miles/hour

Now, we can plug these values into the formula:

\[ \text{Time} = \frac{3.311 \times 10^8}{7.7 \times 10^6} \]

To simplify this, we'll divide the coefficients and subtract the exponents (since they are in scientific notation):

  1. Divide the coefficients:

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

  1. Subtract the exponents:

\[ 10^8 / 10^6 = 10^{8-6} = 10^2 \]

  1. Combine the results:

\[ \text{Time} \approx 0.430 \times 10^2 \]

  1. Convert to proper scientific notation:

\[ 0.430 \times 10^2 = 4.30 \times 10^1 \]

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

\[ \boxed{4.30 \times 10^1} \text{ hours} \]