An asteroid is heading toward Mars at the rate of 7.7 x 10^4 mi./hr. If the aster is 3.311 x 10^8 miles away from Mars, how many hours will the before it hits Mars, how many hours will it be before it hits Mars? Write the answer in scientific notation, expressed to the exact decimal place.
To find the time it takes for the asteroid to reach Mars, we can use the formula:
time = distance / rate
time = (3.311 x 10^8 miles) / (7.7 x 10^4 mi./hr)
To divide numbers in scientific notation, we divide the coefficients and subtract the exponents:
time = (3.311 / 7.7) x (10^8 / 10^4) = 0.42987 x 10^4
The number 0.42987 can be expressed in scientific notation as:
0.42987 = 4.2987 x 10^-1
Therefore, the time it will take for the asteroid to hit Mars is 4.2987 x 10^-1 x 10^4 hours.
Simplifying, we add the exponents:
10^-1 x 10^4 = 10^(4-1) = 10^3
So, the time it will take for the asteroid to hit Mars is 4.2987 x 10^3 hours.
To find how many hours it will be before the asteroid hits Mars, we can use the formula:
Time = Distance / Rate
Given:
Distance = 3.311 x 10^8 miles
Rate = 7.7 x 10^4 mi/hr
Substituting the values into the formula:
Time = (3.311 x 10^8 miles) / (7.7 x 10^4 mi/hr)
To divide numbers written in scientific notation, we need to divide their coefficients and subtract the exponents:
Time = (3.311 / 7.7) x (10^8 / 10^4) miles/hr
Simplifying the coefficients:
Time = 0.429220779 x 10^4 miles/hr
The time is expressed in scientific notation, with the coefficient rounded to the nearest decimal place and the same exponent:
Time = 0.429 x 10^4 miles/hr
Therefore, it will be approximately 0.429 x 10^4 hours before the asteroid hits Mars.
To find the number of hours it will take for the asteroid to hit Mars, we need to divide the distance between Mars and the asteroid by the rate at which the asteroid is moving.
Given:
Distance = 3.311 x 10^8 miles
Rate = 7.7 x 10^4 mi./hr.
To find the time in hours, we can use the formula:
Time = Distance / Rate
Substituting the given values into the formula:
Time = (3.311 x 10^8 miles) / (7.7 x 10^4 mi./hr.)
To divide numbers in scientific notation, we divide the coefficients and subtract the exponents:
Time = (3.311 / 7.7) x 10^(8-4) miles/hr.
Calculating the coefficient:
Time = 0.4296 x 10^4 miles/hr.
Simplifying the coefficient to one decimal place as requested:
Time = 0.4 x 10^4 miles/hr.
Expressing the answer in scientific notation:
Time = 4 x 10^3 miles/hr.
Therefore, it will take 4 x 10^3 hours for the asteroid to hit Mars.