An asteroid is heading toward Mars at a 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

Answer 1

To find the time it will take for the asteroid to hit Mars, you can use the formula:

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

In this case, the distance is \(3.311 \times 10^8\) miles and the speed is \(7.7 \times 10^4\) mi/hr. Plugging in the values:

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

Now calculating this:

1. Divide the coefficients: \[ \frac{3.311}{7.7} \approx 0.43051 \]

2. Subtract the exponents (since we are dividing powers of 10): \[ 10^8 \div 10^4 = 10^{8 - 4} = 10^4 \]

Now putting it together:

\[ \text{Time} \approx 0.43051 \times 10^4 \]

To express it in proper scientific notation, we move the decimal point one place to the right, which increases the exponent by 1:

\[ = 4.3051 \times 10^3 \]

So, it will take approximately \(4.3051 \times 10^3\) hours for the asteroid to hit Mars.