There are three different kinds of numerical values:
(a) Exact (精确) terminating values : These are expressed to as many figures as are required to give the complete values, without approximation or uncertainty.
Example 1 : 1 inch = 25.4 mm; 25.4 is an exact value 基于国际公认 Example 2 : interest rate = 1.3%; 1.3% is an exact value 基于协议 Example 3 : I have 10 fingers; 10 is an exact value 基于准确点算
(b) Inexact decimal expressions for exactly defined numbers : These numbers can be expressed with any desired accuracy by taking sufficient figures. Many values having a purely mathematical basis fall into this category.
Example 4 : 1/3, e, π
(c) Inexact (非精确) values : Figures which are subject to inherent limitations of accuracy. Experimentally determined values fall into this category.
Example 5 : The steel rod is 132.2 mm; 132.2 is an inexact value as the length may be 132.23 mm if a more precise instrument was used in the measurement.
= = = = =
Because of the uncertainty of inexact values, there are rules of arithmetic operation for the inexact values with reference to their number of significant figures.
Why the concept of Exact Value and Inexact Value is important? Here is my experience:
I know that the average of 0.13, 0.25, 0.19, 0.32,0.41 is
(0.13+0.25+0.19+0.32+0.41)/5=0.26
I would not report that the average = 0.3 by taking into account of the number of significant figure of 5 (i.e. n.s.f.=1 for the number 5), but I did not know the reason in the past. Now, I know that 5 is an exact value, so the rules of arithmetic operation for significant figures do not apply.
(There is another opinion that although 5 is an exact value, if the concept of significant figure must be imposed on it, 5 has infinite number of significant figures, i.e. 5=5.0000……00000)
I am thinking whether the limiting value (极限值, 或称界限值) specified in the testing standard is an exact value. If it is an exact value, I need not consider the number of significant values when I report the measured value, only consider the precision as indicated by the limiting value.
例: 极限值=0.030%, 测定值=0.1573%
My opinion:
(1) 我不认为0.030%是一个有2位有效数字的数, because it is an exact value (2) 0.030%显示了精度要求为千分位
Inexact value ≠ significant figure, I think that significant figure is one of the attributes of inexact value. I am still studying this subject and unable make the precise definitions for them. Perhaps, the following example may illustrate their difference:
If the population of a city is 1.030×106 in government survey record and when it is printed as 1030000 in the newspaper, I would have the following description about the value 1030000:
1030000 is an inexact value (人口统计时是以千为单位的, 不会精确至几百几十的)
The problem is how do you interpret “位”. In the past month, I studied the “significant figure” again and found that there are two meanings of “位”, i.e. “number” and “place”. Example:
(A) 0.00235 : 3位有效数字 (number of significant figures = 3)
(B) 0.00235 : 精确至小数後5位 (5 decimal places)
http://bbs.instrument.com.cn/shtml/20100608/2599734/ 中提到 “药典明确规定了结果的有效位数要和标准一致啊！！”, 这个“位数要和标准一致”中的“位数”应是(B)“place”. If this interpretation is accepted, there is no difference between 国标 and 国外某企业的SOP. (GB/T 8170-2008 Clause 4.3.3.1中用的字是“数位”一致, my interpretation is “in agreement with the places of the limiting value”)
I am writing a notes about the Significant Figure, and really really want to know the exact wording in 中国药典
= = = = = =
My suggestion to your SOP about rounding is “the rounding of the measured value should be in agreement with the limiting value” 轻轻带过, 留有演译的余地;
or more specific “the rounding of the measured value should be in agreement with the places of the limiting value” so as to be in line with GB/T 8170-2008 Clause 4.3.3.1
or “in accordance with xxxxxx unless otherwise specified”
我的社区
签到
迎国庆送壕礼！十月发帖抢大疆云台
【官方邀请】高效液相色谱使用情况有奖调研
喜迎国庆！第十七届原创大赛超级原创日参赛奖励翻倍
丹纳赫四十周年寄语征集领大礼包
