Rules for rounding off of numberical values

This standard applies to various numerical values ​​obtained by test, measurement and calculation in scientific and technological and production activities. When rounding off is required, it shall be carried out in accordance with the rules given in this standard unless otherwise specified. GB 8170-1987 Rules for Rounding Off Numerical Values ​​GB8170-1987 Standard Download Decompression Password: www.bzxz.net
This standard applies to various numerical values ​​obtained by test, measurement and calculation in scientific and technological and production activities. When rounding off is required, it shall be carried out in accordance with the rules given in this standard unless otherwise specified.

National Standard of the People's Republic of China
Rules for rounding off of numerical values
Rules for rounding off of numerical valuesUDC 511.1/2
GB 8170—87
This standard applies to various values ​​obtained by test, measurement and calculation in scientific and technological and production activities. When rounding is required, it should be carried out according to the rules given in this standard unless otherwise specified. 1 Terminology
1.1 Rounding interval
is a way to determine the number of digits to be rounded off. Once the value of the rounding interval is determined, the rounded value should be an integer multiple of the value. Example 1: If the specified 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 one decimal place. www.bzxz.net
Example 2: If the specified rounding interval is 100, the rounding value should be selected from integer multiples of 100, which is equivalent to rounding the value to "hundreds" 1.2 Significant digits
For values ​​without decimal places and ending with the next zero, the number of digits obtained from the leftmost non-zero digit minus the number of invalid zeros (i.e., the zero used for positioning by the instrument) is the number of digits. For other decimal digits, the number of digits obtained from the leftmost non-zero digit is the number of significant digits.
Example 1: 35000, if there are two invalid zeros, it has three significant digits and should be written as 350×102. If there are three invalid zeros, it has two significant digits and should be written as 35×103. Example 2: 3.2, 0.32, 0.032, 0.0032 are all two significant digits, and 0.0320 is three significant digits. Example 3: 12.490 has five significant digits, and 10.00 has four significant digits. 1.30.5-unit rounding (half-unit rounding) means that the rounding interval is 0.5 units of the specified digit, that is, rounding to 0.5 units of the specified digit. For example, rounding 60.28 to 0.5 units of the units digit gives 60.5 (see 5.1 of these Rules for rounding methods). 1.40.2-unit rounding
means that the rounding interval is 0.2 units of the specified digit, that is, rounding to 0.2 units of the specified digit. For example, rounding 832 to 0.2 units of the "hundreds" digit gives 840 (see 5.2 of these Rules for rounding methods). 2Determine the expression of the rounded digits
Specify the digits
Specify the rounding interval as 10\n (n is a positive integer), or specify that the value is rounded to n decimal places; a.
Specify the rounding interval as 1, or specify that the value is rounded to units; b.
Specify the rounding interval as 10\, or specify that the value is rounded to 10\ digits (n is a positive integer), or specify that the value is rounded to "tens", c.
"",""·digits.
2.2Specify that the value is rounded to n significant digits. 3Rounding rules
3.1If the leftmost digit of the number to be discarded is less than 5, it is discarded, that is, the remaining digits remain unchanged. Example 1: Round 12.1498 to a decimal place, and the result is 12.1. Approved by the State Bureau of Standards on August 19, 1987
Implementation on March 1, 1988
GB 8170--87
Example 2: Rounding 12.1498 to two significant digits gives 12. 3.2 When the leftmost digit of the number to be discarded is greater than 5, or is 5, and is followed by a number that is not all 0, the last digit to be retained is increased by 1.
Example 1: Rounding 1268 to the "hundred" digit gives 13×102 (which can be written as 1300 in certain circumstances). Example 2: Rounding 1268 to three significant digits gives 127×10 (which can be written as 1270 in certain circumstances). Example 3: Rounding 10.502 to the unit digit gives 11. Note: In this standard example, "in certain circumstances" means when the rounding interval or significant digits are clear. 3.3 When the leftmost digit of the number to be discarded is 5, and there is no digit on the right or all digits are 0, if the last digit to be retained is an odd number (1, 3, 5, 7, 9), it is rounded up; if it is an even number (2, 4, 6, 8, 0), it is discarded. Example 1: The rounding interval is 0.1 (or 10-1). The proposed rounding value is
Rounding value
Example 2: The rounding interval is 1000 (or 103). The proposed rounding value is
Rounding value
2×103 (can be written as 2000 under certain circumstances)
4×103 (can be written as 4000 under certain circumstances)
Example 3: Round the following numbers to two significant digits. The proposed rounding value is
Rounding value
32×103 (can be written as 32000 under certain circumstances)3.4 When rounding off a negative number, first round off its absolute value according to the above provisions of 3.1 to 3.3, and then add a minus sign in front of the rounded value. Example 1: Round the following numbers to tens. Rounded value
Rounded value
-36×10 (can be written as -360 under certain circumstances)32×10 (can be written as -320 under certain circumstances)
Example 2: Round the following numbers to two significant digits. Rounded value
4 Continuous rounding is not allowed
Rounded value
-36×10 (can be written as 360 under certain circumstances)
4.1 The number to be rounded should be rounded once after the rounding digit is determined, and it shall not be rounded off repeatedly according to the rules in Chapter 3. For example: rounding to 15.4546, the rounding interval is 1. Correct approach:
15.4546- 15
Incorrect approach
15.4546 - 15.455→ 15.46 → 15.5 - 16
4.2 In actual implementation, sometimes the testing and calculation department first reports the obtained value with one or more digits more than the specified rounding digit, and then other departments make the judgment. In order to avoid the error of continuous rounding, the following steps should be followed. 4.2.1 When the rightmost non-zero digit of the reported value is 5, "(+)" or "()" or no sign should be added after the value to indicate that it has been rounded up, rounded up, or not rounded up or not rounded up. For example: 16.50 (+) means the actual value is greater than 16.50, which is rounded off to 16.50; 16.50 (~) means the actual value is less than 601
16.50, which is rounded off to 16.50. GB 8170—87
4.2.2 If the reported value needs to be rounded off, when the leftmost digit of the number to be discarded is 5 and there are no digits or all zeros after it, the value with a (+) sign after it is rounded off to ～, the value with a (-) sign after it is discarded, and the others are still processed according to the rules of Chapter 3. For example: Round the following numbers to the last digit and make a judgment (the reported value is left with one more decimal place). Actual value
Reported value
15.5 （-)
-(15.5(-))
50.5 unit rounding and 0.2 unit rounding
When necessary, 0.5 unit rounding and 0.2 unit rounding can be used. 5.10.5 unit rounding
Rounding value
Multiply the value to be rounded by 2, round according to the rules of Chapter 3 at the designated digit, and divide the resulting value by 2. For example: Round the following numbers to 0.5 units (or rounding intervals) 0.5 interval) proposed rounding value
5.20.2 unit rounding
2A rounding value
(rounding interval is 1)
A rounding value
(rounding interval is 0.5)
Multiply the proposed rounding value by 5, round according to the rules of Chapter 3 at the designated digit, and then divide the resulting value by 5. For example: Round the following numbers to 0.2 units (or rounding interval is 20) in the "hundred" digit. Proposed rounding value Value
Additional Notes:
5A rounding value
(rounding interval is 100)
This standard is proposed by the Institute of Systems Science, Chinese Academy of Sciences. This standard is drafted by the Institute of Systems Science, Chinese Academy of Sciences. The main drafter of this standard is Hao Chuanyi.
This standard is entrusted to the Institute of Systems Science, Chinese Academy of Sciences for interpretation. 602
A rounding value
(rounding interval is 20)
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