Really basic, simple concept question

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Converting metric SI units requires understanding the relationship between different units, particularly when dealing with volume and density. For example, converting 2.7 g/cm^3 to g/m^3 involves recognizing that 1 cm^3 equals 1E-6 m^3, leading to the conversion resulting in 2.7E6 g/m^3. The general rule for converting units is to apply the conversion factor consistently across dimensions, whether for area or volume. When converting units, squaring or cubing the conversion factor is necessary for area or volume, respectively. Mastery of these rules simplifies the process of unit conversion in scientific contexts.
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it's been a while since I've taken any math based classes (all chem and bio for the last few years)... kinda embaressing but what are the rules in converting metric system s.i. units?

i.e. with 2.7 g/cm^3 into meters

would it be .027g/m^3 or would it be 2.7E-6 g/m^3 (cuz i know it would be the second one with volume, but since it is a denomenator here I am not 100% sure)


... what are the general rules when converting units that aren't simply meter or grams, etc.
 
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It can be tricky.
1cm = 0.01m
so 1cm^2 = (0.01m)^2 = 0.0001 m^2
1/cm = 1/0.01m
1/cm^2 = 1/0.01m^2 = 1/0.0001 m^2
1/cm^3 = 1/0.01m^3 = 1/0.000001 m^3 = 1/10^-6 m^3 = 10^6 m^3
 
Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?

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