An asteroid is heading toward Mercury at a rate of 15.4 x10 mi./hr. If the asteroid is 6.622 * 10 ^ 8 miles away from Mercury, how many hours will it be before it hits Mercury? Write the answer in scientific notation, expressed to the exact decimal place.
To find the time it takes for the asteroid to hit Mercury, we need to divide the distance between the asteroid and Mercury (6.622 * 10^8 miles) by the rate at which it is approaching (15.4 * 10^6 miles/hour).
To divide numbers in scientific notation, we divide the coefficients and subtract the exponents.
(6.622 * 10^8 miles) / (15.4 * 10^6 miles/hour) = (6.622 / 15.4) * 10^(8 - 6) = 0.429 OD * 10^2 = 4.29 * 10^(-0.6875) hours
Therefore, it will take approximately 4.29 * 10^(-0.6875) hours for the asteroid to hit Mercury.
To find the number of hours it will take for the asteroid to hit Mercury, we need to divide the distance between the asteroid and Mercury by the speed of the asteroid.
Distance: 6.622 * 10^8 miles
Speed: 15.4 * 10^6 mi/hr
To divide the distances, we subtract the exponents:
8 - 6 = 2
To divide the speeds, we subtract the exponents:
6 - 6 = 0
Now, we divide the distance by the speed:
6.622 * 10^8 miles / 15.4 * 10^6 mi/hr
When we divide the numbers, we subtract the exponents:
8 - 6 = 2
The result is:
6.622 / 15.4 * 10^2
Simplifying the division, we get:
0.42987012987012987012987012987013 * 10^2
In scientific notation, the answer is:
4.30 * 10^0, which is equivalent to 4.30 in decimal notation.
Therefore, it will take approximately 4.30 hours before the asteroid hits Mercury.
To find the number of hours it will take for the asteroid to hit Mercury, we need to divide the distance to be covered by the rate at which the asteroid is moving.
Distance = 6.622 * 10^8 miles
Rate = 15.4 * 10^6 miles per hour
To divide these two values, we subtract the exponents of 10 and divide the coefficients:
(6.622 * 10^8) / (15.4 * 10^6) = (6.622 / 15.4) * (10^8 / 10^6) = 0.42922077922 * 10^2
The resulting value is approximately 0.42922077922 times 10 squared. We can represent it in scientific notation as:
4.2922 x 10^0
However, since the question asks for the answer in scientific notation to the exact decimal place, we need to move the decimal point one place to the right, resulting in a coefficient of 42.922:
42.922 x 10^0
Therefore, it will take approximately 42.922 hours for the asteroid to hit Mercury.