Final answer:
Measurement precision varies with the ruler used; whole centimeter measurements can be certain with any ruler, but tenths and hundredths places are more precise with a millimeter-marked ruler, reducing variation. Without seeing the actual Model 2 ruler, we can ascertain that the value '3 cm' is certain but cannot determine the full exactness of tenths and hundredths.
Step-by-step explanation:
The question asks about the measurements that can be certain on a ruler (Model 2) and understanding the precision of different rulers by comparing them in terms of the variation in measurements provided by students. With either ruler, since the object's length is between 2 and 3 cm, the ones place is certain. However, the tenths digit varies with estimation and is more certain with a ruler that has millimeter markings, allowing for a more precise measurement.
Using the available information, let us address your questions:
- What distances can you be certain of on this ruler? The correct answer cannot be determined without seeing Model 2 ruler. However, with any ruler, you can be certain of the whole centimeters. Therefore, we can be certain at least of the 3 cm value.
- Were the students able to agree on a single value for any digit in their measurements using the ruler in Model 2? Yes, students would agree on whole centimeters represented by the ones place - namely, the value '3' in this case.
- What feature of the ruler in Model 2 made it possible to agree on a value in that digit? The known certainty of the ones place (whole centimeters) makes this agreement possible.
- Which ruler resulted in greater variation? Without the specifics on Model 1, if it is similar to the bottom ruler with no millimeter markings mentioned in the reference, it would have caused greater variation as it would only allow certainty in the ones place, but not in the tenths or hundredths places.