1 Basic concept of significant digits -/LB-t
The significant number of 1. 1 refers to the practical value that can be obtained in drug trials. The inaccuracy of the last digit is allowed, and this value consisting of a reliable digit and the last uncertain digit is a valid digit. The accuracy of the last digit is usually only 1 unit. Urjr [$ p]
1.2 The location of significant digits refers to the location of inaccurate digits. After this position is determined, the following numbers are invalid. The position of the inaccurate number can be any decimal number, which is represented by 10n: n can be a positive integer, such as n= 1, 10n= 10, n=2, 102= 100. N can also be a negative number, such as n =- 1,1= 0.1,n =-2, 10-2 = 0.0 1, ..., Ng.
1.3 significant digit TLT6z[
1.3. 1 In the numerical value with no decimal places and ending with several zeros, the significant digits refer to the digits obtained by subtracting invalid zeros (that is, zeros used only for positioning purposes) from the leftmost digits of non-zero digits to the right digits. For example, there are two invalid zeros in 35000, that is, three valid numbers, which should be written as 350×102; If there are three invalid zeros, it is two significant digits, which should be written as 35× 103. m=qyPY
1.3.2 In other decimal digits, the significant digit refers to the digit counting from the leftmost digit of non-zero digits to the right. For example, 3.2, 0.32, 0.032 and 0.0032 all have two significant digits, 0.0320 has three significant digits, 10.00 has four significant digits, and 12.490 has five significant digits. 3 & amp5AbIZ
1.3.3 Discontinuous numerical values (such as numbers, fractions, multiples, nominal concentrations or labeled quantities) have no inaccurate digits, and their significant digits can be regarded as infinite digits; The significant digits of constant π, e and coefficient √2 can also be regarded as infinite digits. For example, "2" and "4" in the molecular formula "H2S04" are numbers, and "1" in "1" means that its significant digits should be based on the least significant digits of other values in calculation. P.'$L\
1.3.4 pH logarithmic value, its significant digits are determined by the digits after the decimal point, and its integer part only represents the power of its real number. PH = 1 1.26(& lt； H & ltFONT & gt+& gt； = 5.5× 10- 12 mol/L), and its effective digits are only two. Z 1sRLkR^
1.3.5 When the first bit of the effective bit is 8 or 9, its effective bit can be counted by one more bit. For example, 85% and 1 15% can be regarded as three significant figures; 99.0% and 10 1.0% can be regarded as four significant figures. & lt59
2 numerical correction and its entry rules I? Four "*Ob 1N
2. 1 Numerical rounding refers to discarding the digits to be reserved in the proposed rounding, and reserving the last digit or digits according to the discarded digits. ]Ag{#GJ5D
2.2 Rounding interval is a way to determine rounding reserved digits. Once the value of the rounding interval is determined, the rounding value should be an integer multiple of this value. For example, if the rounding range is specified as 0. 1, the rounding value should be selected as an integer multiple of 0. 1, that is, the value should be rounded to one decimal place. k？ Ask \
2.3 expression for determining the number of rounding digits 2/RW(U)
2.3. 1 Specify the number T74. "Look #
2.3. 1. 1 Specify the rounding range as 10-n (n is a positive integer), or specify to round the value to n digits after the decimal point. u！ 9bhL '
2.3. 1.2 specifies that the rounding interval is 1, or specifies that the value is rounded to a number. VO(V & lt； 2lw}
2.3. 1.3 Specify the rounding interval as 10n (n is a positive integer), or round the numerical value to 10n, or round the numerical value to "ten", "hundred" and "thousand". MB3, Illinois
2.3.2 Specify to round the numerical value to n significant digits (n is a positive integer). q a}=p
2.4 Entry Rule T8\%+3e.
2.4. 1 If the leftmost digit of the number to be discarded is less than 5, it will be discarded, that is, the digits will remain unchanged. ]R6Z(^XT,E
Example 1 Round 12. 1498 to one decimal place to get 12. 1. g】。 v
In Example 2, 12. 1498 is reduced to two significant figures, and 12 is obtained. XaR(~2
2.4.2 When the leftmost digit of the number to be discarded is greater than 5, or 5, followed by digits that are not all zeros, it is 1. That is, add 1 to the last digit reserved. Eumdv#Qg
Example: 1 Round 1268 to a hundred to get 13× 102. kJ:zMVN
In Example 2, 1268 is rounded to three significant figures to get 127× 10. 2mVLRs{_
In Example 3, 10.502 is rounded to one digit to get 1 1. 2Ik@L，
2.4.3 When the leftmost digit of the number to be discarded is 5, and there is no digit on the right or all zeros, if the last digit is odd (1, 3, 5, 7, 9), enter ——, and if it is even (2, 4, 6, 8, 0), it will be discarded. . W q "
Example: 1 The rounding interval is 0. 1 (or 10- 1)? JRyw (q
Suggested rounding value Rounding value +jpC%o}C
1.050 1.0 SK_i 3？
0.350 0.4 1O]27"9
Example 2: The interval of contract modification is 1000 (or 10') J > Uzd,/
Suggested rounding value Rounding value +: oD? h
2500 2× 103 =#c？ g Wb56
3500 4× 103 ! . ot & ampEbE
Example 3 round the following figures to two significant figures v]. mv/
Revision value of the proposed revision value &; i~AXNw
0.0325 0.032 inch wPFQXU
32500 32× 103 6QOdd 6_d
2.4.4 Continuous modification of the contract is not allowed. The proposed revision quantity shall be revised once after it is confirmed, and it is not allowed to modify the contract repeatedly according to the previous rules (2.4.1-2.1.3). & ltE | K & lt}W#
The example revision is about 15.4546, and the revision interval is l.
The correct way is:15.4546-15; . wD & gt0Ig
The incorrect practices are:15.4546→15.455→15.46→15.5→16. } V3p & lt
2.4.5 For the convenience of memory, the above-mentioned rules of entering the room can be summarized as the following formula: four hospitals, six hospitals and five hospitals. If the number five is not zero, enter one; If the number after five is zero, it will look at the number before five; If the number is odd before five, it will enter one. No matter how many digits there are, they must be rounded up at one time. However, when the contract is revised according to the method of British, American and Japanese Pharmacopoeia, it can be rounded off. S & lt& ltxlW
3 operation rules When performing mathematical operations, the effective figures in addition, subtraction, multiplication and division are treated differently: HlB'yOHv!
3. 1 When multiple values are added or subtracted, the absolute error of the sum or difference obtained must be greater than that of any value. Therefore, when adding or subtracting, the numerical value with the largest absolute error (that is, the largest number of inaccurate digits) shall prevail, so as to determine the number of digits reserved by other numerical values in the operation and the effective number of digits of the calculation result. ，XW6W & ampvR；
3.2 When multiple numerical values are multiplied and divided, the relative error of the product or quotient obtained must be greater than that of any numerical value. Therefore, in the multiplication and division operation, the numerical value with the largest relative error (that is, the numerical value with the least significant digits) should be used as the standard to determine the number of digits reserved by other numerical values in the operation and the significant digits of the calculation result. Bourcq Zier
3.3 During the operation, in order to reduce the rounding error, one extra digit can be temporarily reserved for rounding other values, and when the operation result comes out, the extra digits are discarded according to the significant digits. :Yb:) WV，p。
Example:113.65+0.00823+1.633 =? M%:ACLYP
In this example, the values are added and subtracted. The absolute error of the three values is 13.65, and the last digit is the percentile (two decimal places). Therefore, all other figures are temporarily kept to one thousandth, that is, 0.00823 is changed to 0.008, 1.633, and the operation is: kRskeMr:Rd.
13.65+0.008+ 1.633 = 15.29 1 Z \ xR+3
Finally, the calculation result is modified, and 15.438+0 should only be kept to the percentile and modified to 15.29. @4h。 ?
Example 214.131× 0.07654 ÷ 0.78 =? ~，Q+E8
This example is digital multiplication and division. Among the three numerical values, 0.78 has the least significant digits, only two significant digits, so each numerical value should temporarily keep three significant digits for operation, and the final result will be revised to about two significant digits. i } RxTmG & lt
14. 13 1×0.07654÷0.78 @ 6ZQkX/
= 14. 1×0.0765÷0.78J } kat PHS
= 1.08÷0.78 & gt； t？ ; *K\x "
= 1.38 +=Crfvt
= 1.4//& gt； f#8Ho
Example 3 calculation of ofloxacin (c:. HDI & gtR4，04)。 (& lt(8(} x
In the product of elements, the significant digits of atomic number can be regarded as infinite digits, so the product can be located according to the significant digits of each atomic number; In the addition of each product, because the molecular weight value specified in the drug code is reserved to two decimal places, the product of each element should be rounded to one thousandth (three decimal places) and then added; Then the calculation result is rounded to the nearest percentile. (m =-oQ & amp； Romania Romania
12.0 1 1× 18+ 1.00794×20+ 18.9984032+ 14.006747×3+ 15.9994×4 P $ N \ o @
= 2 16.20+20. 1588+ 18.9984032+42.02624 1+63.9976 3uz @ JY " mK
= 2 16.20+20. 159+ 18.998+42.020+63.998 f？ ^ko9d
=36 1.375 gE0k|Z(RF
=36 1.38 ^|Of
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4. 1 Record the test value correctly. The number of effective digits should be determined according to the sampling amount, the precision of measuring tools, the allowable error of detection methods and the limit provisions in the standard. The detected value must be consistent with the accuracy of measurement. If there is one inaccurate figure, all accurate figures should be recorded. weU 3 nnn
4.2 Correctly master and apply the rules. No matter what method is used to calculate, the entry and exit rules should be implemented, and the calculation should be carried out with a calculator. After modification, the calculation results should be recorded. 9sf zs] Yeah.
4.3 According to the sampling requirements, select the corresponding measuring tools. & amp{]zL
4.3. 1 "Accurate weighing" means that weighing is very important, accurate to 0. 1% of the weight taken, and analytical balance or semi-micro analytical balance can be selected. "Accurate weighing" should choose a pipette that meets the national standard; If necessary, a correction value should be added. 1 \ =)b & lt； y
4.3.2 When the sampling amount is about XX, it means that the sampling amount does not exceed (100 10)% of the specified amount. 6.ASLH3#
4.3.3 If the precision of sampling quantity is not specified, the corresponding quantity shall be selected according to the significant digits of its value. When taking 5ml, 5.0ml or 5.00ml quantitatively, measure with a 5 ~ 10ml measuring cylinder, a 5 ~ 10ml graduated pipette or a 5ml pipette, respectively. & ltkN4 @ bd
4.4 Before judging whether the drug quality meets the requirements, all the data should be calculated according to the rule of rounding to take effective figures and values, and the calculation results should be rounded to the effective figures specified in the standard before making a judgment. = J & virtual reality
For example, the drying loss of pentobarbital sodium should not exceed 4.0%. Today's sample 1.0042g, the weight loss after drying is 0.0408g Please judge whether it meets the requirements. e； GLPB
In this example, three numbers are multiplied and divided, of which 0.0408 has least significant bit, which is three significant bits, which shall prevail. 9E5Ec~l
1.0408÷ 1.004 x 100.0% = 4.064% As }:~ Jy |
Because the limit stipulated in the drug code is no more than 4.0%, the calculation result is revised from 4.064% to 4. 1%, which is more than 4.0%. It should be judged as non-compliance (no more than 4.0%). Z0uo。 H@。 ordinary
However, because this example stipulates that the significant digit of the limit of 4.0% is two digits, one more digit can be temporarily reserved in the calculation process (that is, three significant digits can be reserved). @M-i$ q[4
0.0408÷ 1.00× 100% = 4.08% 3 tzb @ T
If the result is rounded to two significant figures, it is 4. 1%, which is greater than the specified limit of 4.0%, and it shall be judged as non-compliance. Modify the above limit to "no more than 4%", TJ $ &；; Eighty-nine
0.04 1÷ 1.0× 100% = 4. 1% N3dS % F，_
If further revised to one significant figure, it is 4%. If the limit of 4% is not exceeded, it shall be judged as compliant (not exceeding 4%).