An asteroid is heading toward Mars at the rate of 7.7 × 104

Question

mi/hr. If the asteroid is 3.311 × 108
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)
a × 10b

a =

b =

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

Now, we can plug in the values:

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

First, we will divide the coefficients:

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

Next, we will handle the powers of 10:

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

Now we can combine these results:

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

To express this in proper scientific notation, we need a format of \( a \times 10^b \) where \( 1 \leq a < 10 \). We can convert \( 0.430 \times 10^4 \) to scientific notation:

\[ 0.430 \times 10^4 = 4.30 \times 10^3 \]

Thus, in scientific notation:

• \( a = 4.30 \)
• \( b = 3 \)

Final answer:

• \( a = 4.30 \)
• \( b = 3 \)