The greatest possible error for a measurement typically depends on the precision of the measuring instrument used. In this case, since the doorway width is measured as 1.20 m, we can assume standard precision.
If we take the measurement to two decimal places (as indicated by 1.20 m), a common approach is to assume that the least count (or the smallest unit of measurement) is 0.01 m (or 1 cm). Therefore, the greatest possible error, often referred to as the absolute uncertainty, is half of the smallest unit, which is:
\[ \text{Greatest Possible Error} = \frac{0.01 m}{2} = 0.005 m \]
So, the greatest possible error of your measurement of the doorway width is ±0.005 m (or ±5 mm). This means the actual width could be as low as 1.195 m or as high as 1.205 m.