1. **State the problem:** We have a rectangle with length $64$ mm and width $37$ mm, each measured correct to the nearest millimeter. We want to understand the possible range of the rectangle's dimensions due to this rounding. 2. **Understanding the rounding:** When a measurement is rounded to the nearest millimeter, the actual length could be up to $0.5$ mm more or less than the stated value. 3. **Calculate the possible ranges:** - Length range: from $64 - 0.5 = 63.5$ mm to $64 + 0.5 = 64.5$ mm - Width range: from $37 - 0.5 = 36.5$ mm to $37 + 0.5 = 37.5$ mm 4. **Interpretation:** This means the actual length could be anywhere between $63.5$ mm and $64.5$ mm, and the actual width could be anywhere between $36.5$ mm and $37.5$ mm, due to rounding to the nearest millimeter.