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 out 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/hr

Now, we can substitute the values into the formula:

\[ \text{Time} = \frac{3.311 \times 10^8 \text{ miles}}{7.7 \times 10^4 \text{ miles/hr}} \]

To divide these numbers in scientific notation, we divide the coefficients and subtract the exponents:

\[ \text{Time} = \frac{3.311}{7.7} \times 10^{8 - 4} = \frac{3.311}{7.7} \times 10^4 \]

Calculating \(\frac{3.311}{7.7}\):

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

Now, substituting this back into our equation, we have:

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

Now, we can convert \(0.430\) into scientific notation:

\[ 0.430 = 4.30 \times 10^{-1} \]

Thus:

\[ \text{Time} \approx 4.30 \times 10^{-1} \times 10^4 = 4.30 \times 10^{3} \]

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

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