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

Question

7.7
×
10
4
mi./hr. If the asteroid is 3.311×10^8
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 point)
hours

Answer 1

To determine how many hours it will take for the asteroid to hit Mars, we can use the formula for time, which is:

\[ \text{Time} = \frac{\text{Distance}}{\text{Rate}} \]

Here, the distance is \(3.311 \times 10^8\) miles, and the rate is \(7.7 \times 10^4\) miles per hour.

Now we can substitute the values into the formula:

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

To simplify this, we can perform the division:

1. Divide the coefficients: \[ \frac{3.311}{7.7} \approx 0.4300 (to 4 decimal places) \]

2. Subtract the exponents of \(10\): \[ 10^8 / 10^4 = 10^{8-4} = 10^4 \]

Now, combining both parts from the division:

\[ \text{Time} = 0.4300 \times 10^4 \]

To express this in proper scientific notation, we adjust it:

\[ 0.4300 \times 10^4 = 4.300 \times 10^3 \]

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

\[ \boxed{4.300 \times 10^3} \text{ hours} \]