Judgment : 1. The writ petition coming on for preliminary hearing in ‘B’ Group is considered for final disposal, having regard to the facts and circumstances of the case. 2. Heard the learned Counsel for the petitioner and the learned Counsel for the respondents. 3. The petitioner having completed her Bachelor of Science degree with aggregate marks of 54.71% from the N.T.R. University of Health Sciences in the year 1997, had registered herself as a Public Health Nurse and Midwife. And was also registered as a nurse under the provisions of the Andhra Pradesh Nurses and Midwifes (Extension and Amendment) Act, 1964. She was appointed as a working Staff Nurse at the Primary Health Centre, Nagasamudram (AP) on 8-7-1999. She had served for eight years and three months in the said Institutions. With an intention to pursue a Post-graduate course in M.Sc. (Nursing) (hereinafter referred to as ‘the PG course’ for brevity) had made a representation to the Regional Director of Medical Health Services (FAC), seeking permission to pursue the same. The authority, in turn, had by a communication, stated that it had no objection for the petitioner to pursue the PG course, with the second respondent-College. 4. According to the petitioner, the prescribed eligibility to secure admission to the said course was 55% marks and since the petitioner’s aggregate marks was 54.71%, she had approached respondent 3 requesting the issuance of a certificate of eligibility, to take up the course, on the basis of those marks. The respondent 3 had, in turn, communicated to the petitioner and intimated her that 0.50% would normally be rounded-off to the next digit and informed her to approach the concerned authority of the institute in that regard. Accordingly, she had approached respondent 1 and requested for issuance of such a certificate, which was issued. 5. With the said eligibility certificate in hand, she had obtained admission in the second respondent-college for the PG course under the management quota. On completion of 70% of the course in the first year of the course, when she was preparing to take her annual examination, she was informed by the second respondent to the effect that she was not eligible to take the examination. She had then sought for an explanation of the proposed cancellation of her admission. On completion of 70% of the course in the first year of the course, when she was preparing to take her annual examination, she was informed by the second respondent to the effect that she was not eligible to take the examination. She had then sought for an explanation of the proposed cancellation of her admission. She was intimated that she did not meet the eligible criteria, since she had secured less than 55% in the qualifying examination and therefore, she was not eligible. The petitioner then approached the first respondent seeking reconsideration of her case. She was not immediately informed as to her fate. It is only on 15-12-2008 was she informed that even on a further reconsideration, she was not eligible to take the examination. It is in that background, the petitioner is before this Court. 6. During the pendency of this writ petition, this Court having permitted the petitioner to take her first year examination, she had thereafter, approached this Court by another application in Misc. W.No.80407 of 2010, seeking a direction to the respondents to announce the results of her first year examination, which were withheld; Since she had already paid her examination fees for the second year examination, she was also permitted to take the second year examination, as well. 7. The question that would arise for consideration for this Court is whether the petitioner was indeed eligible to take the PG course, as she had secured 54.71% as against the minimum aggregate of 55%. 8. In this regard, the learned Counsel for the petitioner seeks to place reliance on the text book titled “Introductory Methods of Numerical Analysis” by S.S. Sastry and places reliance on the following extract therein: “1.3 Errors and Their Computations There are two kinds of numbers, exact and approximate numbers. Examples of exact numbers are 1,2,3,….1/2, 3/2,----v2, ?, e, etc., written in this manner. Approximate numbers are those that represent the numbers to a certain degree of accuracy. Thus, an approximate value of ? is 3.1416, or if we desire a better approximation, it is 3.14159265. But we cannot write the exact value of ?. The digits that are used to express a number are called significant digits or significant figures. Thus, the numbers 3.1416. 0.66667 and 4.0687 contain five significant digits each. Thus, an approximate value of ? is 3.1416, or if we desire a better approximation, it is 3.14159265. But we cannot write the exact value of ?. The digits that are used to express a number are called significant digits or significant figures. Thus, the numbers 3.1416. 0.66667 and 4.0687 contain five significant digits each. The number 0.00023 has, however, only two significant digits, 2 and 3, since the zeros serve only to fix the position of the decimal point. Similarly, the numbers 0.00145, 0.000145 and 0.0000145 all have three significant digits. In case of ambiguity, the scientific notation should be used. For example, in the number 25,600, the number of significant figures is uncertain whereas the numbers 2.56x 104, 2.560 x 104 and 2.5600 x 10 4 have three, four and five significant digits, respectively. In numerical computations, we come across numbers, which have large number of digits, and it will be necessary to cut them to a usable number of figures. This process is called rounding off. It is usual to round-off numbers according to the following rule: To round-off a number to n significant digits, discard all digits to the right off the nth digit, and if this discarded number is.- .(a) less than half a unit in the nth place, leave the nth digit unaltered; .(b) greater than half a unit in the nth place, increase the nth digit by unity; .(c) exactly half a unit in the nth place, increase the nth digit by unity if it is odd; otherwise, leave it unchanged. The number thus rounded-off is said to be correct to n significant figures. Example 1.1 The numbers given below are rounded-off to four significant figures: 1.6583 to 1.658 30.0567 to 30.06 0.859378 to 0.8594 3.14159 to 3.142 In hand computations, the round-off error can be reduced by carrying out the computations to more significant figures at each step of the computations. A useful rule is: at each step of the computation, retain at least one more significant figure than that given in the data, perform the last operation and then round-off. However, most computers allow more number of significant figures than are usually require in engineering computations. Thus, there are computers, which allow a precision of seven significant figures in the range of about 10-38 to 10-39. However, most computers allow more number of significant figures than are usually require in engineering computations. Thus, there are computers, which allow a precision of seven significant figures in the range of about 10-38 to 10-39. Arithmetic carried out with this precision is called single precision arithmetic, and several computers implement double precision arithmetic, which could be used in problems requiring greater accuracy. Usually, the double precision arithmetic is carried out to 15 decimals with a range of about 10-308 to 10308. In MATLAB, there is a provision to use double precision arithmetic. In addition to the round-off error discussed above, there is another type of error which can be caused by using approximate formulae in computations – such as one that arises when a truncated infinite series is used. This type of error is called truncation error and its study is naturally associated with the problem of convergence. Truncation error in a problem can be evaluated and we are often required to make it as small as possible. Sections 1.4 and 1.5 will be devoted to a discussion of these errors”. Further, he would submit that the above view of the learned author would clearly demonstrate that the rule of mathematical calculation insofar as rounding-off the numbers is concerned, if applied in the case on hand, the petitioner would have to be considered as having obtained 55%, as she has secured more than 54.50% and hence, would seek an appropriate direction. 9. The learned Counsel would also seek to place reliance on an unreported decision of this Court in the case of Rajeev M. v The Registrar, Viswesvaraya Technological University, Belgaum, W.P. No.51369 of 2004, disposed of on 15-9-2006, wherein the facts were, that the petitioner therein was a B.Sc., graduate and the aggregate percentage of marks secured by him was 49.88% in the qualifying examination for admission to the M.C.A. course. The marks prescribed was 50% in the qualifying examination. As in the present case on hand, he was treated as being ineligible. The marks prescribed was 50% in the qualifying examination. As in the present case on hand, he was treated as being ineligible. In that circumstance, the petitioner having approached this Court, this Court while placing reliance on several judgments of the Supreme Court, namely.- .(i) M/s. Motilal Padampat Sugar Mills Company Limited v State of Uttar Pradesh and Others ( AIR 1979 SC 621 : (1979) 2 SCC 409 : (1979)44 STC 42 (SC): (1979) 118 ITR 326 (SC)); .(ii) Rajendra Prasad Mathur v Karnataka University and Another (1986 (2) Kar.L.J.282 (SC): ILR 1986 Kar.2495 (SC): AIR 1986 SC 1448 ); (iii) A. Sudha v University of Mysore and Another ( AIR 1987 SC 2305 : (1987) 4 SCC 537 ); (iv) Kum. D.H. Samudhyatha v Visweswaraiah Technological University (VTU), Belgaum and Another (2003 (4) Kar.L.J.265: ILR 2003 Kar.302). This Court has held that the petitioner therein having completed two years of studies and when he was on the verge of completing the course. And this Court having permitted him to pursue the studies and even having directed the University to announce the results of the first year and having allowed the student to complete the course, equity demanded that the petitioner therein be permitted to complete the course. While also taking note of the fact that the Court being fully aware of the need to strictly adhere to the eligibility standards prescribed in academic matters, it was held that the authorities acted belatedly and were responsible for the student to pursue the studies over two precious years, there would not have been any occasion to strain the strict adherence to academic prescriptions by informing the petitioner that he was not eligible to pursue the course, for no fault of his. The learned Counsel would thus contend that the petition be allowed as both law and equity demand it. 10. While the learned Counsel for the respondents would vehemently oppose the present writ petition and submit that the matter is squarely covered by a decision of this Court in the case of Miss N. Gayathramma v Rajiv Gandhi University of Health Sciences (ILR 2010 Kar.2249) and would further submit that there is another unreported judgment of this Court, wherein a similar question was considered by following the above cited reported judgment and therefore, the decision cited by the petitioner, cannot be accepted. He would further submit that notwithstanding the rule of mathematics as regards ‘rounding off’ of numbers, the academic standards prescribed by the Universities would have to be strictly adhered to. As for instance if a student who secures 59.99% is not entitled to be graded as having secured a first class, if the requirement is 60%, to be so graded. 11. The marks secured by the petitioner in the case on hand in her qualifying examination is 54.71%, which is less than 55%, by reference to any of rule of Mathematics as regards ‘rounding-off of numbers’ the eligibility criteria cannot be watered down. The question of the petitioner being entitled to claim the rule of ‘rounding-off’ of the numbers, is not permissible. 12. In the light of the above contentions, the question that would arise for consideration, as already stated is: “Whether the petitioner who has secured 54.71% in her qualifying examination and who has been permitted by the authorities to pursue the Post-graduate course in M.Sc. (Nursing) is enabled to claim that she has secured 55%?” Apart from the authority cited by the Counsel for the petitioner, the following passage from the New Encyclopedia Britannica, 15th Edition, under the chapter “Numerical Analysis” at page 38 of Volume 25 is illuminating: “Errors Most problems involve infinite sets of values, each of which can potentially require an infinite number of digits for exact representation. Digital computation, either human, mechanical, or electronic, is, by its very nature, finite: it involves a finite set of numerical values, each of which is represented in a finite set of digits. These two approximations of infinite quantities by finite ones lead to the two types of error in numerical computation, round-off and truncation error. A numerical analyst is interested in determining the size of possible errors in a calculation. Analystists try to find bounds on errors or estimates of errors. A bound is a value that the analyst can guarantee the error will not exceed. An estimate is a value that the analyst believes is an approximation of the error (error estimates typically vary from the true error by a factor of 2). The word error is unfortunate because it suggests a mistake or sin. Round-off and truncation errors are unavoidable: the job of the numerical analyst is to find out how to compute accurately and efficiently in their presence. The word error is unfortunate because it suggests a mistake or sin. Round-off and truncation errors are unavoidable: the job of the numerical analyst is to find out how to compute accurately and efficiently in their presence. Finite-precision errors: round-off: The precision of a value is indicated by the number of digits used in its representation. It is typically between seven and 15 decimal digits, depending on the type of computer and calculation. Finite precision means that most values cannot be represented exactly, but that there is some round-off error in the computed approximation. For example, if 4/3 is represented by the five significant decimal digits as 1.3333 (the most accurate possible using five digits), there is a round-off error of 0.0000333… or 1/3 x 10-4, is illustrated below.- Decimal representation correctvalue 1.3333333…. 5-digit representation 1.3333 Round-off error 0.0000333…. All calculation are subject to the effects of round-off errors. Round-off errors, which are proportional to the size of the value containing the error when a fixed number of significant digits is used, can be as large as 5 in the first neglected place or one-half in the last retained place. When a value is added to a much smaller value, the round-off can be large relative to the smaller value. For example, if 23.456 is added to 10.518 in five digits, the result is 23.467, with a round-off error of -04.482. If 23,456 is subtracted from the answer, the result is 11. Thus, in five-digit arithmetic, (23.456 + 10.518)-23,456=11.0, which has an error in the third place. After the addition, the error was less than one-half in the last place, but the subtraction removed the three leading digits, 234, moving this error to the third place. This phenomenon is called cancellation. It does not cause errors but makes the size of errors already introduced larger relative to the computed result. Thus, although round-off errors are small, their effect in the final answer can be large, so that one of the tasks of the numerical analyst is to devise or modify computational schemes to minimise the effect of these errors”. (emphasis supplied) 13. The rule of Mathematics as regards ‘rounding-off of numbers’ would have to be applied to the case on hand. (emphasis supplied) 13. The rule of Mathematics as regards ‘rounding-off of numbers’ would have to be applied to the case on hand. When rules and axioms of mathematics are applied while calculating the marks and in arriving at percentages, there is no reason as to why the said rule ought not to be applied in the case of rounding-off of numbers. It is indeed disturbing that a University which imparts education and enlightens the world with knowledge, should dither in computing numbers. It would be a narrow and harsh view to hold that the academic standards prescribed by the University was a bar to adopt the rule of mathematics in ‘rounding-off of numbers’. Therefore, the argument of the learned Counsel for the respondents, is not acceptable. If the rule of mathematics is applied for one purpose, it has to be applied in all circumstances and therefore, in construing whether 54.71% would be 54% or 55%, the answer would certainly be that it is 55%. Therefore, there is no hesitation in holding that notwithstanding the strict eligibility criteria and the mandate that standards prescribed by the University, would be made applicable and that this Court ought not to interfere. The rules of academic standards would not be destroyed by virtue of treating the percentage of marks secured by the petitioner as 55% in her qualifying examination, as against 54.71%. Therefore, in the facts and circumstances of the case on hand, the view taken by the authorities is therefore, not in accordance with the rules of Mathematics as regards ‘rounding-ff of numbers’ and therefore, the percentage of marks secured by the petitioner in her qualifying examination shall be construed as 55% and she is to be held eligible for admission to the PG course. Incidentally, she has already completed the examination but the results are withheld, the same may be announced. 14. At this stage, the Counsel for the respondents would point out that this ruling would have a far-reaching implication. As for instance, where students who may have even secured 59.99% of marks would yet not be entitled to claim the marks obtained by them as 60% as per the Academic Standards prescribed by the Universities. It is claimed that by virtue of this decision, this would now be watered down. As for instance, where students who may have even secured 59.99% of marks would yet not be entitled to claim the marks obtained by them as 60% as per the Academic Standards prescribed by the Universities. It is claimed that by virtue of this decision, this would now be watered down. The Rules of Mathematics are the basis to calculate percentages, there is no legal impediment for the Universities to adopt the said rule. In fact the Universities should. The petition is allowed accordingly. The impugned communication dated 29-11-2008 in No. AC2/ADM/M.Sc. (N) 2008-09 issued by the respondent 1 vide Annexure-G is hereby quashed.