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

Answer 1

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

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

Given:

• Distance to Mars = \( 3.311 \times 10^8 \) miles
• Speed of the asteroid = \( 7.7 \times 10^4 \) miles/hour

Now we can plug in the values:

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

To divide these values in scientific notation, we can 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 we can write it as:

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

To express \(0.430\) in proper scientific notation, we can rewrite it:

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

Thus:

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

So, the time before the asteroid hits Mars is:

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