Am asteroid is heading toward mars at the rate of 7.7 x 10/4 mi./hr. If the asteroid is 3.311 x 10.8 miles away from Mars, how many hours will it be before it hits Mars? Write in scientific notation, expressed to the exact decimal
To find the number of hours before the asteroid hits Mars, we need to divide the distance between the asteroid and Mars by the rate at which the asteroid is moving.
Distance = 3.311 x 10.8 miles
Rate = 7.7 x 10^(-4) mi./hr
Number of hours before impact = Distance / Rate
= (3.311 x 10.8 miles) / (7.7 x 10^(-4) mi./hr)
To divide numbers in scientific notation, divide the coefficients and subtract the exponents:
= (3.311 / 7.7) x 10^(10.8 - (-4))
= 0.4299 x 10^(10.8 + 4)
Since 0.4299 is less than 1, we can express it in scientific notation:
= 4.299 x 10^(-1) x 10^(10.8 + 4)
To add the exponents, multiply the base by 10 raised to the sum of the exponents:
= 4.299 x 10^(-1 + 10.8 + 4)
= 4.299 x 10^(13.8)
So, it will be approximately 4.299 x 10^(13.8) hours before the asteroid hits Mars.