To find the measure of AC, we follow the steps based on the problem description.
1. **Identifying the Problem**: Nozomi constructs a copy of segment AB, which has a length of 22.3 millimeters, using point B as an endpoint.
2. **Drawing the Segment**: When constructing a copy of segment AB starting at point B, we place point C such that BC is equal in length to AB.
3. **Finding Lengths**: Since AB is 22.3 mm, and segment BC (the copy of AB) is also 22.3 mm, we have:
- \( AB = 22.3 \text{ mm} \)
- \( BC = 22.3 \text{ mm} \)
4. **Adding the Lengths**: To find the total length of AC, we add the lengths of AB and BC:
\[
AC = AB + BC = 22.3 \text{ mm} + 22.3 \text{ mm} = 44.6 \text{ mm}
\]
Thus, the measure of AC is **44.6 millimeters**.