数字修约间隔请教？ [复制链接]

请KIIICN先生看看下面的标准,共同学习一下,共同提高!!!àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

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中华人民共和国国家标准——数值修约规则（GB8170—87）

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

本标准适用于科学技术与生产活动中试验测定和计算得出的各种数值．需要修约时，除另有规定者外，应按本标准给出的规则进行。àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

1　术àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
            语àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

1.1修约间隔àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

系确定修约保留位数的一种方式．修约间隔的数值一经确定，修约值即应为该数值的整数倍àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
            。àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

例1：如指定修约间隔为0.1，修约值即应在0.1的整数倍中选取，相当于将数值修约到一位小数。àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

例2：如指定修约间隔为100，修约值即应在100的整数倍中选取，相当于将数值修约到àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
            “àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
            百àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
            ”àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
            数位。àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

1.2　有效位数àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
            àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

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对没有小数位且以若干个零结尾的数值，从非零数字最左一位向右数得到的位数减去无效零（即仅为定位用的零）的个数；对其他十进位数，从非零数字最左一位向右数而得到的位数，就是有效位数。àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

例1：35000，若有两个无效零，则为三位有效位数，应写为350×10 2 ；若有三个无效零，则为两位有效位数，应写为35×10 3 。àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

例2：3.2，0.32，0.032，0.0032均为两位有效位数；0.0320为三位有效位数。àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

例3：12.490为五位有效位数；10.00为四位有效位数。àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

1.3　0.5单位修约（半个单位修约）àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

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指修约间隔为指定数位的0.5单位，即修约到指定数位的0.5单位。àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

例如，将60.28修约到个数位的0.5单位，得60.5（修约方法见本规则5.1）àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

1.4　0.2单位修约àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

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指修约间隔为指定数位的0.2单位，即修约到指定数位的0.2单位。àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

例如，将832修约到àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
            “àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
            百àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
            ”àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
            数位的0.2单位，得840（修约方法见本规则5.2）àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

2　确定修约位数的表达方式àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

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2.1　指定数位àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

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a. 指定修约间隔为10 n （n为正整数），或指明将数值修约到n位小数；àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

b. 指定修约间隔为1，或指明将数值修约到个数位；àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

c. 指定修约间隔为10 n ，或指明将数值修约到10 n 数位（n为正整数），或指明将数值修约到àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
            “àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
            十àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
            ”àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
            ，àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
            “àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
            百àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
            ”àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
            ，àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
            “àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
            千àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
            ”àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
            ……数位。àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

2.2　指定将数值修约成n位有效位数àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

3　进舍规则àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

3.1　拟舍弃数字的最左一位数字小于5时，则舍去，即保留的各位数字不变。àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

例1：将12.1498修约到一位小数，得12.1。àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

例2：将12.1498修约成两位有效位数，得12。àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

3.2　拟舍弃数字的最左一位数字大于5；或者是5，而其后跟有并非全部为0的数字时，则进一，即保留的末位数字加1。àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

例1：将1268修约到àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
            “àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
            百àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
            ”àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
            数位，得13×10 2 （特定时可写为1300）。àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

例2：将1268修约成三位有效位数，得127×10（特定时可写为1270）。àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

例3：将10.502修约到个数位，得11。àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

注：本标准示例中，àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
            “àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
            特定时àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
            ”àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
            的涵义系指修约间隔或有效位数明确时。àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

3.3　拟舍弃数字的最左一位数字为5，而右面无数字或皆为0时，若所保留的末位数字为奇数（1，3，5，7，9）则进一，为偶数（2，4，6，8，0）则舍弃。àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

例1：修约间隔为0.1（或10 -1 ）àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

拟修约数值　　修约值àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

1.050　　　　　1.0

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

0.350　　　　　0.4

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

例2：修约间隔为1000（或10 3 ）àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

拟修约数值　　修约值àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

2500　　　　　2×10 3 （特定时可写为2000）àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

3500　　　　　4×10 3 （特定时可写为4000）àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

例3：将下列数字修约成两位有效位数àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

拟修约数值　　修约值àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

0.0325　　　　0.032àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

32500　　　　32×10 3 （特定时可写为32000）àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

3.4　负数修约时，先将它的绝对值按上述3.1~3.3规定进行修约，然后在修约值前面加上负号。àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

例1：将下列数字修约到àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
            “àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
            十àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
            ”àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
            数位àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

拟修约数值　　修约值àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

-355　　　　　-36×10（特定时可写为-360）àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

-325　　　　　-32×10（特定时可写为-320）àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

例2：将下列数字修约成两位有效位数àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

拟修约数值　　修约值àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

-365　　　　　-36×10（特定时可写为-360）àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

-0.0365　　　àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
            －0.036

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

4　不许连续修约àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

4.1　拟修约数字应在确定修约位数后一次修约获得结果，而不得多次按第3章规则连续修约。àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

例如：修约15.4546，修约间隔为1

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

正确的做法：àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

15.4546→15

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

不正确的做法：àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

15.4546→15.455→15.46→15.5→16

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

4.2　在具体实施中，有时测试与计算部门先将获得数值按指定的修约位数多一位或几位报出，而后由其他部门判定。为避免产生连续修约的错误，应按下述步骤进行。àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

4.2.1报出数值最右的非零数字为5时，应在数值后面加àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
            “àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
            （＋）àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
            ”àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
            或àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
            “àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
            （－）àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
            ”àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
            或不加符号，以分别表明已进行过舍、进或未舍未进。àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

如：16.50（＋）表示实际值大于16.50，经修约舍弃成为16.50；16.50（－）表示实际值小于16.50，经修约进一成为16.50。àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

4.2.2　如果判定报出值需要进行修约，当拟舍弃数字的最左一位数字为5而后面无数字或皆为零时，数值后面有(+)号者进一，数值后面有(-)号者舍去，其他仍按第3章规则进行。àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

例如：将下列数字修约到个数位后进行判定（报出值多留一位到一位小数）。àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

实测值　　报出值　　　　　修约值àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

15.4546　　15.5（一）　　　15

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

16.5203　　16.5（＋）　　　17

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

17.5000　　17.5　　　　　　18àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

-15.4546　　－（15.5(一)）-15

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

5　0.5单位修约与0.2单位修约àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

必要时，可采用0.5单位修约和0.2单位修约。àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

5.1　0.5单位修约àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

将拟修约数值乘以2，按指定数位依第3章规则修约，所得数值再除以2。àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

如：将下列数字修约到个数位的0.5单位（或修约间隔为0.5）àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

拟修约数值　　乘2　　　2A修约值　　　　　A修约值àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

（A）　　　　（2A）　　（修约间隔为1）　（修约间隔为0.5）àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

60.25　　　　120.50　　120　　　　　　　　60.0àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

60.38　　　　120.76　　121　　　　　　　　60.5àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

-60.75　　　 -121.50　　-122　　　　　　　-61.0àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

5.2　 0.2单位修约àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

将拟修约数值乘以5，按指定数位依第3章规则修约，所得数值再除以5。àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

例如：将下列数字修约到àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
            “àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
            百àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
            ”àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
            数位的0.2单位（或修约间隔为20）àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

拟修约数值　　乘5　　　5A修约值　　　　　　A修约值àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

（A）　　　　（5A）　　（修约间隔为100）　（修约间隔为20）àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

830　　　　　　4150　　4200　　　　　　　　840àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

842　　　　　　4210　　4200　　　　　　　　840àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

-930　　　　　-4650　　-4600　　　　　　　-920àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

附加说明：àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
            àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

本标准由中国科学院系统科学研究所提出。àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

本标准由中国科学院系统科学研究所负责起草。àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

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本标准主要起草人吴传义。àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½
                

àŸóp÷³ƒbbs.3c3t.com±ìƒáî3³y½

本标准委托中国科学院系统科学研究所负责解释。

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