Measurement applications: limits of accuracy

Task goals

• Apply the convention that a measurement "given to the nearest X" has an implied tolerance of plus-or-minus half of X, and state the resulting interval of possible true values.
• Calculate the central (best) estimate of a measurement-based quantity -- area, perimeter, or volume -- from the given measurements.
• Recompute the same calculation using the most extreme plausible combination of inputs to find the minimum possible final answer.
• Recompute the same calculation using the most extreme plausible combination of inputs to find the maximum possible final answer.
• Correctly identify, for a given formula's structure, which extreme (upper or lower bound) of EACH input genuinely produces the overall minimum or maximum -- recognising that for a calculation containing a subtraction step, the minimum of the total can require the MAXIMUM of the subtracted piece, not a blind "all lower bounds" rule.
• Propagate two or more compounding measurement tolerances (from different measured quantities, potentially with different stated precisions) through a multi-step calculation.
• Use a calculated minimum or maximum bound as an input to a further material-quantity, discrete-purchase, or cost calculation.
• Determine whether a calculated uncertainty range changes a real-world decision (a discrete-purchase quantity, a budget compliance check, or a minimum-size requirement), and justify the conclusion with the actual minimum/maximum figures.
• Recognise that an uncertainty range sometimes does NOT change the real-world decision, and explain why the central estimate alone was already a safe enough basis for that particular decision.
• Communicate a written discussion of measurement uncertainty's real-world significance, referencing the specific minimum/maximum values found.