Question

An asteroid is heading toward Mars at the rate of 7.7×104
7.7
×
10
4
mi./hr. If the asteroid is 3.311×108
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)

Answer 1

To find out how many hours it will take for the asteroid to hit Mars, we can use the formula:

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

Given that the distance to Mars is \(3.311 \times 10^8\) miles and the rate at which the asteroid is approaching is \(7.7 \times 10^4\) miles per hour, we can substitute these values into the formula:

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

Now, we can perform the division:

1. Divide the coefficients:
\[
\frac{3.311}{7.7} \approx 0.430
\]

2. Subtract the exponents:
\[
10^8 \div 10^4 = 10^{8 - 4} = 10^4
\]

Now, combine the results:

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

To express this in proper scientific notation, we adjust \(0.430\) to \(4.30\) and decrease the exponent by 1:

\[
4.30 \times 10^{3}
\]

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

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