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.(1 point)
The correct answer is 4.3x10 to the power of 3 hours.
To find the number of hours it will take for the asteroid to hit Mars, we divide the distance from Mars by the rate at which it is approaching.
Number of hours = distance from Mars / rate of approach
Number of hours = (3.311×10^8 miles) / (7.7×10^4 mi./hr)
We can simplify this by dividing the coefficients and subtracting the exponents.
Number of hours = (3.311 / 7.7) × 10^(8-4)
Number of hours = 0.429 × 10^4
Converting this number to scientific notation:
Number of hours = 4.29 × 10^(-1+5)
Number of hours = 4.29 × 10^4
Therefore, it will take approximately 4.29 × 10^4 hours for the asteroid to hit Mars.
To find the time it takes for the asteroid to hit Mars, we can use the formula:
Time = Distance / Rate
Given:
Rate = 7.7×10^4 mi./hr
Distance = 3.311×10^8 miles
Plugging in the values into the formula:
Time = 3.311×10^8 miles / 7.7×10^4 mi./hr
To divide the distances, we subtract the exponents since they have the same base:
Time = (3.311 / 7.7) × 10^(8 - 4) miles/hr
Simplifying the division:
Time ≈ 0.429 × 10^(8 - 4) miles/hr
Subtracting the exponents:
Time = 0.429 × 10^4 miles/hr
The final answer in scientific notation is approximately 4.29 x 10^3 hours.
To calculate the time it will take for the asteroid to hit Mars, we can use the formula:
Time = Distance / Speed
In this case, the distance is 3.311×10^8 miles and the speed is 7.7×10^4 mi/hr.
Plugging these values into the formula, we get:
Time = 3.311×10^8 miles / 7.7×10^4 mi/hr
To divide values in scientific notation, we can divide the numbers and subtract the exponents:
Time = (3.311 / 7.7) × 10^(8-4)
Simplifying the division:
Time = 0.4292 × 10^4
Now, we want to express the answer in scientific notation with the exact decimal place. With 4 as the exponent, we can write it as:
Time = 4.292 × 10^3
Therefore, it will take approximately 4.292 × 10^3 hours for the asteroid to hit Mars.