ASTM E29-93a(1999)
(Practice)Standard Practice for Using Significant Digits in Test Data to Determine Conformance with Specifications
Standard Practice for Using Significant Digits in Test Data to Determine Conformance with Specifications
SCOPE
1.1 This practice is intended to assist the various technical committees in the use of uniform methods of indicating the number of digits which are to be considered significant in specification limits, for example, specified maximum values and specified minimum values. Its aim is to outline methods which should aid in clarifying the intended meaning of specification limits with which observed values or calculated test results are compared in determining conformance with specifications. Reference to this practice is valid only when a choice of method has been indicated, that is, either absolute method or rounding method .
1.2 This practice is intended to be used in determining conformance with specifications when the applicable ASTM specifications or standards make direct reference to this practice.
1.3 This practice describes two commonly accepted methods of rounding data, identified as the Absolute Method and the Rounding Method. In the application of this practice to a specific material or materials it is essential to specify which method is intended to apply. In the absence of such specification, reference to this practice, which expresses no preference as to which method should apply, would be meaningless. The choice of method is arbitrary, depending upon the current practice of the particular branch of industry or technology concerned, and should therefore be specified in the prime publication.
1.4 Section 7 of this practice gives guidelines for use in recording, calculating, and reporting the final result for test data.
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Standards Content (Sample)
NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
Please contact ASTM International (www.astm.org) for the latest information.
Designation: E 29 – 93a (Reapproved 1999)
Standard Practice for
Using Significant Digits in Test Data to Determine
Conformance with Specifications
ThisstandardisissuedunderthefixeddesignationE 29;thenumberimmediatelyfollowingthedesignationindicatestheyearoforiginal
adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.Asuperscript
epsilon (ϵ) indicates an editorial change since the last revision or reapproval.
This standard has been approved for use by agencies of the Department of Defense.
1. Scope E 380 Practice for Use of the International System of Units
(SI) (the Modernized Metric System)
1.1 This practice is intended to assist the various technical
committees in the use of uniform methods of indicating the
3. Terminology
number of digits which are to be considered significant in
3.1 significant digit, n—any of the figures 0 through 9,
specification limits, for example, specified maximum values
excepting leading zeros and some trailing zeros, which is used
and specified minimum values. Its aim is to outline methods
with its place value to denote a numerical quantity to some
which should aid in clarifying the intended meaning of
desired approximation.
specification limits with which observed values or calculated
3.1.1 The digit zero may either indicate a specific value or
test results are compared in determining conformance with
indicate place only. Zeros leading the first nonzero digit of a
specifications. Reference to this practice is valid only when a
number indicate order of magnitude only and are not signifi-
choice of method has been indicated, that is, either absolute
cantdigits.Forexample,thenumber0.0034hastwosignificant
method or rounding method.
digits. Zeros trailing the last nonzero digit for numbers
1.2 This practice is intended to be used in determining
represented with a decimal point are significant digits. For
conformance with specifications when the applicable ASTM
example, the numbers 1270. and 32.00 each have four signifi-
specifications or standards make direct reference to this prac-
cant digits. The significance of trailing zeros for numbers
tice.
represented without use of a decimal point can only be
1.3 This practice describes two commonly accepted meth-
identified from knowledge of the source of the value. For
odsofroundingdata,identifiedastheAbsoluteMethodandthe
example, a modulus strength, stated as 140 000 Pa, may have
Rounding Method. In the application of this practice to a
as few as two or as many as six significant digits.
specific material or materials it is essential to specify which
3.1.2 To eliminate ambiguity, the exponential notation may
method is intended to apply. In the absence of such specifica-
be used. Thus, 1.40 3 10 indicates that the modulus is
tion, reference to this practice, which expresses no preference
reported to the nearest 0.01 3 10 or 1000 Pa.
as to which method should apply, would be meaningless. The
3.1.3 Use of appropriate SI prefixes is recommended for
choice of method is arbitrary, depending upon the current
metric units to reduce the need for trailing zeros of uncertain
practice of the particular branch of industry or technology
significance. Thus, 140 kPa and 0.140 MPa each indicate that
concerned, and should therefore be specified in the prime
the modulus is reported to the nearest 1 kPa or 1000 Pa, while
publication.
140 kPa may again have two or three significant digits.
1.4 Section 7 of this practice gives guidelines for use in
recording, calculating, and reporting the final result for test
4. Expression of Numerical Requirements
data.
4.1 The unqualified statement of a numerical limit, such as
2. Referenced Documents “2.50 in. max,” cannot, in view of different established
practices and customs, be regarded as carrying a definite
2.1 ASTM Standards:
operational meaning concerning the number of digits to be
E 456 Terminology Relating to Quality and Statistics
retained in an observed or a calculated value for purposes of
determining conformance with specifications.
4.2 Absolute Method—In some fields, specification limits of
ThispracticeisunderthejurisdictionofASTMCommitteeE-11onQualityand
Statistics and is the direct responsibility of Subcommittee E11.10 on Sampling and
2.5 in. max, 2.50 in. max, and 2.500 in. max are all taken to
Data Analysis.
imply the same absolute limit of exactly two and a half inches
Current edition approved March 15, 1993. Published May 1993. Originally
and for purposes of determining conformance with specifica-
published as E 29 – 40. Last previous edition E 29 – 93.
Annual Book of ASTM Standards, Vol 14.02. tions,anobservedvalueoracalculatedvalueistobecompared
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
Please contact ASTM International (www.astm.org) for the latest information.
E 29 – 93a (1999)
directly with the specified limit. Thus, any deviation, however 6.2 How Applied—With the rounding method, an observed
small, outside the specification limit signifies nonconformance value or a calculated value should be rounded by the procedure
with the specifications. This will be referred to as the absolute prescribed in 4.3 to the nearest unit in the designated place of
method. figures stated in the standard, as, for example, “to the nearest
4.3 Rounding Method—In other fields, specification limits kPa,” “to the nearest 10 ohms,” “to the nearest 0.1 percent,”
of 2.5 in. max, 2.50 in. max, 2.500 in. max are taken to imply etc. The rounded value should then be compared with the
that, for the purposes of determining conformance with speci- specified limit, and conformance or nonconformance with the
fications, an observed value or a calculated value should be specification based on this comparison.
rounded to the nearest 0.1 in., 0.01 in., 0.001 in., respectively,
6.3 How Expressed—This intent may be expressed in the
and then compared with the specification limit. This will be
standard in one of the following forms:
referred to as the rounding method.
6.3.1 If the rounding method is to apply to all specified
limits in the standard, and if all digits expressed in the
5. Absolute Method
specification limit are to be considered significant, this may be
indicated by including the following statement in the standard:
5.1 Where Applicable—The absolute method applies where
itistheintentthatalldigitsinanobservedvalueoracalculated The following applies to all specified limits in this standard: For purposes of
determining conformance with these specifications, an observed value or a cal-
value are to be considered significant for purposes of deter-
culated value shall be rounded “to the nearest unit” in the last right-hand digit
mining conformance with specifications. Under these condi-
used in expressing the specification limit, in accordance with the rounding
method of ASTM Practice E 29, for Using Significant Digits in Test Data to De-
tions, the specified limits are referred to as absolute limits.
termine Conformance with Specifications.
5.2 How Applied—With the absolute method, an observed
value or a calculated value is not to be rounded, but is to be
6.3.2 Iftheroundingmethodistoapplyonlytothespecified
compared directly with the specified limiting value. Confor-
limits for certain selected requirements, this may be indicated
mance or nonconformance with the specification is based on
by including the following statement in the standard:
this comparison.
The following applies to specified limits for requirements on (tensile
5.3 How Expressed—This intent may be expressed in the strength), (elongation), and ( . ) given in ., (applicable section number and
title) and ( . ) of this standard: For purposes of determining conformance with
standard in one of the following forms:
these specifications, an observed value or a calculated value shall be rounded
5.3.1 Iftheabsolutemethodistoapplytoallspecifiedlimits
to the nearest 1kPa for (tensile strength), to the nearest (1 percent) for (elonga-
tion), and to the nearest ( . ) for ( . ) in accordance with the rounding-off
in the standard, this may be indicated by including the
method of ASTM Practice E 29 Using Significant Digits in Test Data to Deter-
following sentence in the standard:
mine Conformance with Specifications.
For purposes of determining conformance with these speci-
6.3.3 If the rounding method is to apply to all specified
fications,allspecifiedlimitsinthisstandardareabsolutelimits,
limits in a table, this may be indicated by a note in the manner
as defined inASTM Practice E 29, for Using Significant Digits
shown in the following examples:
in Test Data to Determine Conformance with Specifications.
5.3.2 Iftheabsolutemethodistoapplytoallspecifiedlimits 6.3.3.1 Example 1—Same significant digits for all items:
of some general type in the standard (such as dimensional
Chemical Composition,
% mass
tolerance limits), this may be indicated by including the
following sentence in the standard:
Copper 4.5 6 0.5
For purposes of determining conformance with these speci- Iron 1.0 max
Silicon 2.5 6 0.5
fications, all specified (dimensional tolerance) limits are abso-
Other constituents (magnesium + zinc + manganese) 0.5 max
lute limits, as defined in ASTM Practice E 29, Using Signifi-
Aluminum remainder
cant Digits in Test Data to Determine Conformance with
NOTE 1—For purposes of determining conformance with these speci-
Specifications.
fications, an observed value or a calculated value shall be rounded to the
5.3.3 Iftheabsolutemethodistoapplytoallspecifiedlimits
nearest 0.1 percent, in accordance with the rounding method of ASTM
given in a table, this may be indicated by including a footnote
Practice E 29, for Using Significant Digits in Test Data to Determine
with the table as follows:
Conformance with Specifications.
A
Capacity Volumetric Tolerance
6.3.3.2 Example 2—Significant digits not the same for all
mL 6 mL
items; similar requirements:
10 0.02
Chemical Composition, % mass
25 0.03
min max
50 0.05
100 0.10
Nickel 57 .
A
Chromium 14 18
Tolerance limits specified are absolute limits as defined in ASTM Practice
E 29, for Using Significant Digits in Test Data to Determine Conformance with Manganese . 3
Silicon . 0.40
Specifications.
Carbon . 0.25
Sulfur . 0.03
6. Rounding Method
Iron remainder
6.1 WhereApplicable—The rounding method applies where
NOTE 2—For purposes of determining conformance with these speci-
it is the intent that a limited number of digits in an observed
fications, an observed value or a calculated value shall be rounded “to the
value or a calculated value are to be considered significant for
nearest unit” in the last right-hand significant digit used in expressing the
purposes of determining conformance with specifications. limiting value, in accordance with the rounding method ofASTM Practice
NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
Please contact ASTM International (www.astm.org) for the latest information.
E 29 – 93a (1999)
E 29, Using Significant Digits in Test Data to Determine Conformance
rounded to the nearest 1 000 is at once 89 000; it would be
with Specifications.
incorrect to round first to the nearest 100, giving 89 500 and
then to the nearest 1 000, giving 90 000.
6.3.3.3 Example 3—Significant digits not the same for all
6.6 Special Case, Rounding to the Nearest 50, 5, 0.5, 0.05,
items; dissimilar requirements:
etc.—If in special cases it is desired to specify rounding to the
Tensile Requirements
nearest 50, 5, 0.5, 0.05, etc., this may be done by so indicating
Tensile strength, psi 60 000 to 72 000
in the standard. In order to round to the nearest 50, 5, 0.5, 0.05,
Yield point, min, psi 33 000
etc., double the observed or calculated value, round off to the
Elongation in 2 in., min % 22
nearest 100, 10, 1.0, 0.10, etc., in accordance with the
NOTE 3—For purposes of determination of conformance with these
procedure in 6.4, and divide by 2. For example, in rounding
specifications,anobservedvalueoracalculatedvalueshallberoundedoff
6 025 to the nearest 50, 6 025 is doubled giving 12 050 which
to the nearest 1000 psi for tensile strength and yield point and to the
nearest 1 percent for elongation, in accordance with the rounding method becomes 12 000 when rounded to the nearest 100 (6.4.3).
of ASTM Practice E 29 for Using Significant Digits in Test Data to
When 12 000 is divided by 2, the resulting number, 6 000, is
Determine Conformance with Specifications.
theroundedvalueof6 025.Inrounding6 075tothenearest50,
6 075 is doubled giving 12 150 which becomes 12 200 when
6.4 Rounding Procedure—The actual rounding procedure
rounded to the nearest 100 (6.4.3). When 12 200 is divided by
shall be as follows:
2, the resulting number, 6 100, is the rounded value of 6 075.
6.4.1 When the digit next beyond the last place to be
retained is less than 5, retain unchanged the digit in the last
7. Guidelines for Retaining Significant Figures in
place retained.
Calculation and Reporting of Test Results
6.4.2 When the digit next beyond the last place to be
7.1 General Discussion—Rounding test results avoids a
retained is greater than 5, increase by 1 the digit in the last
misleading impression of precision while preventing loss of
place retained.
informationduetocoarseresolution.Anyapproachtoretention
6.4.3 When the digit next beyond the last place to be
of significant digits of necessity involves some loss of infor-
retained is 5, and there are no digits beyond this 5, or only
mation; therefore, the level of rounding should be carefully
zeros, increase by 1 the digit in the last place retained if it is
selected considering both planned and potential uses for the
odd, leave the digit unchanged if it is even. Increase by 1 the
data. The number of significant digits must, first, be adequate
digit in the last place retained, if there are digits beyond this 5.
for comparison against specification limits (see 6.2). The
6.4.4 This rounding procedure may be restated simply as
following guidelines are intended to preserve the data for
follows: When rounding a number to one having a specified
statistical summaries. For certain purposes, such as where
number of significant digits, choose that which is nearest. If
calculations involve differences of measurements close in
two choices are possible, as when the digits dropped are
magnitude, and for some statistical calculations, such as paired
exactlya5ora5 followed only by zeros, choose that ending
t-tests, autocorrelations, and nonparametric tests, reporting
in an even digit. Table 1 gives examples of applying this
data to a greater numb
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