Light travels at an approximate rate of 1.9. x 10^5 mi/sec. There are about 3.2 x 10^7 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.

Answer 1

To find the number of miles light travels in a year, we multiply the rate of light by the number of seconds in a year:

1.9 x 10^5 mi/sec * 3.2 x 10^7 sec/year

To multiply these numbers, we add their exponents and multiply their coefficients:

(1.9 * 3.2) * (10^5 * 10^7) mi

6.08 * 10^(5+7) mi

6.08 * 10^12 mi

In scientific notation, light travels approximately 6.08 x 10^12 miles in a year.

Answer 2

The average tectonic plate moves at the rate of 0.006 m per year. How many meters would it move in 2 x 10^6 years? Write the answer in scientific notation, expressed to the exact decimal place.

Answer 3

To find the number of meters the tectonic plate would move in 2 x 10^6 years, we multiply the rate of movement (0.006 m/year) by the number of years:

0.006 m/year * 2 x 10^6 years

To multiply these numbers, we multiply their coefficients and add their exponents:

(0.006 * 2) * (10^6 m * 1 year)

0.012 * 10^6 m

To express this answer in scientific notation to the exact decimal place, we multiply the coefficient by 10 and decrease the exponent by 1:

1.2 * 10^5 m

Therefore, the tectonic plate would move approximately 1.2 x 10^5 meters in 2 x 10^6 years.