An asteroid is heading toward Mars at the rate of 7.7×10^4

mi./hr. If the asteroid is 3.311×10^8
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 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.

  1. Dividing the numeric parts: \[ \frac{3.311}{7.7} = 0.4301 \text{ (approximately)} \]

  2. 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.