Question

Question
NASA scientists are tracking an asteroid that is on a potential collision course with Mars. Using telescopes and radar, they calculate that the asteroid is currently 3.311 × 10⁸ miles away from the planet. Their data also shows that the asteroid is moving steadily at an average speed of 7.7 × 10⁴ miles per hour.

If the asteroid continues at this constant speed, approximately how many hours will it take to reach Mars? Express your answer in scientific notation.

(1 point)
Responses

4.3×105
hr
4 point 3 times 10 to the 5th power hr

4.3×106
hr
4 point 3 times 10 to the 6th power hr

4.3×103
hr
4 point 3 times 10 cubed hr

4.3×104
hr

Answer 1

To find the time it takes for the asteroid to reach 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 per hour

Now, substituting these values into the formula:

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

To divide the numbers in scientific notation, we perform the division of the coefficients and subtract the exponents:

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

Calculating the coefficient:

\[
\frac{3.311}{7.7} \approx 0.4303
\]

And for the exponent:

\[
10^{8-4} = 10^4
\]

Combining these results, we have:

\[
\text{Time} \approx 0.4303 \times 10^4
\]

To express this in proper scientific notation, we convert \(0.4303\) to \(4.303\) by shifting the decimal one place to the right, which means we must decrease the exponent by 1:

\[
\text{Time} \approx 4.303 \times 10^3
\]

Rounding \(4.303\) to 2 significant figures gives us \(4.3\):

\[
\text{Time} \approx 4.3 \times 10^3 \text{ hr}
\]

Thus, the approximately time for the asteroid to reach Mars is:

\[
\boxed{4.3 \times 10^3 \text{ hr}}
\]