A calculated result is reasonable if it is close to a sensible estimate, has the expected order of magnitude and satisfies the restrictions of the context. Estimate using rounded input values before calculating accurately, then compare the two results.
How to Check Reasonableness
This is part of SL 1.6, Approximating and estimating, which is common to Mathematics: Applications and Interpretation SL and HL. The aim is not to reproduce the exact result, but to check whether it is plausible.
| Check | What to do | Warning sign |
|---|---|---|
| Estimate | Round inputs to convenient values and calculate mentally | The accurate result is far from the estimate |
| Order of magnitude | Check whether the answer should involve tens, hundreds or thousands | A misplaced decimal point changes the magnitude |
| Bounds | Use known upper and lower limits where appropriate | The result lies outside the possible interval |
| Context | Check units, signs and physical restrictions | Negative length, probability above , or a non-integer number of people |
For example, suppose
Estimate by rounding , , and :
The GDC gives
Since is close to and has the same order of magnitude, the result is reasonable. A result such as or would suggest a decimal-point or data-entry error.
A common misconception is that estimating means rounding the final answer. It does not: estimation normally means simplifying the input values first to predict the approximate size of the answer.
Exam Technique
In an IB response, show the rounded values and the estimated calculation, not only the statement “reasonable.” Then compare explicitly: “The calculated value is close to the estimate and has the correct order of magnitude, so it is reasonable.” Keep full GDC precision during the accurate calculation and round only the final result.
