The speed of light in a vacuum is exactly c 299792458 meters

The speed of light in a vacuum is exactly c 299792458 meters per second and an international yard is exactly 0.9144 meters. A commonly used approximation for the speed of light is 186,000 miles per second. a. Calculate the relative error in approximating with 186,000 miles per second. Converting this approximation to meters per second, the percent relative error is percent. b. Acommonly used factor for converting measurements in inches to to centimeters is 2.54 centimeters per inch. The relative emcrin using this approximation is

Solution

1 mile = 1760 yards

1 mile = 1760 * 0.9144 m= 1609.344 meters

c= 299792458 m/s = 186282.3971 miles per second

Approximated speed of light c\' = 186000 miles per second = 299337984 meters per second

Relative error = c - c\' = 454474 m/s = 282.3971 miles per second

Percent relative error = (c - c\')/c *100 = 0.1516%

1 yard = 36 inches = 0.9144 m = 91.44 cm

1 inch = 2.54 cm

Its equal to approximated value 2.54 cm.