Some of the basic prefixes used are: kilo 10 centi 10-2 micto 10 naio 10- Theref

Question

Some of the basic prefixes used are: kilo 10 centi 10-2 micto 10 naio 10- Therefore, a centimeter is equal to 10-2 meters. When combining quantities in mathematical equntions, it's important to be sware of the units involved. Sometimes we nced to convert from one unit of measurement to another Example: Convert 60.0 mph to meters/secoud, knowing that 1 mile The easiest way to do this is to write the numiber out Bs a fraction 1.61 kilometers. Then, next to the mumber write a series of fractions, such that the numerator of each fraction is equal to the denominator of each fraction, and the units of one cancel one of the wnits in a previous fraction Finally, canceling out all units on top with the same unit on bottom. The result is the converted value, multiply all of the numbers on top, dividing by all of the numbers on bottom, and 26.8 meters/second ROBLEMS Determine the following conversions. (1) How many centimeters are there in a kilometer? How many seconds are there in a year (given that there are 365.25 days in a year)? 6u 3) A lightyear is the distance light travels in one year. If light travels at a speed of 3.0 x 10 meters/second, how long is a lightyear in meters? onvert the following. ) 22 parsecs to lightyears (Given that 1 pc = 3.26 ly)

Explanation / Answer

1)

1 km = 1 km (1000 m/1 km) (100 cm /1 m )

1 km = 1000 x 100 cm = 105 cm

2)

1 year = 1 yr (365.25 days/1 yr) (24 hours/1 day) (3600 sec/1 hour)

1 year = (365.25) (24) (3600) sec = 3.2 x 107 sec

3)

v = speed of light = 3 x 108 m/s

t = time of 1 yr in second =  3.2 x 107 sec

distance is given as

d = v t = (3 x 108) ( 3.2 x 107) = 9.6 x 1015 m

hence 1 ly =  9.6 x 1015 m

22 parsec = 22 parsec (3.26 ly/1 pc) = 71.72 ly

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