Final answer:
In the metric system, 4 cm converts to 0.04 m and 3 m converts to 300 cm. Therefore, the simplest form of 4 cm to 3 m ratio would be 1:75 (in cm) or 0.01333:1 (in m).
Step-by-step explanation:
The question pertains to the conversion of units in the metric system, specifically, from centimeters to meters. The key to understanding this conversion is recognizing that the metric system is designed around powers of 10, which makes conversions straightforward. In this case, we know that there are 100 centimeters in one meter. Therefore, to convert 4 cm to meters, you would divide it by 100, yielding 0.04 m. Simultaneously, 3 meters is equivalent to 300 cm.
Therefore, if we structure the original ratio (4 cm to 3 m) in terms of the same units, it would convert to a ratio of 4 cm to 300 cm or 0.04 m to 3 m. Simplifying the ratio in both cases gives 1:75 (for the cm to cm case), and 0.01333:1 (for the m to m case).
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