A physics question i do not understand Please help

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The discussion focuses on calculating the area and volume of a room with dimensions 6.0 m x 4.0 m and a height of 3.0 m. To find the area in different units, the correct approach involves converting meters to centimeters and millimeters by using the appropriate conversion factors. The user is confused about the conversion process, particularly when squaring the conversion factors for area and cubing them for volume. It is clarified that when squaring the conversion factor for area (100 cm/1 m), both sides must be squared, resulting in 10,000 cm² per m². Understanding these conversions is essential for accurately calculating area and volume in various units.
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Homework Statement



The floor of a room measures 6.0 m x 4.0 m. Calculate its area in m^2, cm^2 and mm^2. The room height is 3.0. Calculate its volume in m^3, cm^3 and mm^3.

Homework Equations


centi = 10^-2
milli = 10^-3

The Attempt at a Solution


To get it into cm^2 and mm^3 i tried multiplying the numbers by the value of centi and milli but this is wrong. Please could you show me how to do it and explain why :D
Thank you so much! x
 
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If 100 centimeter = 1 meter, then the ratio 100cm/1m = 1, correct? What happens if you square both sides?
 

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