# Demonstrate how to convert miles/hour to cm/s by converting 45 mi/h to cm/s.

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### 1 Answer

The best way to do any kind of conversion, but especially those which switch between the English system and SI (metric system) is to use conversion factors.

A conversion factor is a fraction which is created from a mathematical expression of a definition relating measured quantities. The fraction is constructed in such a way as to cause the units we wish to eliminate will cancel and the units we wish to have left remain.

To do this conversion we need to have some expressions that relate the quantities to be changed. They would be

1.0 miles = 1.6 km which gives two conversion factors 1.0 mi/1.6 km and 1.6 km/1.0 mi

1.0 km = 1,000 m = 100,000 cm which gives the conversions 1.0km/100,000cm and 100,000cm/1km

1.0 hour = 3,600 s which gives 1.0h/3,600s and 3,600s/1.0h

To change 45 mile/hour we need to multiply by the appropriate fractions

45 mi/h X 1.6 km/1.0 mi = 72 km/h

72 km/h X 100,000cm/km = 7,200,000 cm/h

7,200,000 cm/h X 1.0 h/3,600s = 2,000 cm/s

Or we can do it in one string of calculations:

45 mi/h X 1.6km/mi X100,000 cm/km X 1.0 hr/3,600 s =

2,000 cm/s