Final answer:
The correct ratio for reproducing a 4 cm by 4 cm picture on a 3 mm by 3 mm well is 1:4 or 1/4. This represents a scale factor, which can be applied to find the actual dimension when only the scale dimension is known.
Step-by-step explanation:
The question is asking for the correct ratio to use when reproducing a 4 cm by 4 cm picture on a smaller 3 mm by 3 mm well. Scale factor is an important concept in this context. To determine the appropriate scale ratio from the original picture size to the new size, you'll need to convert the measurements to the same units and then calculate the ratio. Since there are 10 mm in 1 cm, a 4 cm dimension is equal to 40 mm. Therefore, the scale ratio would be 3 mm (new size) to 40 mm (original size), which simplifies to 1:4 or 1/4.
By understanding this concept, you can apply it to other problems as well. For example, when given the scale dimension and asked to find the actual dimension, you would set up a proportion. If you had a scale ratio of 1:4 and a scale dimension of 4, the proportion would be 1:2=4:x, where x is the actual dimension that you are trying to find.