This standard specifies the rules for rounding off values, the expression and determination methods of numerical limits, relevant terms and symbols, and the method for comparing measured values ​​or calculated values ​​with the limit values ​​specified in the standard. This standard applies to various values ​​obtained by testing and calculation in scientific and 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 applies to the compilation of various standards or other technical specifications and the determination of test results. This standard replaces GB/T8170-1987 and GB/T1250-1989. Compared with GB/T 8170-1987 and GB/T 1250-1989, the main changes in the technical content of this standard include: - The standard format has been modified in accordance with the requirements of GB/T 1.1-2000 "Guidelines for Standardization Part 1: Structure and Writing Rules of Standards"; - The terms "rounding of values" and "limit values" have been added, the definition of "rounding interval" has been modified, and the terms "significant digits", "rounding of 0.5 units" and "rounding of 0.2 units" have been deleted; - In Chapter 3, the content of "specifying the number of significant digits to be rounded to" has been deleted, and the content of "specifying the number of significant digits to be rounded to" has been retained. "When the number of digits is not determined"; - When necessary, add the symbol "+" or "-" in the upper right corner of the rounded value instead of after the value to indicate that the value has been "rounded down" or "rounded up"; - In the two judgment methods for comparing the measured value or its calculated value with the limit value, add "When the standard or relevant documents stipulate the use of one of the comparison methods, once determined, it shall not be changed"; delete the content related to the absolute limit value; - When using the rounding method for comparison, emphasize "When the test or calculation accuracy allows, the obtained value should first be reported with one or more digits more than the specified rounding digit, and then rounded to the specified digit according to the procedure of 3.2." GB/T 8170-2008 Rules for rounding off values ​​and the expression and determination of limit values ​​GB/T8170-2008 standard download decompression password: www.bzxz.net
This standard specifies the rules for rounding off values, the expression and determination methods of numerical limit values, the relevant terms and symbols, and the method of comparing the measured value or its calculated value with the limit value specified in the standard. This standard applies to various values ​​obtained by testing and calculation in scientific and 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 applies to the preparation of various standards or other technical specifications and the determination of test results.
This standard is integrated and revised on the basis of GB/T8170-1987 "Rules for rounding off values" and GB/T1250-1989 "Expression and determination methods of limit values".
This standard replaces GB/T8170-1987 and GB/T1250-1989.
Compared with GB/T8170-1987 and GB/T1250-1989, the main changes in the technical content of this standard include: --- The standard format has been modified
according to the requirements of GB/T1.1-2000 "Guidelines for Standardization Part 1: Structure and Writing Rules of Standards" ; --- The terms numerical rounding and limit numerical value have been added, the definition of rounding interval has been modified, and the terms significant digits, 0.5 unit rounding and 0.2 unit rounding have been deleted; --- In Chapter 3, the numerical rounding rules have been deleted, and the content related to the specified number of significant digits to be rounded to has been retained; --- When necessary, the symbol + or - is added to the upper right corner of the rounded value instead of after the value to indicate that the value is rounded up or down; ---In the two judgment methods for comparing the measured value or its calculated value with the limit value, it is added that when the standard or relevant documents stipulate the use of one of the comparison methods, once determined, it shall not be changed; the content about the absolute limit value is deleted; ---When using the rounding method for comparison, it is emphasized that when the test or calculation accuracy allows, the obtained value should be reported one or more digits more than the specified rounding digit, and then rounded to the specified digit according to the procedure of 3.2. This standard is proposed by the China National Institute of Standardization. This standard is under the jurisdiction of the National Technical Committee for Standardization of Statistical Methods. The drafting units of this standard are: China National Institute of Standardization, Institute of Mathematics and Systems Science, Chinese Academy of Sciences, Guangzhou Product Quality Supervision and Inspection Institute, Wuxi Product Quality Supervision and Inspection Institute, Fuzhou Chunlun Tea Co., Ltd. Drafters of this standard: Chen Yuzhong, Yu Zhenfan, Feng Shiyong, Deng Suixing, Ding Wenxing, Dang Hua, Chen Huaying, Fu Tianlong.

ICS 03.120.30
National Standard of the People's Republic of China
GB/R 8170---2008
Replaces GB/T 1250-1989, GB/T 81701987 Rules of rounding off for numerical values ​​& expression and judgement of limiting values ​​Issued on 16 July 2008
General Administration of Quality Supervision, Inspection and Quarantine of the People's Republic of China National Standardization Administration
2009-01-01
GB/T 8170--2008
This standard is integrated and revised on the basis of GB/T8170-1987 "Numerical value revision rules" and GB/T1250-1989 "Expression and determination method of limit values".
This standard replaces GB/T 8170-: 1987 and GB/T 1250-1989. Compared with GB/T8170-1987 and GB/T1250-1989, the main changes in the technical contents of this standard include: the standard format has been modified according to the requirements of GB/T1.12000 Guidelines for Standardization Part 1: Structure and Writing Rules of Standards;
: "The terms "rounding of values" and "limit values" have been added, the definition of "rounding interval" has been modified, and the terms "significant digits", "rounding of 0.5 units" and "rounding of 0.2 units" have been deleted; - In Chapter 3, the content of "specifying that values ​​are rounded to n significant digits" has been deleted, and "the situation of specifying digits" has been retained
... When necessary, the symbol "" or "" is added to the upper right corner of the rounded value instead of after the value, indicating that its value has been "rounded down" or "rounded up". In the two judgment methods for comparing the measured value or its calculated value with the limit value, "When the standard or relevant documents stipulate the use of one of the comparison methods, once determined, it shall not be changed" is added; the content about the absolute limit value is deleted; when using the rounding method for comparison, it is emphasized that "when the test or calculation accuracy allows, the obtained value should be reported one or more digits more than the specified rounding digit, and then rounded to the specified digits according to the procedure of 3.2. This standard is proposed by the China National Institute of Standardization. This standard is under the jurisdiction of the Technical Committee on Standardization of Statistical Methods. Drafting units of this standard: China National Institute of Standardization, Institute of Mathematics and Systems Science, Chinese Academy of Sciences, Guangzhou Product Quality Supervision and Inspection Institute, Wuxi Product Quality Supervision and Inspection Institute, Fuzhou Chunlun Tea Co., Ltd. The authors of this standard: Chen Yuzhong, Ding Zhenfan, Feng Yong, Deng Suixing, Ding Wenxing, Juehua, Chen Huaying, Jian Tianlong, 1 Range
Numerical rounding rules and expression and judgment of limit values ​​GB/T 8170--2008
This standard specifies the rules for rounding off numerical values, the expression and delimitation of numerical limits, the relevant terms and their symbols, and the method for comparing measured values ​​or calculated values ​​with the limit values ​​specified in the standard. This standard applies to various numerical values ​​obtained by testing and calculation in scientific, technological and production activities. When the obtained numerical values ​​need to be rounded off, they should be rounded off according to the rules specified in this standard.
This standard applies to customer maintenance or other technical non-standard writing and the judgment of test results. 2 Terms and Definitions
The following terms and definitions apply to this standard.
Rounding off for numerical values ​​The process of omitting the last few digits of the original value and adjusting the remaining last digits so that the final value is closest to the original value.
Note: The value after numerical rounding is called the rounded value (of the original value). 2.2
Rounding interval interval
The minimum numerical unit of the rounding value.
Note: The rounding value is the integer multiple of the rounding interval. Example 1: If the rounding interval is 0.1, the rounding value should be selected from the integer multiples of 0.1, which is equivalent to rounding the value to the decimal place. Example 2: If the rounding interval is 100, the rounding value should be selected from the integer multiples of 100, which is equivalent to rounding the value to the "hundred" place. 2.3
Limiting value limiting value wes
The limit of the numerical range of the indicator specified in the standard (or technical specification) and given in quantitative form and meeting the requirements of the standard (or technical specification).
3 Rules for rounding off values
3.1 Determine the rounding interval
a) Specify the rounding interval as 10-(n is a positive integer), or specify that the value is rounded to a decimal placeb) Specify the rounding interval as 1, or specify that the value is rounded to \ decimal places; ) Specify the rounding interval as 10\ (a positive integer), specify that the value is rounded to 10\ digits, or specify that the value is rounded to "tens", "stations", "trillions", etc.
3.2 Rounding rules
3.2.1 If the leftmost digit of the number to be discarded is less than 5, it is discarded and the remaining digits remain unchanged. Example: Round 12,1498 to the unit digit, and you get 12; round 12.1498 to one decimal place, and you get 12.1. 3.2.2 If the leftmost digit of the proposed extravagant number is 5, then add 1 to the last digit of the number to be retained. Example: Round 1268 to the hundredth digit, and you get 13×10° (which can be written as 1300 in certain cases). Note: In non-standard examples, "specific cases" refers to when the interval between roundings is clear. 3.2.3 If the leftmost digit of the proposed extravagant number is 5, and there is a non-zero digit after it, then add 1 to the last digit of the number to be retained. GB/T 8170-—2008
Example: Round 10.5002 to the nearest digit to get 11. 3.2.4 When the leftmost digit of the number to be discarded is 5 and there are no digits or all digits after it are 0, if the last digit to be retained is an odd number (1, 35, 7, 9), then add 1 to the last digit of the number to be retained; if the last digit to be retained is an even number (0, 2, 4, 6, 8), then discard it. 1: The rounding interval is 0.1 (or 10-)
Proposed rounding value
Rounding value
10×10- (can be written as 1.0 in certain situations)4×10-1 (can be written as 0.4 in certain situations) Example 2: The rounding interval is [H00 (or 10\) Proposed rounding value
Rounding value
2×10 (can be written as 2000 in certain situations)4×103 (can be written as 4000 in certain situations)3.2.5 When rounding off a negative number, first round off its absolute value according to the provisions of 3.2.1 to 3.2.4, and then add a negative sign 1 in front of the obtained value Example 1: Round the following numbers to the "tens\" digit: Proposed rounding value
—355
—325| |tt||Rounded value
—36×10 (can be written as—360 in certain occasions)—32×10 (written as—320 in certain occasions) Example 2: Round the following numbers to three decimal places, that is, the rounding interval is 10: Proposed rounding value
3.3 Continuous rounding is not allowed
Rounded value
-36×10-3 (can be written as—0.036 in certain occasions) 3.3.1 Proposed rounding number is rounded once after determining the rounding interval or specifying the rounding digit, and it is not allowed to be rounded repeatedly according to the rule of 3.2.
Example 1: Rounding to 97.46, the rounding interval is 1. Correct approach: 97.16·-97;
Correct approach: 97.46→97.5 ×98. Example 2: Rounding off 15.4546, the rounding interval is 1. The correct way is: 15.4546-→15;
is not correct: 15.4546→15.455→15.46-→15.516. 3.3.2 In the specific implementation, sometimes the test and calculation department first reports the obtained value according to the specified rounding digit, and then other departments make judgments. In order to avoid the error of continuous rounding, the following steps should be followed: 3.3.2.1 When the rightmost non-zero number of the reported value is 5, a "+" or "-" or no symbol should be added to the upper right corner of the value, indicating that rounding has been performed, not included or not included.
Example: 16.50+ means the actual value is greater than 16.50 and is rounded off to 16.50; 16.50- means the actual value is less than 16.50 and is rounded off to 16.50.
3.3.2.2 If the reported value needs to be rounded off, when the leftmost digit of the number to be rounded off is 5 and there are no digits or all 0s after it, the value with a “yu” in the upper corner is rounded off, and the value with a “一” is rounded off, and the others are still rounded off according to 3.2. Example 1: Round the following numbers to the nearest decimal place (the reported value is rounded to one more decimal place). Measured value
15. 454 6
—15.4546
16. 520 3
—16.520 3
Reported value
Rounded value
3. 40. 5 unit rounding and 0.2 unit rounding When rounding a value, if necessary, 0.5 unit rounding or 0.2 unit rounding can also be used. 3.4.10.5 unit rounding (half unit rounding) 0.5 unit rounding means rounding the value to be rounded to 0.5 units according to the specified rounding interval. CB/T 8170—2008
0.5 unit rounding method is as follows: multiply the proposed rounding value X by 2, round 2X according to the specified rounding interval in accordance with the provisions of 3.2, and divide the resulting value (2X rounding value) by 2.
Example: Round the following numbers to the "unit" digit 0,5 unit rounding. Proposed rounding value X
3.4.20.2 unit rounding
2X rounding value
X rounding value
0.2 unit rounding means rounding the proposed rounding value to 0.2 units according to the specified rounding interval. The 0.2 unit rounding method is as follows: multiply the proposed rounding value X by 5, round 5X according to the specified rounding interval in accordance with the provisions of 3.2, and then divide the resulting value (5X rounding value) by 5.
Example: Round the following numbers to 0.2 units of the "hundred" digit Rounding value to be rounded X
4 Representation and judgment of limit values
-4 650
4,1 General principles for writing limit values
5X rounding value
—4 600
X revised value
4.1.1 The limit values ​​shall be specified for indicators or parameters given in quantitative form in the standard (or other technical specifications). The limit value indicates the boundary value of the numerical range that meets the requirements of the standard. It is expressed by giving the minimum limit value and (or) the maximum limit value, or giving the basic value and the limit deviation value. 4.1.2 The representation form and number of digits of the limit value in the standard should be appropriate, and all significant digits should be written. The degree of accuracy of the written digits should be able to ensure the performance and quality of the product or other standardized objects. 4.2 Terms for expressing limit values
4.2.1 Basic terms
4.2.1.1 Basic terms and symbols for expressing limit values ​​are shown in Table 1. Table 1 Basic terms and symbols for expressing limit values ​​Basic terms
Greater than A
Greater than or equal to
Less than or equal to A
To 1: A is the limit value.
Basic terms in specific situations
Abstract A
Less than A
Not less than A
Not less than and
Not less than A
Note 2: The following conventional terms are allowed to express limit values: a) Exceeding A, indicating a value greater than A (≥A); higher than 4
Abstract A
Not less than A
Not higher than A
When the measured value or calculated value is exactly A, it does not meet the requirements; when the measured value or calculated value is exactly A, it does not meet the requirements; when the measured value or calculated value is exactly A, it meets the requirements; when the measured value or calculated value is exactly A, it meets the requirements. 3
GB/T 8170--2008
) "not A\, index value is less than A (A)
c) "A and above\ or "less than A", index value is greater than or equal to A (≥A)d) "less than A\\ at most A", index value is less than or equal to A (≤A). Example 1: Residual phosphorus in the pot <0.035% A=0.035% Example 2: Tensile strength of wire rope = 22×J0° (MPa), A=22×10° (MPa), 4.2.1.2 Basic terms can be used in combination to express the limit value range. For a specific assessment indicator X, the following terms and symbols are allowed (see Table 2). Generally, only one symbol expression should be used in the same standard.
Table? For a specific assessment indicator X, the combination of terms and symbols that are allowed to express the limit value is basic terminology
Fuding or equal to A Less than or equal to B
Greater than AHLess than or equal to B
Greater than or equal to A and less than Bwww.bzxz.net
Greater than A and less than B
4.2.2 Numerical values ​​with limit deviation values
Combination of permitted terms
From A to B
Exceed A to B
At least A less than B
Exceed A less than
Expression method T
AX≤B
A≤XB
Expression method 耳
A~≤B
4.2.2.1 Basic numerical value A with absolute upper limit deviation value ++b and absolute lower limit deviation value -b2, means that from A-ba to A---b1 meets the requirements, recorded as A2.
Note: When bb, A can be simply recorded as Aup.
Example: 80 mm: refers to the range from 79 mm to 82 mm that meets the requirements. 4.2.2.2 The basic value A has a relative upper deviation of 1.% and a relative lower deviation of -6.%, which means that the relative deviation of the measured value or its calculated value R to A (R-A)/AI from -% to +6% meets the requirements, recorded as A. Note: When 6-6, % can be recorded as A(1+%). Example: 5100(1+5%), refers to the relative deviation of the measured value or its calculated value R(2) to 5100 [(R-510)/510] from -5% to 15% meets the requirements,
4.2.2.3 For the basic value A, if the upper deviation of -b and (or) the lower deviation of -b2 make A+ and (or) A- not meet the requirements, brackets should be added and written as A (excluding A) or A (excluding) A (excluding b) Example 1: 80-(excluding 2) mm, refers to the range from 79 i to close to but less than 82 mm meets the requirements. Example 2: 510Q (1 ± 6%) (excluding 5%), refers to the measured value or its calculated value R (0) for 5100 from the deviation value [(R--510)/5101 from 5% to close to but less than 10% meets the requirements. 4.3 Method for comparing the measured value or its calculated value with the limit value specified in the standard 4.3.1 General
4.3.1.1 When judging whether the measured value or its calculated value meets the requirements of the standard, the measured value or its calculated value obtained by the test should be compared with the limit value specified in the standard. The comparison method can be: a) full value comparison method;
b) rounded value comparison method.
4.3.t.2 When there is no special provision for the limit value (including the value with the limit deviation value) in the standard or relevant documents, the full value comparison method should be used. If the rounded value comparison method is specified, it should be explained in the standard. 4.3.1.3 If the standard or relevant documents stipulate the use of one of the comparison methods, ...- once determined, shall not be changed. 4.3.2 Full value comparison method
The measured value or calculated value obtained by the test is not rounded off (or rounded off, but it should be marked as being obtained by including, adding or not adding or not rounding off GB/T 8170-2008
), and the value is compared with the specified limit value. As long as it exceeds the range specified by the limit value (regardless of the degree of excess), it is judged as not meeting the requirements. See Table 3.
4.3.3 Rounded value comparison method
4.3.3.1 The measured value or its calculated value is rounded off, and the rounded digits should be consistent with the specified limit value digits. When the test or calculation accuracy permits, the obtained value should first be reported with one or more digits greater than the specified rounding digit, and then rounded to the specified digit according to the procedure in 3.2:
4.3.3.2 Compare the rounded value with the specified limit value. As long as it exceeds the specified range of the limit value (regardless of the degree of excess), it will be judged as not meeting the requirements. See Table 3 for examples. Table 3 Examples and comparison items of full value comparison method and rounded value comparison method
Tensile strength/
Mass fraction of NaOII
Mass fraction of carbon steel/
Mass fraction of silver in medium carbon steel/
Diameter of coil/
Diameter of cooked strip/
Diameter of coil/
Limiting value
2:14X109
7. 2---1. 6
10.0±0.1
(excluding 0. 1)
1. 0±0. 1
(small including +G.J）
Measured value
Calculated value
Compare with the full value
Whether it meets the requirement
Does not meet
Does not meet
Does not meet
Does not meet
Does not meet
Does not meet
Does not meet
Does not meet
Rounded value
13×100
14×100
14X100
14x100
Compare with the revised value
Whether it meets the requirement|| tt||Not compliant
Technical symbol
Not compliant
Not compliant
Not compliant
Not compliant
Not compliant
Not compliant
CB/T8170-2008
Diameter of coil/
Limit value
(excluding -0.1)
Table 3 (continued)
Specified value or
its calculated value
Compare with the full value
whether it meets the requirements
Not compliant
Note: The examples in the table do not mean that such limit values ​​should be compared with the full effective value method or the rounded value comparison method. 4.3.4 Comparison of two determination methods
Rounding If
Compare by rounded value
Whether it meets the requirements
It meets
Not meets
For examples of the comparison results of the measured value or its calculated value with the specified limit value in different situations using the remainder value comparison method and the rounded value comparison method, see Table 3. For the same limit value, if it meets the requirements itself, the full value comparison method is relatively stricter than the rounded value comparison method. References
G3/6991999 High-quality carbon cable structural steel
[2] JIS Z 8401 Rules for Rourndirig off of Nunber ValuesGB/T8170—2008
GB/T 8170-2008
National Standard of the People's Republic of China
Rules for rounding off values ​​and expression and determination of limit valuesGB/T 8170---20U8
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