This document provides the rules for rounding off numerical values from the Indian Standard IS 2 (1960). It aims to provide a uniform procedure for rounding values to promote transparency. The key points are:
1. It defines terminology like number of decimal places, significant figures, and fineness of rounding.
2. The rules for rounding to a unit of fineness are to keep the last figure unchanged if the next figure is <5, and increase the last figure by 1 if the next figure is >5 or is 5 followed by non-zero figures.
3. Rounding should be done in one step to most accurately calculate sums and averages of rounded values.
El documento presenta información sobre el portafolio estudiantil de fisiología humana de una estudiante de enfermería de la Universidad Técnica de Ambato. Incluye la misión y visión de la universidad, la facultad y la carrera de enfermería, así como el syllabus de la asignatura de fisiología humana con objetivos, unidades temáticas, horarios y métodos de evaluación.
O seu grande momento está se aproximando e as emoções aumentam a cada dia. Quando chegue a hora, os noivos irão sentir todo tipo de sensações, terão várias ações que expressarão distintos sentimentos. Estes movimentos devem ser imortalizados por meio de belas imagens que traduzem este instante. Este é o objetivo da Com Carinho Fotografias.
Las enfermedades autoinmunes son afecciones en las que el sistema inmune ataca células y tejidos sanos del propio organismo. Este documento escrito por la estudiante de enfermería Soledad Jiménez para su tutor el Dr. Gustavo Moreno, explora las enfermedades autoinmunes como parte de su curso de Fisiología Humana en el tercer semestre de la carrera de Enfermería de la Universidad Técnica de Ambato en Ecuador durante el año 2016.
La coagulación sanguínea es un proceso fisiológico normal que detiene el sangrado. El documento es un informe de la estudiante de enfermería Soledad Jiménez sobre la coagulación sanguínea para su tutor el Dr. Gustavo Moreno en la Universidad Técnica de Ambato en Ecuador en 2016.
Este documento presenta una actividad de aprendizaje propuesta para Microsoft Word 2013 que incluye 13 pasos para configurar y personalizar un documento sobre el cuento "Pacoyunque" de César Vallejo, como aplicar formatos, guardar el archivo en la nube OneDrive, agregar propiedades y configurar la impresión. El objetivo es que los estudiantes demuestren su dominio de las herramientas básicas de Word.
El documento presenta información sobre el portafolio estudiantil de Farmacología de la estudiante Soledad Jiménez de la Universidad Técnica de Ambato en Ecuador. Incluye la misión y visión de la universidad, la facultad de Ciencias de la Salud y la carrera de Enfermería, así como el syllabus de la asignatura de Farmacología I que incluye objetivos, contenidos, profesores y horarios.
El documento trata sobre el sistema nervioso central y fue escrito por la estudiante Soledad Jiménez para su tercer semestre de la carrera de Enfermería en la Universidad Técnica de Ambato bajo la tutoría del Dr. Gustavo Moreno.
La guía presenta orientaciones para la formulación del Proyecto Educativo Institucional (PEI) de las instituciones educativas del Perú. Explica que el PEI es un instrumento de planificación a mediano plazo que orienta la gestión de la institución educativa y define su estructura en tres secciones: identificación de la IE, análisis situacional y propuesta de gestión. Asimismo, detalla las cuatro etapas del proceso de formulación del PEI: acciones iniciales, análisis de resultados e implementación, identificación de la
El documento presenta información sobre el portafolio estudiantil de fisiología humana de una estudiante de enfermería de la Universidad Técnica de Ambato. Incluye la misión y visión de la universidad, la facultad y la carrera de enfermería, así como el syllabus de la asignatura de fisiología humana con objetivos, unidades temáticas, horarios y métodos de evaluación.
O seu grande momento está se aproximando e as emoções aumentam a cada dia. Quando chegue a hora, os noivos irão sentir todo tipo de sensações, terão várias ações que expressarão distintos sentimentos. Estes movimentos devem ser imortalizados por meio de belas imagens que traduzem este instante. Este é o objetivo da Com Carinho Fotografias.
Las enfermedades autoinmunes son afecciones en las que el sistema inmune ataca células y tejidos sanos del propio organismo. Este documento escrito por la estudiante de enfermería Soledad Jiménez para su tutor el Dr. Gustavo Moreno, explora las enfermedades autoinmunes como parte de su curso de Fisiología Humana en el tercer semestre de la carrera de Enfermería de la Universidad Técnica de Ambato en Ecuador durante el año 2016.
La coagulación sanguínea es un proceso fisiológico normal que detiene el sangrado. El documento es un informe de la estudiante de enfermería Soledad Jiménez sobre la coagulación sanguínea para su tutor el Dr. Gustavo Moreno en la Universidad Técnica de Ambato en Ecuador en 2016.
Este documento presenta una actividad de aprendizaje propuesta para Microsoft Word 2013 que incluye 13 pasos para configurar y personalizar un documento sobre el cuento "Pacoyunque" de César Vallejo, como aplicar formatos, guardar el archivo en la nube OneDrive, agregar propiedades y configurar la impresión. El objetivo es que los estudiantes demuestren su dominio de las herramientas básicas de Word.
El documento presenta información sobre el portafolio estudiantil de Farmacología de la estudiante Soledad Jiménez de la Universidad Técnica de Ambato en Ecuador. Incluye la misión y visión de la universidad, la facultad de Ciencias de la Salud y la carrera de Enfermería, así como el syllabus de la asignatura de Farmacología I que incluye objetivos, contenidos, profesores y horarios.
El documento trata sobre el sistema nervioso central y fue escrito por la estudiante Soledad Jiménez para su tercer semestre de la carrera de Enfermería en la Universidad Técnica de Ambato bajo la tutoría del Dr. Gustavo Moreno.
La guía presenta orientaciones para la formulación del Proyecto Educativo Institucional (PEI) de las instituciones educativas del Perú. Explica que el PEI es un instrumento de planificación a mediano plazo que orienta la gestión de la institución educativa y define su estructura en tres secciones: identificación de la IE, análisis situacional y propuesta de gestión. Asimismo, detalla las cuatro etapas del proceso de formulación del PEI: acciones iniciales, análisis de resultados e implementación, identificación de la
This document outlines rules for rounding numerical values in calculations and measurements according to the Indian Standard IS: 2-1960. It provides definitions for terms like number of decimal places and significant figures. The main rules prescribed are:
1) Round to the nearest whole number, leaving unchanged values less than 0.5 and increasing values above 0.5. For values of exactly 0.5, round up if the preceding digit is odd and leave unchanged if even.
2) For non-unity fineness of rounding (e.g. 0.1 or 10), divide the value by the fineness, round the quotient according to the above rule, and multiply the rounded quotient by the fineness.
3)
This document outlines rules for rounding off numerical values in calculations and measurements to provide more rational results. It defines key terms like number of decimal places and significant figures. The main rules prescribed are: for unit rounding, keep or increase the last figure based on the next figure; for other rounding levels, divide by the rounding level and round the quotient according to unit rounding rules. The goal is to produce more accurate sums and averages when rounding multiple values.
This document is the Indian Standard (Part 1) from 1985 that establishes a series of preferred numbers for use in engineering and technical standards. It contains:
- The basic series of preferred numbers from 1 to 10 in factors of R5, R10, R20 and R40, with their theoretical values, calculated values, and percentages differences.
- An exceptional R80 series of preferred numbers from 1 to 1.8.
- Commentary on the definition and terminology of preferred numbers, designation and use of the basic series, and methods for deriving additional series from the basic ones.
The standard aims to provide authoritative and readily accessible preferred number values for technical use, while guiding their appropriate selection and
This document provides the standard test method for measuring the temperature index of insulation or sheathing material for electric cables. It specifies using a test apparatus that determines the oxygen index at increasing temperatures in increments of 20°C or less, starting at ambient temperature. The temperature index is determined by extrapolating the data points of oxygen index versus temperature to where the oxygen index is 21%, the concentration of oxygen in air. This provides an assessment of the material's properties under heat and fire.
Is 919.1.1993 iso systems of limits and fits,Vishal Mistry
This document provides information on an Indian standard regarding the ISO system of limits and fits. It establishes the bases of the ISO system including standard tolerances and fundamental deviations. The standard defines key terms used such as shaft, hole, size, deviation, tolerance, and fits. It provides graphical representations of tolerances and deviations. The standard aims to promote accuracy and consistency in manufacturing parts that interface through standardized tolerances and limits.
Is 919.1.1993 iso systems of limits and fits,Vishal Mistry
This document provides information on an Indian standard regarding the ISO system of limits and fits. It establishes the bases of the ISO system including standard tolerances and fundamental deviations. The standard defines key terms used such as shaft, hole, size, deviation, tolerance, and fits. It provides graphical representations of tolerances and deviations. The standard aims to promote accuracy and consistency in manufacturing parts that interface through standardized tolerances and limits.
The sequential inversion technique (SIT) and differential coefficients method (DCM) are two methods discussed to reconstruct true transient emission signals from measurements taken by analyzers, which introduce delays and dispersion. The SIT reconstructs the input second by second based on the measured response and dispersion characteristics. Testing with real data showed it can accurately reconstruct signals without noise. However, reconstruction fails if the dispersion characteristics change or there is signal noise. The DCM defines the real input as a linear combination of the output and its derivatives. It was more accurate than SIT when noise was present. Both methods aim to compensate for measurement delays and dispersion to obtain instantaneous emissions from analyzer readings.
this book gives the testing procedure for performance of a positive displacement compressor.
it is a complete compilation for the manufacturing of the testing equipment as well
easy to understand and gives an accuracy of 5%
This is a subsidiary indian standard to ISO 1217, and ISO 5167
Iso 2858 end suction centrifugal pumps (16 bar)BESANT VARGHEES
This document is the Indian Standard for end-suction centrifugal pumps with a maximum operating rating of 16 bar. It specifies the principal dimensions and nominal duty point for these pumps.
The standard provides guidelines for pump designation based on inlet diameter, outlet diameter, and impeller diameter. It includes a table listing nominal duty points and key dimensions for various pump sizes.
The standard also specifies that the static test pressure shall be 1.5 times the maximum discharge pressure up to 24 bar. Manufacturers and users should agree on the relationship between cold test pressure and hot operating pressure.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Low power test pattern generation for bist applicationseSAT Journals
Abstract This paper proposes a novel test pattern generator (TPG) for built-in self-test. Our method generates multiple single input change (MSIC) vectors in a pattern, i.e., each vector applied to a scan chain is an SIC vector. A reconfigurable Johnson counter and a scalable SIC counter are developed to generate a class of minimum transition sequences. The proposed TPG is flexible to both the test-per-clock and the test-per-scan schemes. A theory is also developed to represent and analyze the sequences and to extract a class of MSIC sequences. Analysis results show that the produced MSIC sequences have the favorable features of uniform distribution and low input transition density. Simulation results with ISCAS benchmarks demonstrate that MSIC can save test power and impose no more than 7.5% overhead for a scan design. It also achieves the target fault coverage without increasing the test length. Keywords—Built-in self-test (BIST), low power, single-input change (SIC), test pattern generator (TPG)
This document provides information on the disclosure of a public safety standard from the Bureau of Indian Standards to promote transparency and access to information. It aims to make this standard available, especially to disadvantaged communities and those in education.
The standard is IS 2720-16 (1987) which outlines the laboratory method for determining the California Bearing Ratio (CBR) of soils. The CBR is an index used to evaluate the strength of soil subgrades for flexible pavement design. This particular standard was first published in 1965 and revised in 1979 and 1987 to establish a uniform testing procedure and incorporate experience gained from its use in research laboratories. It describes the apparatus, sample preparation methods, testing procedures, and calculations for determining the CBR
Comparison of Estimated Torques Using Low Pass Filter and Extended Kalman Fil...IAES-IJPEDS
Torque calculation process is one of the major concerns for controlling induction motors in industry, which requires very accurate state estimation of unmeasurable variables of nonlinear models. This can be solved if the variables used for torque calculation is accurately estimated. This paper presents a torque calculation based on a voltage model represented with a low-pass filter (LPF), and an extended Kalman filter (EKF). The experimental results showed that the estimated torque at low speed based on EKF is more accurate in the expense of more complicated and larger computational time.
Vibration analysis applied to conveyor belt.IRJET Journal
1) Researchers analyzed vibration frequencies of a conveyor belt carrying different weights to compare results.
2) Vibration measurements were taken of the conveyor belt carrying 1kg, its normal weight, and 4kg, which causes more effort.
3) Mathematical calculations and graphs of the belt, motor, and bearing frequencies were produced to analyze the effects of different weights and extend equipment life.
IRJET- Vibration Analysis and Design Modification of Automobile SilencerIRJET Journal
This document presents a study on vibration analysis and design modification of an automobile silencer. The study aims to analyze vibrations in an existing silencer using finite element analysis (FEA) and experimental modal analysis. Natural frequencies are obtained and compared to validate the FEA results. The silencer geometry is then modified to optimize natural frequencies. Modal analysis is performed on the modified design and natural frequencies are compared to the existing silencer. Results show that increasing the silencer mass, by increasing baffle plate thickness, leads to decreased natural frequencies, while decreasing the mass increases natural frequencies.
This document provides a summary of an Indian Standard code of practice for laying concrete pipes. It begins by stating that the standard lays out methods for determining loads on pipes and their required strength, as well as procedures for handling, laying, and jointing pipes. This is to ensure pipes manufactured according to other specified standards are not subjected to excessive loads. The document then provides extracts from the Indian Standard code, including definitions, methods for calculating pipe loads and strength requirements, guidelines for handling, bedding, backfilling, and jointing of pipes.
The document discusses the design and analysis of injector nozzles for minimizing thrust loss. The objectives are to fabricate a thrust measurement system and measure thrust loss with different injector nozzle designs including ramped nozzles. Analytical calculations were performed using isentropic equations to estimate thrust ranges from 30.06N to 72.52N for various stagnation pressures and nozzle designs. Computational fluid dynamics analysis was also conducted using a shear stress transport turbulence model to simulate different nozzle designs and obtain thrust values for validation. Experimental thrust measurements will also be taken and compared to the analytical and computational results.
IRJET- Experimental Investigation of Flow through Perforated Plate in Conical...IRJET Journal
This document describes an experimental investigation of flow through a perforated plate inside a conical diffuser. The goal is to improve the axial flow and achieve higher static pressure rise without total pressure loss. A supersonic wind tunnel was used to test a conical diffuser with an angle of 7 degrees that had two perforated plates placed inside at a distance of 450mm from the inlet. Pressure values were measured using a manometer at various ports and the coefficient of pressure was calculated both without and with the perforated plates. The results found that the addition of the perforated plates improved the flow uniformity and increased the static pressure rise inside the diffuser compared to when no plates were used.
DESIGN OF INTELLIGENT CONTROL SYSTEM USING ACOUSTIC PARAMETERS FOR GRINDING M...cscpconf
This paper utilizes acoustic parameters such as FS,NC, N, P, INC, FL, FH, W for acoustic signals S of different running conditions of a ballmill to deriveout the acoustic signatures and
hence control signals, which is to be used for designing the control systems of the mill. The parameters FS, NC, N, P, INC, FL, FH and W are represented by sample rate in Hz, number of
cepstral coefficients, length of frame in samples, number of filters in filter bank, frame increment, low end of the lowest filter, high end of highest filter and the window over which the analysis is to be performed respectively. The work establishes an
appropriate theoretical background that helps to predict dynamic breakage characteristics with respect to particle size
distribution of materials, adequately supported by experimental data. The signatures of different running conditions of grinding mill have been extracted from the captured signal in time frame
these have been used as feedback signal to monitor the grinding operation. Condenser based microphones have been used for capturing acoustic signals in time domain directly in
computers and stored for further analysis. Matlab R2010b has been used for different analysis of the experiment. On analyzing the signatures, it has been observed whether the fines are
produced progressively to attain the desired size range or the mill producing undesired products. Thus, the approach has been used in this paper has the ability to arrive in the stage of
optimum grinding by tuning parameters of the mill in real time, and also it can prevent the mill to enter into an erroneous state. Moreover, on study it has found that the present scheme can be
used more accurately in comparison to the earlier work of the author. This paper presents an implementation scheme to use acoustic signal as the control signal to regulate the operation of
a grinding mill.
This document outlines rules for rounding numerical values in calculations and measurements according to the Indian Standard IS: 2-1960. It provides definitions for terms like number of decimal places and significant figures. The main rules prescribed are:
1) Round to the nearest whole number, leaving unchanged values less than 0.5 and increasing values above 0.5. For values of exactly 0.5, round up if the preceding digit is odd and leave unchanged if even.
2) For non-unity fineness of rounding (e.g. 0.1 or 10), divide the value by the fineness, round the quotient according to the above rule, and multiply the rounded quotient by the fineness.
3)
This document outlines rules for rounding off numerical values in calculations and measurements to provide more rational results. It defines key terms like number of decimal places and significant figures. The main rules prescribed are: for unit rounding, keep or increase the last figure based on the next figure; for other rounding levels, divide by the rounding level and round the quotient according to unit rounding rules. The goal is to produce more accurate sums and averages when rounding multiple values.
This document is the Indian Standard (Part 1) from 1985 that establishes a series of preferred numbers for use in engineering and technical standards. It contains:
- The basic series of preferred numbers from 1 to 10 in factors of R5, R10, R20 and R40, with their theoretical values, calculated values, and percentages differences.
- An exceptional R80 series of preferred numbers from 1 to 1.8.
- Commentary on the definition and terminology of preferred numbers, designation and use of the basic series, and methods for deriving additional series from the basic ones.
The standard aims to provide authoritative and readily accessible preferred number values for technical use, while guiding their appropriate selection and
This document provides the standard test method for measuring the temperature index of insulation or sheathing material for electric cables. It specifies using a test apparatus that determines the oxygen index at increasing temperatures in increments of 20°C or less, starting at ambient temperature. The temperature index is determined by extrapolating the data points of oxygen index versus temperature to where the oxygen index is 21%, the concentration of oxygen in air. This provides an assessment of the material's properties under heat and fire.
Is 919.1.1993 iso systems of limits and fits,Vishal Mistry
This document provides information on an Indian standard regarding the ISO system of limits and fits. It establishes the bases of the ISO system including standard tolerances and fundamental deviations. The standard defines key terms used such as shaft, hole, size, deviation, tolerance, and fits. It provides graphical representations of tolerances and deviations. The standard aims to promote accuracy and consistency in manufacturing parts that interface through standardized tolerances and limits.
Is 919.1.1993 iso systems of limits and fits,Vishal Mistry
This document provides information on an Indian standard regarding the ISO system of limits and fits. It establishes the bases of the ISO system including standard tolerances and fundamental deviations. The standard defines key terms used such as shaft, hole, size, deviation, tolerance, and fits. It provides graphical representations of tolerances and deviations. The standard aims to promote accuracy and consistency in manufacturing parts that interface through standardized tolerances and limits.
The sequential inversion technique (SIT) and differential coefficients method (DCM) are two methods discussed to reconstruct true transient emission signals from measurements taken by analyzers, which introduce delays and dispersion. The SIT reconstructs the input second by second based on the measured response and dispersion characteristics. Testing with real data showed it can accurately reconstruct signals without noise. However, reconstruction fails if the dispersion characteristics change or there is signal noise. The DCM defines the real input as a linear combination of the output and its derivatives. It was more accurate than SIT when noise was present. Both methods aim to compensate for measurement delays and dispersion to obtain instantaneous emissions from analyzer readings.
this book gives the testing procedure for performance of a positive displacement compressor.
it is a complete compilation for the manufacturing of the testing equipment as well
easy to understand and gives an accuracy of 5%
This is a subsidiary indian standard to ISO 1217, and ISO 5167
Iso 2858 end suction centrifugal pumps (16 bar)BESANT VARGHEES
This document is the Indian Standard for end-suction centrifugal pumps with a maximum operating rating of 16 bar. It specifies the principal dimensions and nominal duty point for these pumps.
The standard provides guidelines for pump designation based on inlet diameter, outlet diameter, and impeller diameter. It includes a table listing nominal duty points and key dimensions for various pump sizes.
The standard also specifies that the static test pressure shall be 1.5 times the maximum discharge pressure up to 24 bar. Manufacturers and users should agree on the relationship between cold test pressure and hot operating pressure.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Low power test pattern generation for bist applicationseSAT Journals
Abstract This paper proposes a novel test pattern generator (TPG) for built-in self-test. Our method generates multiple single input change (MSIC) vectors in a pattern, i.e., each vector applied to a scan chain is an SIC vector. A reconfigurable Johnson counter and a scalable SIC counter are developed to generate a class of minimum transition sequences. The proposed TPG is flexible to both the test-per-clock and the test-per-scan schemes. A theory is also developed to represent and analyze the sequences and to extract a class of MSIC sequences. Analysis results show that the produced MSIC sequences have the favorable features of uniform distribution and low input transition density. Simulation results with ISCAS benchmarks demonstrate that MSIC can save test power and impose no more than 7.5% overhead for a scan design. It also achieves the target fault coverage without increasing the test length. Keywords—Built-in self-test (BIST), low power, single-input change (SIC), test pattern generator (TPG)
This document provides information on the disclosure of a public safety standard from the Bureau of Indian Standards to promote transparency and access to information. It aims to make this standard available, especially to disadvantaged communities and those in education.
The standard is IS 2720-16 (1987) which outlines the laboratory method for determining the California Bearing Ratio (CBR) of soils. The CBR is an index used to evaluate the strength of soil subgrades for flexible pavement design. This particular standard was first published in 1965 and revised in 1979 and 1987 to establish a uniform testing procedure and incorporate experience gained from its use in research laboratories. It describes the apparatus, sample preparation methods, testing procedures, and calculations for determining the CBR
Comparison of Estimated Torques Using Low Pass Filter and Extended Kalman Fil...IAES-IJPEDS
Torque calculation process is one of the major concerns for controlling induction motors in industry, which requires very accurate state estimation of unmeasurable variables of nonlinear models. This can be solved if the variables used for torque calculation is accurately estimated. This paper presents a torque calculation based on a voltage model represented with a low-pass filter (LPF), and an extended Kalman filter (EKF). The experimental results showed that the estimated torque at low speed based on EKF is more accurate in the expense of more complicated and larger computational time.
Vibration analysis applied to conveyor belt.IRJET Journal
1) Researchers analyzed vibration frequencies of a conveyor belt carrying different weights to compare results.
2) Vibration measurements were taken of the conveyor belt carrying 1kg, its normal weight, and 4kg, which causes more effort.
3) Mathematical calculations and graphs of the belt, motor, and bearing frequencies were produced to analyze the effects of different weights and extend equipment life.
IRJET- Vibration Analysis and Design Modification of Automobile SilencerIRJET Journal
This document presents a study on vibration analysis and design modification of an automobile silencer. The study aims to analyze vibrations in an existing silencer using finite element analysis (FEA) and experimental modal analysis. Natural frequencies are obtained and compared to validate the FEA results. The silencer geometry is then modified to optimize natural frequencies. Modal analysis is performed on the modified design and natural frequencies are compared to the existing silencer. Results show that increasing the silencer mass, by increasing baffle plate thickness, leads to decreased natural frequencies, while decreasing the mass increases natural frequencies.
This document provides a summary of an Indian Standard code of practice for laying concrete pipes. It begins by stating that the standard lays out methods for determining loads on pipes and their required strength, as well as procedures for handling, laying, and jointing pipes. This is to ensure pipes manufactured according to other specified standards are not subjected to excessive loads. The document then provides extracts from the Indian Standard code, including definitions, methods for calculating pipe loads and strength requirements, guidelines for handling, bedding, backfilling, and jointing of pipes.
The document discusses the design and analysis of injector nozzles for minimizing thrust loss. The objectives are to fabricate a thrust measurement system and measure thrust loss with different injector nozzle designs including ramped nozzles. Analytical calculations were performed using isentropic equations to estimate thrust ranges from 30.06N to 72.52N for various stagnation pressures and nozzle designs. Computational fluid dynamics analysis was also conducted using a shear stress transport turbulence model to simulate different nozzle designs and obtain thrust values for validation. Experimental thrust measurements will also be taken and compared to the analytical and computational results.
IRJET- Experimental Investigation of Flow through Perforated Plate in Conical...IRJET Journal
This document describes an experimental investigation of flow through a perforated plate inside a conical diffuser. The goal is to improve the axial flow and achieve higher static pressure rise without total pressure loss. A supersonic wind tunnel was used to test a conical diffuser with an angle of 7 degrees that had two perforated plates placed inside at a distance of 450mm from the inlet. Pressure values were measured using a manometer at various ports and the coefficient of pressure was calculated both without and with the perforated plates. The results found that the addition of the perforated plates improved the flow uniformity and increased the static pressure rise inside the diffuser compared to when no plates were used.
DESIGN OF INTELLIGENT CONTROL SYSTEM USING ACOUSTIC PARAMETERS FOR GRINDING M...cscpconf
This paper utilizes acoustic parameters such as FS,NC, N, P, INC, FL, FH, W for acoustic signals S of different running conditions of a ballmill to deriveout the acoustic signatures and
hence control signals, which is to be used for designing the control systems of the mill. The parameters FS, NC, N, P, INC, FL, FH and W are represented by sample rate in Hz, number of
cepstral coefficients, length of frame in samples, number of filters in filter bank, frame increment, low end of the lowest filter, high end of highest filter and the window over which the analysis is to be performed respectively. The work establishes an
appropriate theoretical background that helps to predict dynamic breakage characteristics with respect to particle size
distribution of materials, adequately supported by experimental data. The signatures of different running conditions of grinding mill have been extracted from the captured signal in time frame
these have been used as feedback signal to monitor the grinding operation. Condenser based microphones have been used for capturing acoustic signals in time domain directly in
computers and stored for further analysis. Matlab R2010b has been used for different analysis of the experiment. On analyzing the signatures, it has been observed whether the fines are
produced progressively to attain the desired size range or the mill producing undesired products. Thus, the approach has been used in this paper has the ability to arrive in the stage of
optimum grinding by tuning parameters of the mill in real time, and also it can prevent the mill to enter into an erroneous state. Moreover, on study it has found that the present scheme can be
used more accurately in comparison to the earlier work of the author. This paper presents an implementation scheme to use acoustic signal as the control signal to regulate the operation of
a grinding mill.
Open Source Contributions to Postgres: The Basics POSETTE 2024ElizabethGarrettChri
Postgres is the most advanced open-source database in the world and it's supported by a community, not a single company. So how does this work? How does code actually get into Postgres? I recently had a patch submitted and committed and I want to share what I learned in that process. I’ll give you an overview of Postgres versions and how the underlying project codebase functions. I’ll also show you the process for submitting a patch and getting that tested and committed.
Predictably Improve Your B2B Tech Company's Performance by Leveraging DataKiwi Creative
Harness the power of AI-backed reports, benchmarking and data analysis to predict trends and detect anomalies in your marketing efforts.
Peter Caputa, CEO at Databox, reveals how you can discover the strategies and tools to increase your growth rate (and margins!).
From metrics to track to data habits to pick up, enhance your reporting for powerful insights to improve your B2B tech company's marketing.
- - -
This is the webinar recording from the June 2024 HubSpot User Group (HUG) for B2B Technology USA.
Watch the video recording at https://youtu.be/5vjwGfPN9lw
Sign up for future HUG events at https://events.hubspot.com/b2b-technology-usa/
4th Modern Marketing Reckoner by MMA Global India & Group M: 60+ experts on W...Social Samosa
The Modern Marketing Reckoner (MMR) is a comprehensive resource packed with POVs from 60+ industry leaders on how AI is transforming the 4 key pillars of marketing – product, place, price and promotions.
The Ipsos - AI - Monitor 2024 Report.pdfSocial Samosa
According to Ipsos AI Monitor's 2024 report, 65% Indians said that products and services using AI have profoundly changed their daily life in the past 3-5 years.
1. Disclosure to Promote the Right To Information
Whereas the Parliament of India has set out to provide a practical regime of right to
information for citizens to secure access to information under the control of public authorities,
in order to promote transparency and accountability in the working of every public authority,
and whereas the attached publication of the Bureau of Indian Standards is of particular interest
to the public, particularly disadvantaged communities and those engaged in the pursuit of
education and knowledge, the attached public safety standard is made available to promote the
timely dissemination of this information in an accurate manner to the public.
इंटरनेट मानक
“!ान $ एक न' भारत का +नम-ण”
Satyanarayan Gangaram Pitroda
“Invent a New India Using Knowledge”
“प0रा1 को छोड न' 5 तरफ”
Jawaharlal Nehru
“Step Out From the Old to the New”
“जान1 का अ+धकार, जी1 का अ+धकार”
Mazdoor Kisan Shakti Sangathan
“The Right to Information, The Right to Live”
“!ान एक ऐसा खजाना > जो कभी च0राया नहB जा सकता है”
Bhartṛhari—Nītiśatakam
“Knowledge is such a treasure which cannot be stolen”
“Invent a New India Using Knowledge”
है”ह”ह
IS 2 (1960): Rules for Rounding off Numerical Values [MSD
3: Statistical Methods for Quality and Reliability]
5. Indian Standard
RULES FOR ROUNDING OFF
NUMERICAL VALUES
(Revised)
Engineering Standards Sectional Committee, EDG I
Chairman
Hit K. S. KRISHNAN Council of Scientific & Industrial Research,
New Delhi
SURI S. B. J08m
SURI R. N. KAPUR
DR R. S. KRI8uNAN
SHRI S. R. MElIRA
Smu BAI.ESIIWAR NATIl
DEPUTY DIRI!.CTOR GENERAL
OIlSF.RVATORIES
DnU:'CTOR
Research, Design & Standardization Organizalrun
( Ministry of Railways)
Central Board of Irrigation & Power, New Delhi
OF Directorate General of Observatories (Ministry of
Transport & Communications), New Delhi
Engineering Research Department, Oovernmcni of
Andhra Pradesh
Institution of Engineers ( India), Calcutta
Indian Engineering Association, Calcutta
Indian Institute of Science, Bangalore
Couneil of Scientific & Industrial Researchs
New Delhi
5mu S. N. l>.tl1KERJ1 Government Test House, Calcutta
Smu K. D. BnATTAcHARJI:E ( Alternate)
DR B. R. NIJIIAWAN Council of Scientific & Industrial Research,
New Delhi
SURI V. R. RAOHAVAN Central Watt-r & Power Commission, Nf'w Delhi
BR.o J. R. SA.MIOI'f Controller of Development (Armaments) (Ministry
of Defeaee )
J,T.COL R.JANAR.oHANAM (Altel'1lall)
Memb'r!
Smu PREM PRAKASH ( Altrmate to
Dr K. S. Krishnan)
A5SISTANT DIRECTOR
( Ctnttirrs.t1 011page2 )
BlJREAU OF INDIAN STANDARDS
MANAK BHAVAN. 9 UAIIADUR SHAH ZAFAR MARO
NEWDEUU 110002
6. IS: 2 ·1960
( (.&lIli,l/Ir"from flllgt: J )
JIembers
SIIRI R. ';. SARM.
SHRIJ. M. SINHA
SJlRIJ. M. TIU!.OAN
Uin:ctoralt: Gl~nl'ral uf Supplics at Dispoaals
( Ministry of Works, Houllng at Supply)
Engincering Association of India, Calcutta
Ministry of Transport at Communications (Roads
Wing)
SURI T. N. ~HARO""iA ( .Ullmate)
LT-GBN H. Wn.I.IA)IS Council (If Scientific & IndultriaIRc.n·an:1i,
New Delhi
DII LAT. C. VERMAN (J:.~io) Director, lSI
.SURI J. P. MElIllO,.R.", Deputy Director ( Engg ), IS r
( .~llernQlIl )
S,crrtari,·s
Dit A, K. GUPTA Assistant Director ( Stal ), lSI
:-)1111.1 B. N. StKl'lli Extra Assistant Director ( Stat), lSI
2
7. AMENDMENT NO. 1 FEBRUARY 1997
TO
IS 2: 1960 RULES FOR ROUNDING ors
NUMERICAI.. VALVES
( Revised)
(Page 3, clause 0.4 ) - Insert the following after first entry:
IS 1890 (PARTO ) : 1995/1S0 31-0: 1992 QUANTI11FS AND UNITS: PART 0
GENFRALPRINCIPLES ( FIRST REVISION)
( Page 8, clause 3.3 ) -- Insert the foJlowing new clause after 3.3:
"3.4 The rules given in 3.1, 3.2 and 3.3 should be used only if no specific
criteria for the selection ()fthl~ rounded number have to be taken into account, In
cases, where specific limit ('Maximum' or 'Minimum') has been stipulated or
where specifically mentioned in the requirement, it may he advisable always to
round in one direction.
Examples:
I) The requirement of leakage current for domestic electrical appliances
is 210 !-tA (rms) maximum,
The rounding may be done in one direction. For example, if a test result
is obtained as 210.], it will be rounded up and reported as 211 !-tA.
2) The requirement for cyanide (as eN) for drinking water is specified as
O'<~5 IllgIJ, maximum beyond which drinking water shall be considered
toxic.
The rounding may be done in one direction. For example, if 8 test result
is obtained as 0.051 mg/l, it will he rounded up and reported as
0.06 mg/l.
3) The requirement for minimum thickness of the body of LPG cylinder is
2.4 mm.
The rounding may be done in one direction. For example, if It le-st result
is obtained as 2.39 mill, it will be rounded down and reported as 2.3
10m.
8. Amend No.1 to IS Z: l'60
4) The requirement for Impact-Absorption for Protective Helmets for
Motorcycle Riders is:
'The conditioned helmet tested shall meet the requirements, when
tbe resultant acceleration (RMS value of acceleration measured
along tbree directions) measured at the centre of gr!vity of tbe
beadform shall be s 150 go (where go ::: 9.81 m/sec) for any 5
milliseconds continuously and at no time exceeds 300 go.'
The rounding may be done ill one direction. If a test result is obtained as
150.1 go, it will be rounded up and reported as 151 go."
(MSD 1 )
2
9. AMENDMENT NO.2 OCTOBER 1997
TO
IS 2: 1960 RULES FOR ROUNDING OFF
NUMERICAL VALUES
( Reyised)
(Amendment No.1, February 1997, Page I, clause 3.4, line 4 ) - Delete
tbe word 'always' appearing after the word 'advisablc'.
(MSD 1)
10. AMENDMENT NO.3 AUGUST 2000
TO
IS 2: 1960 RULES FOR ROUNDING OFF
NUMERICAL VALVES
( Revised)
( Page 5, clause 3.1, para 1 ) - Substitute the first sentence for the
following:
'In case the fineness of rounding is unity in the last place retained, the following
rules (except in 3.4) shall be followed:'
(Amendment No.1, February 1997, clause 3.4 ) - Substitute the second
sentence for the following:
'In all cases, where safety requirements or prescribed limits have to be respected,
rounding offshould be done in one direction only.'
(Amendment No.1, February 1997, clause 3.4 ) - Delete all the exaUlplea
given under this clause.
(Amendment No.2, October 1997) - Delete this amendment.
(MSD3 )
11. IS: 2-1960
Indian Standard
RULES FOR ROUNDING OFF
NUMERICAL VALUES
( Revised)
o. FOREWORD
0.1 This Indian Standard (Revised) was adopted by the Indian Standards
Institution on 27 July 1960, after the draft finalized by the Engineering
Standards Sectional Committee had been approved by the Engineering
Division Council.
0.2 To round off a value is to retain a certain number of figures, counted
jrom the lift, and drop the others so as to give a more rational form to the
value. As the result ofa test or of a calculation is generally rounded off
for the purpose ofreporting or for drafting specifications, it is necessary to
prescribe rules for ' rounding off' numerical values as also for deciding on
• the number of figures' to be retained.
0.3 This standard was originally issued in 1949 with a view to promoting
the adoption of a uniform procedure in rounding off numerical values.:
However, the rules given referred only to unit fineness of rounding ( su 2.3 )
and in course of years the need was felt to prescribe rules for rounding
off numerical values to fineness of rounding other than unity. Moreover,
it was also felt that the discussion on the number offigures to be retained as
given in the earlier version required further elucidation. The present revision
is expected to fulfil these needs.
0.4 In preparing this standard, reference has been made to the following:
IS: 787-1956 GuIDE FOR INTBR-CONVBlUION 011' VALva. FROM ONE
SYSTEM OF UNITS TO ANOTHER. Indian Standards Institution.
B.S. 1957: 1953 PRUBNTATION OF NUKltlUCAL VALUES ( FINBNESS OP
EXPREISION; ROUNDINO 011' NUMBERS). British Standards Insti-
tution.
AMERICAN STANDARD Z 25.1-1940 RULES FOR ROUNDING OFF
NUMltRICAL VALUES. American Standard. Auociation.
ASTM DUIGNATION: E 29-50 RECO.....NDED PRAOTICB FOR DElIO-
NATINO SIONlflCANT PUCU IN SPEOI.,BD VALuas. American
Society for 'resting and Materials.
JAKBS W. SoAllBOROUOH. Numerical Mathematical AnaJ)'IiJ. Balti-
more. The John Hopkins Preas, 1955.
3
12. DlCimDl PltUu
5
4-
6
2
2
Signijieant Figures
5
3
6
10
5
6
4
5
4
IS: 2 .1960
1. SCOPE
1.1 This standard prescribes rules for rounding off numerical.values for the
purpose of reporting results of a test, an analysis. a measurement or a cal-
culation. and thus assisting in drafting specifications. It also makes recom-
mendations as to the number of figures that should be retained in course
of computation,
2. TERMINOLOGY
2.0 For the purpose of this standard. the following definitions shall apply.
2.1 Nu.ber or Dedm." Places - A value is said to have as many
decimal places as there are number offigures in the value, counting from the
first figure after the decimal point and ending with the last figure on the right.
&tampllS:
Valu,
0'02950
21-0295
2 000'000 00 I
291'00
10'32 X 101
( SII Note I )
NOTa I-For the PW'P'1e of this It'ndard, the expression 10'32 x 101 should be
taken to conaist of two partl. the value proper which is 10'32 aDd the unit of Vlptcuion
for the value, 10.,
2.2 NlUDber orSigaiaeaDt Figures - A value is said to have as many
significant figures as there are number of significant digits (,tI Note 2)
in the value. counting from the left-moat nOlN,tTO digit and ending with the
right-moat digit in the value.
Exampl,s:
Valu,
0'029500
0'0295
10'0295
2000'000 001
5677'0
567700
56'77 X lOt
.' 0056'770
3900
(St' Note 3 )
NOTB 2 - Any of the dititl, 1. 2, 3 9 occurrin, in a value than be a ailni.
fiCIIDt digit(I); and zero 'ball be • Iigni6caDt digit only whrn it is preceded by lOme
4
13. IS: 2 -1960
other digit ( excepting zeros) on its left. When appearing in the power of 10 to indicate
the magnitude of the unit in the expression of a value, zero shan nOI be a significant
digit.
NOTa 3 - With a view to removing any ambiguity regarding the significance of the
zeros at the end in a value like 3 900, it would be a"vHys desirable to write the value in
the power-often notation. For example, 3 gOO may be written as 3'9 x 103,3'90 X 103
or 3'900 X 103 depending upon the last figurc(s) in the value to which it is desired to
impart significancl".
2.3 FIDeDe•• of ROIIDcUll. - The unit to which a value is rounded off.
For example, a value may be rounded to the nearest 0'00001,0'0002,
0'000 5, 0'001, 0'002 5, 0'005, 0'01, 0'07, I, 2'5, lO, 20, 50, 100 or any
other unit depending on the fineness desired,
3. RULES FOR ROUNDING
3.0 The rule usually followed in rounding off a value to unit fineness of
rounding is to keep unchanged the last figure retained when the figure next
bcyond is less than.') and to increase by I the last figure retained when the
figure ncxt beyond is more than 5. There is diversity of practice when the
figure next beyond the last figure retained is 5. III such cases, some corn-
puters 'round up', that is, increase hy I, the last figure retained: others
, round down " that is, discard everything beyond the last figure retained,
Obviously, if the retained value is always' rounded up , or always' round-
ed down', the sum and the average of a series of values so rounded will
be larger or smaller than the corresponding sum or average of the unround-
ed values. , However, if rounding oft" is carried out in accordance with the
rules slated in 3.1 in one step (see 3.3), the slim and the average of the
rounded values would be more nearly correct than in the previous caSC5
( see Appendix A ).
3.1 ROllllcUDg Oft'to UDit Finellea8 - In case the fineness of rounding is
unity in the last place retained, the following rules shall be followed:
. Rule I -- When the figure next beyond the last figure Or place to
be retained is less than 5, the figure in the last place retained shall he
left unchanged.
RuLe II···- Wht~n the figure next beyond the last figure or place
to be retained is more than 5 or is 5 followed by any figures other
than zeros, the figure in the last place retained shall be increased
by l.
Rule 11/--- When the figure next beyond the last figure or place
to be retained is 5 alone or 5 followed by zeros only, the figure in the
last place retained shall be (a) increased by 1 if it is odd and (b) left
unchanged if even (zero would be regarded as an even number Ior
this purpose).
5
14. bh 2·1960
Some examples illustrating the application of Rules I to III are given
in Table I.
TABLE I EXA.MPLES OF ROUNDING OFF VA.LVES TO UNIT FINENESS
VAunt FnrENUI Olr ROUNDING------A.-____ .
1 0·1 0·01 0·001
r---.A.~
• ~
, r----.A.---~ r-----A...----'"
Rounded Rule Rounded Rule Rounded Rule Rounded Rule
Value Value Value Value
7·2604- 7 I 7.3 Ii 7·26 1 7·260 I
14·725 15 II )4·7 I 14·72 III (b) )4.·725
3·4-55 3 I 3·5 n 3·46 III(a) 3·455
13·545001 14- II 13·5 1 13·55 11 13·545 I
8·725 9 II 8·7 I 8·72 III(b) 8·725
19·205 19 I 19·2 I 19·20 III(b) 19·205
0·5499 1 II 0·5 I 0.55 II 0·550 II
0-6501 1 II 0·7 II 0.65 1 0·650 I
00()49 50 0 I 0·0 1 0·05 II 0·050 111(a)
3.1.1 The rules for rounding laid down in 3.1 may be extended to apply'
when the fineness of rounding is 0'10, 10, 100, I 000, etc. For example,
2'43 when rounded to fineness 0'10 becomes 2'40. Similarly, 712 and 715
when rounded to the fineness 10 become 710 and 720 respectively,
3.2 Roaadi...g Oft" to Fi...e...ess Other than Unity-· In case the fineness
of rounding is not unity, but, say, it is n, the given value shall be rounded
off according to the following rule:
Rule IV - When rounding to a fineness n, other than unity, the
given value shall be divided by n, The quotient shall be rounded off to
the nearest whole number in accordance with the rules laid down
in 3.1 for unit fineness of rounding. The number so obtained, that
is, the rounded quotient, shall then. be multiplied by n to get the final
rounded value.
Some examples illustrating the application of Rule IV are given in
Table II.
NOTE 4 - The ruJea for rounding oft'a value to any linenf'SS of rounding, II, may allO
be alated in line itb thOle for unitfineneas of rounding ( &,. 3.1 ) as follows:
Divide the given value by II 10 that an iotqJral quotient and a rC'mainder are
obtained. Round oft'tbe value in the following manner:
a) Irthe remainder islf:l!l tban 11/2, the value shall be rounded down aueh that
the rounded value is an integral multiple ofII.
6
15. IS 12 -1960
b) If the remainder is greater than n/2, the value shall be rounded up sueh
that the rounded value is an integral multiple of n.
e) If the remainder is exactly equal to n/2, that rounded value shall be cbOlC.D
which is an integral multiple of 2n.
TABLE D EXAMPLES OF ROUNDING OFF VALUES TO FINENESS
OTHER THAN UNIT
VALUE FINENESS OF QUOTIENT ROUNDIill FINAL ROUNDKD
ROUNDINO, n QUOTIENT VALUE
(1) (2) (3) =( I)/(2) (4) (5)=(2) X (4)
1.6478 0·2 8·239 8 1.6
2-70 0·2 13·3 14 2·8
2·4968 0·3 8·3227 8 204·
1·75 0·5 3·5 4 2·0
0·68721 0·07 9·8173 10 0·70
0·875 0·07 12-5 12 0·84
325 50 6·5 6 3 X 102
1025 50 20·5 20 10 x 102
3.2.1 Fineness of rounding other than 2 and 5 is seldom called for In
practice. For these cases, the rules for rounding may be stated in
simpler form as follows:
a) Rounding off to fineness 50, 5, 0'5, 0'05, 0'005, etc.
RuLe V - When rounding to 5 units, the given value shall be
doubled and rounded off to twice the required fineness of rounding in
accordance with 3.1.1. The value thus obtained shall be halved to
get the final rounded value.
For example, in rounding off 975 to the nearest 50, 975 is doubled
giving I 950 which becomes 2000 when rounded off to the nearest 100; when
2 000 is divided by 2, the resulting number I 000 is the rounded value of
975.
b) Rounding off to fineness 20,2,0'2,0'02,0'002, etc.
Rule VJ -- When founding to 2 units, the given value shall be
halved and rounded off to half the required fineness of rounding in
accordance with 3.1. The value thus obtained shall then he doubled
to get the final rounded value.
FOf example, in rounding off 2'70 to the nearest 0-2, 2'70 is halved
giving 1'35 which becomes 1'4 when rounded off to the nearest 0'1; when
1'4 is doubled, the resulting number 2'8 is the founded value.
7
16. IS: 2 -1960
3.3 Successive Rouading - The final rounded value shall be obtained
from the most precise value available in ant" step only and not from a series
of successive roundings. For example, the value 0'549 9, when rounded to
one significant figure, shall be written as 0'5 and not as 0'6 which is obtained
as a result ofsuccessive roundings to 0'550,0-55, and 0'6. It is obvious that
the most precise value available is nearer to 0'5 and not to 0-6 and that
the error involved is less in the former case, Similarly, 0'650 I shall be
rounded off to O'7 in one step and not successively to 0'650, 0'65 and 0'6,
since the most precise value available here is nearer to 0'7 than to 0'6
( seealso Table I ).
NOTE 5 - In those cases where a final rounded value terminates with 5 and it is
intended to usc it in further computation, it may be helpful to use a ,+, or '-' sign after
the Iinal 5 to indicate whether a subsequent rounding should be up or down. Thus
3'214 7 may be written as 3-215- when rounded to :1 fineness of rounding 0'001. If
further rounding to three significanr figures is desired, this number would be rounded
down and written as 3-21 which is in error by less than half a unit in the last place; ,
other.....ise, rounding of 3-215 would have yielded 3'22 which is in error by mort than half
a unit in the last place. Similarly, :-1-:.105 4 could be written as 3'205+ when rounded
to 4 significant figures. Further rounding to 3 significant figures would yield the
value as 3-21.
In case the final 5 is obtained exactly, it would he indicated by leaving the 5 as such
without using '+' or '-' sign. In subsequent rounding the 5 would then be treated in
accordance with Rule Ill.
4. NUMBER OF FIGURES TO BE RETAINED
4.0 Pertinent to the application of the rules for rounding off is the under-
lying decision as to the number offigures that should be retained in a given
problem. The original values requiring to be rounded off may arise as a
result of a test, an analysis or a measurement, in other words, experimental
results, or they may arise from computations involving several steps.
4.1 Experilnental Results - The number of figures to he retained in an
experimental result, either for the purpose of reporting or for guiding the
formulation of specifications will depend on the significance of the figures
in the value. This aspect has been discussed in detail under 4 of IS: 787-
1956 to which reference may be made for obtaining helpful guidance.
4.2 Computations -In computations involving values of different
accuracies, the problem as to how many figures should he retained at various
steps assumes a special significance as it would affect the accuracy of the
final result. The rounding offerror will, in fact, be injected into computation
every time an arithmetical operation is performed. It is, therefore, necessary
to carry out the 'Computation in such a manner as would obtain accurate
results consistent with the accuracy of the data in hand.
4.2.1 While it is not possible to prescribe details which may be followed
in computations of various types, certain basic rules may be recommended
8
17. IS: 2·1960
for single arithmetical operations which, when followed, will save labour
and at the same time enable accuracy of original data to be normally
maintained in the final answers.
4.2.2 As a guide to the number of places or figures to be retained in the
calculations involving arithmetical operations with rounded or approximate
values, the following procedures are recommended:
a) Addition - The more accurate values shall be rounded off so as to
retain one more place than the last significant figure in the least
accurate value. The resulting sum shall then be rounded off to
the last significant place in the least accurate value.
b) Subtraction -- The more accurate value ( of the two given values)
shall be rounded off, before subtraction, to the same place as the
last significant figure in less accurate value; and the result shall be
reported as such (see also Note 6 ).
c) Multiplicatiofl and Dioision -- The number of signijicant figures
retained in the more accurate values shall be kept one more than
that in the least accurate value. The result shall then be rouuded
off to the same number ofsignificant figures as in the least accurate
value.
d) When a long computation is carried out in several steps, the inter-
mediate results shall be properly rounded at the end of each step
so as to avoid the accumulation of rounding errors in such cases.
It is recommended that, at the end of each step, one more signi-
ficant figure may be retained than is required under (a), (b) and
(c) (see also Note 7).
NOTr. 6 --- Tile loss of the significant figures in the" subtraction of two nearly equal
values is the Krratcst soirce of inaccuracy in most computations, and it forms the
weakest link ill a chain computation where it occurs. Thus, if the values O'16~1 52 and
()'168 71 arc each correct to five significant figures, their difference O'O()O 81. which has
only two significant figures. is quite lik.e1y to introduce inaccuracy in subsequent
computation,
If, however, the diffcrcnct: of two values is desired to be correct 10 k ,i~niljcant figures
and if it is known beforehand that the lirst m significant figures at the left will disappear
by subtraction, then the number of significant figures to hI" retained ill earh of thr-
values shall be m +k ( se«Example -1).
Non; 7 - To ensure a greater degree of accuracy in th.. computations. it is also
desirable to avoid or defer . I long as possible certain approximation operations like
that of the division or square root. For example, in the determination of sucrose by
volumetric method, the expression ~OWl (fa _1..1) may be better evaluated by taking
It'. VI Vl
iu calculational form as 20Wl (it Vl - ft V:!)(1411 1'1 I'. which would defer the division
until the last operation orthe calculation.
9
18. IS: 2-1960
4.2.3 Examples
Example 1
Required to find the sum of the rounded olT value's 461-32. ~81'6
76'854 and 1-7462. . ,
Since the least accurate value 381 -() is known only to the first decimal
place, all other values shall be rounded off to one more place,
that is, to two decimal places and then added as shown below:
461'32
381'6
76'8fi
4'7.-,
924':;2
The resulting sum shall then be reported to the same decimal place
as in the least accurate value, that is, as 924·S.
B:tample 2
Required to find the sum of the values 2B '1·90, (J!H, 6.57'32, 39500
and 76 939, assuming that the value 3Cl ."i00 is known to the:
nearest hundred only.
Since one of the values is known only to the nearest hundred, the
other values shall be rounded orr to thr- nearest tC'11 and then
added as shown helow:
2849 X IO
R9 X 10
66 X 10
3950 X In
7694 X )(J
14648 x 10
The sum shall then be reported to the nearest hundred as
J 465 X 100 or even as "465 X lOG.
Example 3
Required to find the difference of 679'8 and 76'365, assuming that
each number is known to its last figure but no fnrth('l'.
JO
19. IS: 2 -1960
Since one or the values is known to the first decimal place only, the
other value shall also be rounded off to the first decimal place
and then the difference shall be found.
679'8
76'4
603'4
The difference, 603'4, shall be reported as such.
Example 4-
Required to evaluate y'2'52 - V2'49 correct to live significant
figures.
Since V~F5'2 = 1'587 450 7~
V2'49 = 1'577 973 3B
and three significant fig-ures at the left wilJ disappear on sub-
traction, the number of significant figures retained in each value
shall be B as shown below:
1'587150 II
}·.577 9i3 4-
()o()09177 4
The result, O·oO!)!-77 4, shall be reported as such (or as
9'477 4 )< 10-3 ) .
H:Aample .'i
Required to evaluate '35-2/12, given that the numerator is correct
to its last Iigure-.
Since the numerator here is correct to three significant figures, the
denominator shall be taken as vi['= 1'414. Then,
35'2......_-= 2H~9
J··Hl
and the result shall he reported as 2'J.·~.
Esampl« fj
Required to evaluate 3' 78TCj5'6, assuming that the denominator is
true to only two significant figures.
Since the denominator here is corrrect to two significant ligures, each
number in the numerator would be taken up to three significant
II
5- 204 Dcptt. of HIS/200?
20. IS: 2-1960
figures. Thus,
3'78 X 3'14
5'7 = 2'08.
The result shall, however, be reported as 2'1.
APPENDIX A
( Clause 3.0)
VALIDITY OF RULES
•
A-I. The validity of the rules for rounding off numerical values, as given
in 3.1, may be seen from the fact that to every number that is to be ' rounded
down' in accordance with Rule I, there corresponds a number that is to
be ' rounded up' in accordance with Rule II. Thus, these two rules estab-
lish a balance between rounding' down' and' up , for all numbers other
than those that fall exactly midway between two alternatives. In the latter
case, since the figure to be dropped is exactly 5, Rule III, which specifics that
the value should be rounded to its nearest even number, implies that rounding
shall be ' up , when the preceding figures are I, 3, 5, 7, 9 and' down' when
they are 0, 2, 4, 6, 8. Rule III hence advocates a similar balance between
rounding' up , and' down' (see also Note 8). This implies that if the above
rules are followed in a large group ofvalues in which random distribution of
figures occurs, the number' rounded up' and the number ' rounded down'
will be nearly equal. Therefore, the' sum and the average of the rounded
values will be more nearly correct than would be the case if all were rounded
in the same direction, that is, either all ' up' or all ' down' .
;-';OTE Is- From purely logical considerations, a given value could have as well been
rounded to an odd number ( and not an even number as in Rule III ) when the discard-
ed figures fall exactly midway between two alternatives. Hut there is a practical
aspect to the matter. The rounding off a value to an even number facilitates the
division of the rounded value by 2 and the result of such division gives the correct
rounding of half the original unrounded value. Besides, the ( rounded) even values may
generally be exact'y divisible by many more numbers, even as well as odd, than arc the
( rounded) odd values.
12