An asteroid is heading toward Mars at the rate of 7.7×104 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.
To find the number of hours it will take for the asteroid to hit Mars, we need to divide the distance between the asteroid and Mars by the rate at which it is traveling towards Mars:
Time = Distance / Rate
Time = (3.311×10^8 miles) / (7.7×10^4 mi./hr)
To divide these numbers in scientific notation, we can subtract the exponents of 10 and divide the coefficients:
Time = (3.311/7.7)×(10^8/10^4) hours
Simplifying, we have:
Time = 0.42948052×10^4 hours
Since we want the answer in scientific notation, we need to convert this to a single-digit coefficient:
Time = 4.2948052×10^3 hours
Therefore, it will take approximately 4.2948052×10^3 hours for the asteroid to hit Mars.
To solve this problem, we can use the formula: time = distance / rate.
Given:
Rate = 7.7 × 10^4 mi./hr
Distance = 3.311 × 10^8 miles
Substituting these values into the formula, we get:
Time = (3.311 × 10^8 miles) / (7.7 × 10^4 mi./hr)
To divide these numbers with exponents, we subtract the exponents:
Time = (3.311 / 7.7) × (10^8 / 10^4) miles / mi.
Simplifying the expression:
Time = 0.429 × 10^(8 - 4) hr
Time = 0.429 × 10^4 hr
Writing the final answer in scientific notation, we have:
Time = 4.29 × 10^3 hr
To find the number of hours it will take for the asteroid to hit Mars, we can use the formula:
Time = Distance / Speed
Given:
Distance = 3.311 × 10^8 miles
Speed = 7.7 × 10^4 mi./hr
Substituting the given values into the formula:
Time = (3.311 × 10^8 miles) / (7.7 × 10^4 mi./hr)
We can simplify this expression by dividing the coefficients and subtracting the exponents:
Time = (3.311 / 7.7) × 10^(8 - 4) hours
Time = 0.42987 × 10^4 hours
Since scientific notation has only one digit before the decimal point, we can rewrite this as:
Time ≈ 4.3 × 10^3 hours
Therefore, it will be approximately 4.3 × 10^3 hours before the asteroid hits Mars.