Light travels at an approximate rate of 1.9 × 10 mi./sec. There are about 3.2 x 107 seconds in a year. About
how many miles does light travel in a year? Write the answer in scientific notation. Express the answer to the
exact decimal place. (1 point)
To find the distance light travels in a year, we need to multiply the speed of light by the number of seconds in a year.
Speed of light = 1.9 × 10 mi./sec
Number of seconds in a year = 3.2 × 10^7 seconds
Distance light travels in a year = Speed of light × Number of seconds in a year
Distance light travels in a year = (1.9 × 10)(3.2 × 10^7)
To multiply two numbers in scientific notation, we multiply their coefficients and add their exponents:
Distance light travels in a year = 1.9 × 3.2 × 10^(1+7)
Distance light travels in a year = 6.08 × 10^8
Therefore, light travels approximately 6.08 × 10^8 miles in a year.
The average tectonic plate moves at the rate of 0.006 m per year. How many meters would it move in 2 x 106
years? Write the answer in scientific notation, expressed to the exact decimal place. (1 point)
? m
To find the distance the tectonic plate moves in 2 x 10^6 years, we need to multiply the rate of movement by the number of years.
Rate of movement = 0.006 m/year
Number of years = 2 x 10^6 years
Distance moved in 2 x 10^6 years = Rate of movement x Number of years
Distance moved in 2 x 10^6 years = 0.006 m/year x (2 x 10^6 years)
To multiply two numbers in scientific notation, we multiply their coefficients and add their exponents:
Distance moved in 2 x 10^6 years = 0.006 x 2 x 10^(0+6)
Distance moved in 2 x 10^6 years = 0.012 x 10^6
Since 0.012 is already in decimal notation, we don't need to convert it to scientific notation. The answer is approximately:
Distance moved in 2 x 10^6 years = 0.012 x 10^6 = 12,000 meters.
An asteroid is heading toward Mars at the rate of 7.7 × 104 mi./hr. If the asteroid is 3.311 × 10% 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)
To find the time it will take for the asteroid to reach Mars, we need to divide the distance between the asteroid and Mars by the rate of the asteroid.
Rate of the asteroid = 7.7 × 10^4 mi/hr
Distance between the asteroid and Mars = 3.311 × 10^? miles
We need to convert the distance between the asteroid and Mars to decimal notation first. We know that 10^7 miles is equal to 1 mile, so we divide the given distance by 10^7 to find the decimal value:
Distance between the asteroid and Mars = 3.311 × 10^? / 10^7 = 0.0000003311 miles
Now we can find the time it will take for the asteroid to hit Mars:
Time = Distance / Rate
Time = 0.0000003311 miles / 7.7 × 10^4 mi/hr
To divide two numbers in scientific notation, we divide their coefficients and subtract their exponents:
Time = (0.0000003311 / 7.7) × (10^(-4-4))
Time = 0.00000004296 × 10^(-8)
Since 0.00000004296 is already in decimal notation, we don't need to convert it to scientific notation. The answer is approximately:
Time = 0.00000004296 × 10^(-8) = 4.296 × 10^(-14) hours.
Therefore, it will be approximately 4.296 × 10^(-14) hours before the asteroid hits Mars.
A field of 3.9 mi? is being subdivided into 1.3 × 103 family gardens. How many square miles will there be in
each garden? Write the answer in scientific notation. (1 point)
To find the area of each garden in square miles, we need to divide the total area of the field by the number of family gardens.
Total area of the field = 3.9 mi²
Number of family gardens = 1.3 × 10³ gardens
Area of each garden = Total area of the field / Number of family gardens
Area of each garden = 3.9 mi² / (1.3 × 10³ gardens)
To divide two numbers in scientific notation, we divide their coefficients and subtract their exponents:
Area of each garden = 3.9 / 1.3 × 10^(0-3)
Area of each garden = 3.9 / 1.3 × 10^(3)
Simplifying the division:
Area of each garden = 3.9 / 1.3 × 10^(3)
Area of each garden = 3 × 10^(0-3)
Since 3 is already in decimal notation, we don't need to convert it to scientific notation. The answer is:
Area of each garden = 3 × 10^(-3) mi².
Therefore, each garden will have an area of approximately 3 × 10^(-3) square miles.