1) what is the smallest scale increment of the ruler? 2) what is the distance represented by the dotted line "a" and how much uncertainty is there in this measurement? 3) what is the distance represented by the dotted line "b" and how much uncertainty is there in this measurement?

1) The smallest scale increment is 0.1 cm.

2) The distance represented by the dotted line "a" is 5.25 cm and the uncertainty in this measurement is ± 0.05.

3) The distance represented by the dotted line "b" is 5.85 cm and the uncertainty in this measurement is ± 0.05.

Explanation:

1) The smallest scale increment is 0.1 cm.

That the distance between any two numbers on the ruler (for example; 4&5) is 1.0 cm.There are 10 increments between the two numbers which means that the increment scale (the smallest scale increment) is 0.1 cm.

2) The distance represented by the dotted line "a" is 5.25 cm.

The dotted line "a" lies between 5.2 and 5.3 and it is mainly in the middle between the two smallest increments ≅ 5.25.The uncertainty in this measurement is ± 0.05 as shown in the image attached in the question that the measurement may be off by as much as 0.05 cm above or below its true value.

2) The distance represented by the dotted line "b" is 5.85 cm.

The dotted line "b" lies between 5.8 and 5.9 and it is mainly in the middle between the two smallest increments ≅ 5.85.The uncertainty in this measurement is ± 0.05 as shown in the image attached in the question that the measurement may be off by as much as 0.05 cm above or below its true value.