Short Answer
Rule Statement: Significant Figures and Tolerance Rounding
In engineering drawings, significant figures and decimal places are not decorative. They encode precision, inspection resolution, and conformance rules. A dimension such as 25.0 mm has three significant figures and one decimal place; 25 mm has two significant figures and no decimal place. Under standards such as ASME Y14.5-2018 and ISO 129-1:2018, the number of decimal places often signals the tolerance class or the required measurement resolution.
The central rule is: do not round a measured value before comparing it to a tolerance limit unless the governing standard or drawing explicitly requires rounding. ASTM E29-22 provides a standard practice for using significant digits in test data to determine conformance. ISO 80000-1:2009 Clause 5.3.3 gives general rounding rules. The GUM (JCGM 100:2008) Clause 7.2.2 governs how to report uncertainty with an appropriate number of significant digits.
Round only at the final reporting step. Compare unrounded values to tolerance limits; then round the reported result to the precision justified by the measurement and the drawing.
For calculations, use the classic rules: addition and subtraction are governed by decimal places; multiplication and division are governed by significant figures. Tolerances themselves are absolute limits, not significant-figure quantities. See our related rules on Addition and Subtraction, Multiplication and Division, and Rounding Methods.
Visual/Digit Map: Reading Significance on a Drawing
The following digit map shows how trailing zeros, leading zeros, and notation affect significance.
| Number | Significant Figures | Decimal Places | Drawing Interpretation |
|---|---|---|---|
| 25 | 2 | 0 | Ambiguous trailing zero; often governed by general tolerance block. |
| 25.0 | 3 | 1 | Trailing zero after decimal is significant; indicates tenths precision. |
| 25.00 | 4 | 2 | Indicates hundredths precision; tighter inspection resolution. |
| 0.004560 | 4 | 6 | Leading zeros are not significant; trailing zero is significant. |
| 1200 | 2, 3, or 4 | 0 | Ambiguous unless overline or scientific notation is used. |
| 1.200 × 103 | 4 | 3 | Scientific notation removes ambiguity: 1.200e3 has 4 sig figs. |
Standards Citation: What Governs Tolerance Rounding?
- ASME Y14.5-2018, Dimensioning and Tolerancing, Section 2.3: dimensions should be specified to the number of decimal places appropriate to the tolerance and inspection method.
- ISO 129-1:2018, Technical product documentation — Indication of dimensions and tolerances, Clause 5.2: decimal places, trailing zeros, and dimension indication conventions.
- ASTM E29-22, Standard Practice for Using Significant Digits in Test Data to Determine Conformance with Specifications, Sections 6–7: rounding and significant-digit rules for conformance decisions.
- ISO 80000-1:2009, Quantities and units — Part 1: General, Clause 5.3.3: rounding and significant figures in quantity values.
- JCGM 100:2008 (GUM), Evaluation of measurement data — Guide to the expression of uncertainty in measurement, Clause 7.2.2: reporting uncertainty and significant digits.
Convention Comparison Table
| Context | Rounding Rule | Trailing Zeros | Application to Drawings |
|---|---|---|---|
| ASTM E29-22 | Round observed values to the number of significant digits specified for conformance. | Significant if after decimal or specified by notation. | Used for inspection conformance decisions when invoked by contract. |
| ISO 80000-1:2009 | Round to the required number of significant digits; use half-up or half-even as specified. | Significant when they are required to express precision. | General quantity-value rounding; supports SI and drawing notation. |
| GUM (JCGM 100:2008) | Report uncertainty to one or two significant digits; match measurement decimal place. | Trailing zeros in uncertainty are significant. | Used when measurement uncertainty is reported with a drawing check. |
| ASME Y14.5 / ISO 129-1 | Tolerances are absolute limits; decimal places communicate precision. | 25.0 and 25.00 imply different precision. | Primary drawing conventions for dimensions and tolerances. |
Worked Examples
Example 1: Conformance Check with a Tolerance
A drawing specifies 12.50 ± 0.05 mm. The tolerance limits are 12.45 mm to 12.55 mm. An inspection reads 12.543 mm.
- Do not round 12.543 first.
- Compare 12.543 to the upper limit 12.55.
- 12.543 < 12.55, so the part is within tolerance.
- Report the result as 12.543 mm or round to 12.54 mm if the inspection procedure requires two decimal places.
If the reading were 12.554 mm, it exceeds 12.55 mm and is out of tolerance. Rounding it to 12.55 mm before comparison would incorrectly accept it. This is why ASTM E29-22 and good metrology practice require conformance decisions on unrounded or properly rounded values, not convenient values.
Example 2: Unit Conversion on a Drawing
Convert 1.250 in to millimetres. The exact conversion is 1 in = 25.4 mm.
- 1.250 × 25.4 = 31.75 mm.
- 1.250 has four significant figures; 25.4 is an exact conversion factor.
- The result is 31.75 mm, which has four significant figures.
- If the drawing tolerance is ±0.01 mm, keep 31.75 mm. Do not round to 31.8 mm unless the drawing tolerance permits it.
Example 3: Adding Toleranced Dimensions
Two dimensions are stacked: 10.0 ± 0.1 and 5.00 ± 0.01.
- Nominal sum: 10.0 + 5.00 = 15.00.
- Worst-case tolerance: 0.1 + 0.01 = 0.11.
- Report the stack as 15.00 ± 0.11, not 15.0 ± 0.1.
The tolerance has hundredths precision, so the nominal dimension in the tolerance expression should also be shown to hundredths. This is a drawing convention, not a significant-figure multiplication rule.
Counter-Examples: Common Errors in Tolerance Rounding
- Rounding before comparison: 12.554 mm rounded to 12.55 mm appears to meet 12.50 ± 0.05, but the true value exceeds the upper limit.
- Treating 25 and 25.0 as identical: On a drawing, 25.0 indicates tenths precision; 25 may be governed by a general tolerance block and is ambiguous about trailing zeros.
- Applying multiplication/division sig-fig rules to tolerances: Tolerances add linearly for worst-case stack-up. Significant figures do not truncate the tolerance limits.
- Double rounding: 2.4445 → 2.445 → 2.45 is wrong if two decimal places are required. Round once: 2.44.
- Ignoring the general tolerance block: A dimension without a stated tolerance may still have a default tolerance based on decimal places.
Common Mistakes
- Using a significant-figures calculator to change tolerance limits instead of only to verify reporting precision.
- Assuming exact conversion factors, such as 25.4 mm/in, limit the significant figures of a converted drawing dimension.
- Reporting a measurement with more decimal places than the tolerance or instrument justifies.
- Forgetting that trailing zeros after a decimal point are significant: 25.0 has three significant figures.
- Mixing decimal-place rules and significant-figure rules in the same calculation without tracking which rule applies.
Quick Reference Table
| Situation | Rule | Example |
|---|---|---|
| Addition/subtraction | Round to least number of decimal places. | 10.0 + 5.00 = 15.0 |
| Multiplication/division | Round to least number of significant figures. | 2.50 × 3.0 = 7.5 |
| Tolerance comparison | Compare unrounded value to limits; round only for report. | 12.543 within 12.45–12.55 |
| Trailing zeros | After a decimal, they are significant. | 25.0 = 3 sig figs |
| Unit conversion | Exact factors do not limit sig figs; measured values do. | 1.250 in = 31.75 mm |
| Tolerance stack | Add tolerances linearly for worst-case; match decimal places. | 10.0 ± 0.1 + 5.00 ± 0.01 = 15.00 ± 0.11 |
Practice Problems
- A drawing dimension is 8.00 ± 0.02 mm. A measurement reads 8.024 mm. Is it in tolerance? Answer: No. Limits are 7.98–8.02 mm; 8.024 > 8.02. Rounding to 8.02 would be wrong.
- Convert 0.750 in to millimetres. If 0.750 is a measured value, how many significant figures should the result have? Answer: 0.750 × 25.4 = 19.05 mm. As a measured value with three sig figs, report 19.1 mm. As a drawing dimension, 19.05 mm may be exact by definition.
- Add 3.4 ± 0.1 and 2.56 ± 0.02. What is the nominal and worst-case tolerance? Answer: Nominal 5.96; tolerance ±0.12. Report 5.96 ± 0.12, not 6.0 ± 0.1.
Sources & Further Reading
- ASTM E29-22, Standard Practice for Using Significant Digits in Test Data to Determine Conformance with Specifications, ASTM International.
- ISO 80000-1:2009, Quantities and units — Part 1: General, ISO.
- ASME Y14.5-2018, Dimensioning and Tolerancing, ASME.
- JCGM 100:2008, Evaluation of measurement data — Guide to the expression of uncertainty in measurement (GUM), BIPM.
- ISO 129-1:2018, Technical product documentation — Indication of dimensions and tolerances — Part 1: General principles, ISO.
FAQ
Are significant figures the same as decimal places?
No. Significant figures count all meaningful digits in a value. Decimal places count only digits after the decimal marker. Addition and subtraction use decimal places; multiplication and division use significant figures.
Should I round a measurement before checking tolerance?
No. Compare the unrounded measurement to the tolerance limits unless the governing standard or drawing explicitly requires a rounded conformance rule. ASTM E29-22 provides guidance for conformance decisions.
How do I read 25 vs 25.0 on an engineering drawing?
25.0 has three significant figures and indicates tenths precision. 25 has two significant figures and may be governed by a general tolerance block. Treat them as different unless the drawing states otherwise.
Does the significant figures calculator handle tolerances?
Our calculator verifies significant figures and rounding for reporting. Tolerances are absolute limits; the calculator should not be used to change or relax a tolerance limit.
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