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GB/T 8170-2008: Rules of rounding off for numerical values and expression and judgement of limiting values
GB/T 8170-2008
GB
NATIONAL STANDARD OF THE
PEOPLE’S REPUBLIC OF CHINA
ICS 03.120.30
A 41
Replacing GB/T 1250-1989, GB/T 8170-1987
Rules of rounding off for numerical values and expression and
judgement of limiting values
ISSUED ON: JULY 16, 2008
IMPLEMENTED ON: JANUARY 01, 2009
Issued by: General Administration of Quality Supervision, Inspection and
Quarantine of the People's Republic of China;
Standardization Administration of the People's Republic of China.
Table of Contents
Foreword ... 3
1 Scope ... 5
2 Terms and definitions ... 5
3 Rules of rounding off for numerical values ... 6
4 Expression and judgment of limiting value ... 9
Bibliography ... 15
Rules of rounding off for numerical values and expression and
judgement of limiting value
1 Scope
This Standard specifies the rules for rounding off values, the expression and
determination of numerical limits, relevant terms and their symbols, and the method for
comparing measured values or their calculated values with the limiting values specified
in the standard.
This Standard applies to various values obtained through testing and calculation in
scientific, technological and production activities. When the obtained values need to be
rounded off, they should be rounded off according to the rules given in this standard.
This Standard is applicable to the preparation of various standards or other technical
specifications and the determination of test results.
2 Terms and definitions
For the purposes of this Standard, the following terms and definitions apply.
2.1 rounding off for numerical values
The process of omitting the last several digits of the original numerical value and then
adjusting the last reserved digit to make the final obtained value approximately equal
to the original numerical value.
NOTE: The value after rounding off for numerical values is called the rounded value (of the original
value).
2.2 rounding interval
The minimum numerical value unit of the rounding value.
NOTE: Once the value of the rounding interval is determined, the rounding value is an integer
multiple of that value.
Example 1: If the specified rounding interval is 0.1, the rounding value shall be adopted
from the integral multiples of 0.1; that is equivalent to rounding off the numerical value
to one decimal place.
Example 2: If the specified rounding interval is 100, the rounding value shall be adopted
from the integral multiples of 100; that is equivalent to rounding off the numerical value
to "hundreds" place.
2.3 limiting values
The boundary values of the index values which are presented in number, in compliance
with the standard (or other technical specifications) and has to be assessed as required
by the standard (or other technical specifications).
3 Rules of rounding off for numerical values
3.1 Determination of rounding interval
a) Specify the rounding interval as 10-n (n is a positive integer), or specify that the
value should be rounded to n decimal places;
b) Specify the rounding interval as 1, or indicate that the value is rounded to "one"
digits;
c) Specify the rounding interval to be 10n (where n is a positive integer), or specify
that the value is rounded to 10n digits, or specify that the value is rounded to "tens",
"hundreds", "thousands", etc. digits.
3.2 Rules of rounding off
3.2.1 The numerical value is rounded down if the leftmost one of the numbers intended
to be discarded is less than 5; and the reserved numbers keep unchanged.
Example: Round 12.1498 to the single digit, 12 is obtained. Round 12.1498 to one
decimal place, then 12.1 is obtained.
3.2.2 The numerical value is rounded up if the leftmost one of the numbers intended to
be discarded is more than 5; namely, the last number of the reserved numbers is added
with 1.
Example: Round 1268 to the "hundreds" place, then 13×102 is obtained (it can also be
expressed as 1300 in specified occasions.).
NOTE: In the examples of this standard, 'specified occasions” refers to where rounding interval is
definite.
3.2.3 The numerical value is rounded up if the leftmost one of the numbers intended to
be discarded is 5, and the following ones contain a number which is not "0"; namely,
the last number of the reserved numbers is added with 1.
Example: Round 10.5002 to the single digit, then 11 is obtained.
3.3.2 In specific operation, the test and calculation departments sometimes report the
obtained rounding value with one or several numbers more than the specified rounding
digits and then hand them over to other departments for judgment. To avoid the mistakes
of continuous rounding, the following procedures shall be carried out.
3.3.2.1 If the rightmost nonzero number of the reported numerical value is 5, its top
right corner shall be added with "+" or "-" or nothing to indicate that the original
numerical value has been rounded down, up or neither of them.
Example: 16.50+ indicates that the original value is greater than 16.50 and rounded
down to16.50; 16.50- indicates that the original value is less than 16.50 and rounded up
to 16.50.
3.3.2.2 On the condition of rounding off for the reported numerical values, if the
leftmost one of the numbers intended to be discarded is 5 and no number followed or
all the following numbers are "0", the reported value with "+" is rounded up and the
one with "-" is rounded down. Other procedures are in accordance with 3.2.
Example 1: Round the following numerical values to single digit. (The reported
numbers reserve one more digit to one decimal place).
3.4 0.5 unit rounding and 0.2 unit rounding
0.5 and 0.2 unit rounding may be adopted in rounding off for numerical values, if
necessary.
3.4.1 0.5 unit rounding (half unit rounding)
0.5 unit rounding refers to that the intended value is rounded off based on 0.5 unit
according the specified rounding interval.
Measured value Reported numerical value Rounding value
4.2.2 Values with limit deviations
4.2.2.1 Basic value A with upper deviation +b1 of absolute limit and lower deviation -
b2 of absolute limit refers to the values fromA-b2 to A+b1 meet the requirements and it
is expressed as .
NOTE: Where b1=b2=b, A±b may be short for .
Example: refers to that values from 79 mm to 82 mm meet the requirements.
4.2.2.2 Basic value A with upper deviation +b1% of relative limit and lower deviation -
b2% of relative limit refers to that the relative deviation of measured value or the
calculated value R to A, [(R~A)/A] will meet the requirements from -b2% to +b1% and
expressed as .
NOTE: Where b1=b2=b, may be expressed as .
Example: 510 Ω (1±5%) refers to that the relative deviation , for
measured value or calculated value R(Ω) versus to 510 Ω, from -5% to +5%, meets the
requirements.
4.2.2.3 For basic value A, if the upper deviation of limit +b1 and (or) lower deviation of
limit -b2 makes A+b1 and (or) A-b2 does not meet the requirement, parentheses shall be
added and it will be expressed as (excluding b1 and b2) or (excluding b1),
(excluding b2).
Example 1: (excluding 2) mm refers to that the values from 79 mm to close to but
insufficient than 82 mm meet the requirements.
Example 2: 510 Ω (1±5%) (excluding 5%) refers to that the relative deviation of the
measured value or its calculated value R (Ω) to 510 Ω, [(R-510)/510], will meet the
requirements from -5% to close to but insufficient than +5%.
4.3 Comparison method of the measured value or its calculated value and the
limiting value specified in the standard
4.3.1 General provisions
4.3.1.1 When judging whether the measured value or its calculated value meet the
standard requirements of not, the measured value of test or its calculated value shall be
compared with the limiting value specified in the standard, and any of the following
methods may be adopted for comparison;
a) Complete numerical comparison method;
b) Rounded-off-value comparison method.
4.3.1.2 If no special regulation for limiting value (including values with limit deviations)
is specified in the standard or relevant documents, complete numerical comparison
method shall be adopted. If rounded-off-value comparison method is inquired, it shall
be noted in the standard.
4.3.1.3 If one of comparative methods is specified in the standard or relevant document,
it shall not be changed once been determined.
4.3.2 Complete numerical comparison method
Do not round off the measured value or calculated value (or even though the value has
been rounded off, it shall be indicated that it has been rounded down, up or neither of
them) and then compare this value with specified limiting value; if this value exceeds
the specified limiting value (nor matter large or not), it will be judged as do not meet
the requirements. See Table 3 for examples.
4.3.3 Rounded-off-value comparison method
4.3.3.1 Round off the measured value or its calculated value, and the rounding off digit
shall be consistent with the digit of the specified limiting value.
Where the test or calculation accuracy permits, the obtained values shall be reported
with one or several digits more than the specified rounding off digit and then rounded
off to the specified digit according to the procedures of 3.2.
4.3.3.2 Compare the rounded off values and the specified limiting value, if this value
exceeds the specified range of limiting value (no matter large or not), it will be judged
as do not meet the requirements. See Table 3 for examples.
GB/T 8170-2008
GB
NATIONAL STANDARD OF THE
PEOPLE’S REPUBLIC OF CHINA
ICS 03.120.30
A 41
Replacing GB/T 1250-1989, GB/T 8170-1987
Rules of rounding off for numerical values and expression and
judgement of limiting values
ISSUED ON: JULY 16, 2008
IMPLEMENTED ON: JANUARY 01, 2009
Issued by: General Administration of Quality Supervision, Inspection and
Quarantine of the People's Republic of China;
Standardization Administration of the People's Republic of China.
Table of Contents
Foreword ... 3
1 Scope ... 5
2 Terms and definitions ... 5
3 Rules of rounding off for numerical values ... 6
4 Expression and judgment of limiting value ... 9
Bibliography ... 15
Rules of rounding off for numerical values and expression and
judgement of limiting value
1 Scope
This Standard specifies the rules for rounding off values, the expression and
determination of numerical limits, relevant terms and their symbols, and the method for
comparing measured values or their calculated values with the limiting values specified
in the standard.
This Standard applies to various values obtained through testing and calculation in
scientific, technological and production activities. When the obtained values need to be
rounded off, they should be rounded off according to the rules given in this standard.
This Standard is applicable to the preparation of various standards or other technical
specifications and the determination of test results.
2 Terms and definitions
For the purposes of this Standard, the following terms and definitions apply.
2.1 rounding off for numerical values
The process of omitting the last several digits of the original numerical value and then
adjusting the last reserved digit to make the final obtained value approximately equal
to the original numerical value.
NOTE: The value after rounding off for numerical values is called the rounded value (of the original
value).
2.2 rounding interval
The minimum numerical value unit of the rounding value.
NOTE: Once the value of the rounding interval is determined, the rounding value is an integer
multiple of that value.
Example 1: If the specified rounding interval is 0.1, the rounding value shall be adopted
from the integral multiples of 0.1; that is equivalent to rounding off the numerical value
to one decimal place.
Example 2: If the specified rounding interval is 100, the rounding value shall be adopted
from the integral multiples of 100; that is equivalent to rounding off the numerical value
to "hundreds" place.
2.3 limiting values
The boundary values of the index values which are presented in number, in compliance
with the standard (or other technical specifications) and has to be assessed as required
by the standard (or other technical specifications).
3 Rules of rounding off for numerical values
3.1 Determination of rounding interval
a) Specify the rounding interval as 10-n (n is a positive integer), or specify that the
value should be rounded to n decimal places;
b) Specify the rounding interval as 1, or indicate that the value is rounded to "one"
digits;
c) Specify the rounding interval to be 10n (where n is a positive integer), or specify
that the value is rounded to 10n digits, or specify that the value is rounded to "tens",
"hundreds", "thousands", etc. digits.
3.2 Rules of rounding off
3.2.1 The numerical value is rounded down if the leftmost one of the numbers intended
to be discarded is less than 5; and the reserved numbers keep unchanged.
Example: Round 12.1498 to the single digit, 12 is obtained. Round 12.1498 to one
decimal place, then 12.1 is obtained.
3.2.2 The numerical value is rounded up if the leftmost one of the numbers intended to
be discarded is more than 5; namely, the last number of the reserved numbers is added
with 1.
Example: Round 1268 to the "hundreds" place, then 13×102 is obtained (it can also be
expressed as 1300 in specified occasions.).
NOTE: In the examples of this standard, 'specified occasions” refers to where rounding interval is
definite.
3.2.3 The numerical value is rounded up if the leftmost one of the numbers intended to
be discarded is 5, and the following ones contain a number which is not "0"; namely,
the last number of the reserved numbers is added with 1.
Example: Round 10.5002 to the single digit, then 11 is obtained.
3.3.2 In specific operation, the test and calculation departments sometimes report the
obtained rounding value with one or several numbers more than the specified rounding
digits and th...