1. **State the problem:** We have a barometer reading of 1013.5 hPa with an absolute error less than 0.3 hPa. We need to find the possible range of the actual atmospheric pressure. 2. **Formula and explanation:** The actual pressure $P$ lies within the range given by the reading plus or minus the absolute error: $$1013.5 - 0.3 < P < 1013.5 + 0.3$$ This means the actual pressure can be as low as $1013.5 - 0.3$ and as high as $1013.5 + 0.3$. 3. **Calculate the bounds:** Lower bound: $$1013.5 - 0.3 = 1013.2$$ Upper bound: $$1013.5 + 0.3 = 1013.8$$ 4. **Interpretation:** The actual atmospheric pressure is between 1013.2 hPa and 1013.8 hPa. **Final answer:** $$1013.2\ \text{hPa} < \text{actual atmospheric pressure} < 1013.8\ \text{hPa}$$