Should the ISO 6789:2003 deviation example use 100 or 104?
Applies to: ISO 6789:2003 · Updated 2026-10-28
Technical review: Alston Hsiao (Chieh-Jen Hsiao), CTO, STAND
Clause 6.5, EXAMPLE 1 of ISO 6789:2003 lists x_r1 = 100 N·m but uses 104 N·m in the subsequent calculation; only the latter reproduces −3.85 %, so we consider a misprint in the initial reference value more likely. This is not an official ISO corrigendum, nor does a closer match to an expected result justify changing actual measurement records.
Check the tool value and reference value separately
First locate the example’s tool value, x_a = 100 N·m, then its first reference value, x_r1 = 100 N·m. Compare them with the subsequent calculation of the first deviation. The discrepancy is that the calculation uses 104 in both the numerator and denominator instead of the listed reference value. The tool value remains unchanged; do not replace both quantities together.
The original result is written as −3,85 %, with a comma as the decimal separator; this article uses decimal points in its explanation. That typographical difference does not explain the inconsistent reference values. Check how a number is written separately from which quantity is substituted, so the issue is not mistaken for a decimal-separator or symbol-transcription problem.
Why only one value reproduces the result
Under the deviation formula in 6.4, subtract the reference value from the tool value and use the reference value as the denominator. Keep the tool value unchanged and substitute each of the conflicting reference values to check both calculation paths. The following is our recalculation of the disputed first reading, not a reproduction of a table from the standard.
| Reference value used (N·m) | Our recalculation of A_s1 (%) | Result (%) |
|---|---|---|
| 100 | (100 − 100) × 100／100 | 0 |
| 104 | (100 − 104) × 100／104 | −3.846153… ≈ −3.85 |
In the first path, equal tool and reference values produce zero deviation. The second matches both the substitution in the original calculation and its reported percentage. The basis for our reading is therefore a reproducible calculation, not merely the observation of different numbers. This makes a misprint in the initial reference value the more likely explanation.
Recalculation can establish which set of values agrees with the reported result. It cannot establish what was actually measured or make replacing the initial value with the calculation’s value an official correction.
Cite the example and calculate transparently
When citing the example, record the standard edition, clause, original entries, and adopted reading together, retaining both recalculations. To reproduce the percentage printed in the example, state explicitly that you are using the reference value from its calculation. If you instead calculate with the initially listed value, retain the zero-deviation result. Do not mix the calculation paths.
For actual tool data, use traceable original readings rather than selecting a number to fit the example’s expected answer. Preserve this edition’s sign convention and denominator in the report; do not change formulas to make a result resemble another document. The issue concerns the example’s numerical consistency, not the subtraction order in the deviation formula itself.
This is our reading, not an official ISO corrigendum. When citing this ISO 6789:2003 example, note the inconsistent values in the original text and identify the reference value used in the recalculation.