Answer :
Final answer:
Dimensional analysis is used to convert 3 weeks to milliseconds, 38.1 ft/s to miles/h, and 554 m/(day-kg) to cm^2/(min g). For example, to convert 3 weeks to milliseconds, it is done in steps using conversions of weeks to days, days to hours, hours to minutes, minutes to seconds, and seconds to milliseconds.
Explanation:
To convert the given measurements, we will use the dimensional analysis method. This method involves using conversion factors which are equations that relate two different units. A conversion factor allows us to convert from one unit to another.
To convert 3 weeks to milliseconds:
(a) We start by writing down the value we want to convert, then multiply by a conversion factor in which the unit we start with (in this case, weeks) is in the denominator, and the unit we want to get to (milliseconds) is in the numerator.
- 1 week = 7 days
- 1 day = 24 hours
- 1 hour = 60 minutes
- 1 minute = 60 seconds
- 1 second = 1,000 milliseconds
The conversion becomes: 3 wk * (7 day / 1 wk) * (24 hr / 1 day) * (60 min / 1 hr) * (60 sec / 1 min) * (1,000 ms / 1 sec) = 1,814,400,000 ms.
The other conversions follow similar steps. Remember to always check that the units cancel out correctly.
Learn more about Dimensional Analysis here:
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