请KIIICN先生看看下面的标准,共同学习一下,共同提高!!!ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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中华人民共和国国家标准——数值修约规则(GB8170—87)ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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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。ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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1 术ÉáQx I\Ôbbs.3c3t.com>U^¥Û
语ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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1.1修约间隔ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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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ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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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。ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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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ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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数位。ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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1.2 有效位数ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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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。ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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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 。ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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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。ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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例3:12.490为五位有效位数;10.00为四位有效位数。ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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1.3 0.5单位修约(半个单位修约)ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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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。ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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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)ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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1.4 0.2单位修约ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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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。ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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例如,将832修约到ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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数位的0.2单位,得840(修约方法见本规则5.2)ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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2 确定修约位数的表达方式ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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2.1 指定数位ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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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;ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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b. 指定修约间隔为1,或指明将数值修约到个数位;ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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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ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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千ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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……数位。ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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2.2 指定将数值修约成n位有效位数ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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3 进舍规则ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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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。ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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例1:将12.1498修约到一位小数,得12.1。ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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例2:将12.1498修约成两位有效位数,得12。ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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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。ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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例1:将1268修约到ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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数位,得13×10 2 (特定时可写为1300)。ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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例2:将1268修约成三位有效位数,得127×10(特定时可写为1270)。ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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例3:将10.502修约到个数位,得11。ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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注:本标准示例中,ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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的涵义系指修约间隔或有效位数明确时。ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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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。ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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例1:修约间隔为0.1(或10 -1 )ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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拟修约数值 修约值ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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1.050 1.0 ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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0.350 0.4 ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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例2:修约间隔为1000(或10 3 )ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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拟修约数值 修约值ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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2500 2×10 3 (特定时可写为2000)ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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3500 4×10 3 (特定时可写为4000)ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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例3:将下列数字修约成两位有效位数ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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拟修约数值 修约值ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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0.0325 0.032ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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32500 32×10 3 (特定时可写为32000)ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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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。ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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例1:将下列数字修约到ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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数位ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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拟修约数值 修约值ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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-355 -36×10(特定时可写为-360)ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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-325 -32×10(特定时可写为-320)ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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例2:将下列数字修约成两位有效位数ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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拟修约数值 修约值ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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-365 -36×10(特定时可写为-360)ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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-0.0365 ÉáQx I\Ôbbs.3c3t.com>U^¥Û
-0.036 ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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4 不许连续修约ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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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。ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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例如:修约15.4546,修约间隔为1 ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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正确的做法:ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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15.4546→15 ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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不正确的做法:ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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15.4546→15.455→15.46→15.5→16 ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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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。ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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4.2.1报出数值最右的非零数字为5时,应在数值后面加ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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(+)ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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或ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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(-)ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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或不加符号,以分别表明已进行过舍、进或未舍未进。ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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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。ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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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。ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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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)。ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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实测值 报出值 修约值ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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15.4546 15.5(一) 15 ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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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)ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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拟修约数值 乘2 2A修约值 A修约值ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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(A) (2A) (修约间隔为1) (修约间隔为0.5)ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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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。ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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(A) (5A) (修约间隔为100) (修约间隔为20)ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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附加说明:ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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本标准由中国科学院系统科学研究所提出。ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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本标准由中国科学院系统科学研究所负责起草。ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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本标准主要起草人吴传义。ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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本标准委托中国科学院系统科学研究所负责解释。ÉáQx I\Ôbbs.3c3t.com>U^¥Û
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