The Metric System of Weights and Measures. National Council of Teachers of Mathemil".Tics, Yearbook 2C 1948]
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Varying Constants, Gravitation and Cosmology
Varying constants, Gravitation and Cosmology Jean-Philippe Uzan Institut d’Astrophysique de Paris, UMR-7095 du CNRS, Universit´ePierre et Marie Curie, 98 bis bd Arago, 75014 Paris (France) and Department of Mathematics and Applied Mathematics, Cape Town University, Rondebosch 7701 (South Africa) and National Institute for Theoretical Physics (NITheP), Stellenbosch 7600 (South Africa). email: [email protected] http//www2.iap.fr/users/uzan/ September 29, 2010 Abstract Fundamental constants are a cornerstone of our physical laws. Any constant varying in space and/or time would reflect the existence of an almost massless field that couples to mat- ter. This will induce a violation of the universality of free fall. It is thus of utmost importance for our understanding of gravity and of the domain of validity of general relativity to test for their constancy. We thus detail the relations between the constants, the tests of the local posi- tion invariance and of the universality of free fall. We then review the main experimental and observational constraints that have been obtained from atomic clocks, the Oklo phenomenon, Solar system observations, meteorites dating, quasar absorption spectra, stellar physics, pul- sar timing, the cosmic microwave background and big bang nucleosynthesis. At each step we arXiv:1009.5514v1 [astro-ph.CO] 28 Sep 2010 describe the basics of each system, its dependence with respect to the constants, the known systematic effects and the most recent constraints that have been obtained. We then describe the main theoretical frameworks in which the low-energy constants may actually be varying and we focus on the unification mechanisms and the relations between the variation of differ- ent constants. -
A History of the National Bureau of Standards
APPENDIX A FERDINAND RUDOLPH HASSLER First Superintendent of the Coast Survey and of Weights and Measures When Professor Stratton arrived at the Office of Weights and Measures on B Street in Washington in the spring of 1898 to survey its equipment and operations, he found there in the person of Louis A. Fischer, the adjuster, a link with Ferdinand Rudolph Hassler, the first Superintendent of Weights and Measures in the Federal Government. It was in the atmosphere of the office over which Hassler had presided, Stratton said, with its sacred traditions concerning standards, its unsurpassed instrument shop, its world-known experts in the construction and comparison of standards, and especially in the most precise measurement of length and mass, that the boy Fischer, scarcely over 16, found himself when he entered the employ of Govern- ment in a minor capacity [about the year 18801. * * Scarcely 40 years had passed since the end of Hassler's services and the beginning of Fischer's. His first instructors were the direct disciples of Hassler and he knew and talked with those who had come in personal contact with the first superintendent.1 Fischer's reminiscences concerning the early historyof the Weights and Measures office, gathered from his association with the successors of Hassler, were never recorded, to Stratton's regret, and the only biography of Hassler, by Florian Cajori, professor of mathematics at the University of California, centers on his career in the Coast Survey gathered from his association with the successors of Hassler, were never recorded, to in the history of science in the Federal Government, is the principal source of the present sketch.2 1 Stratton, "Address Memorializing Louis Albert Fischer, 1864.—1921," 15th Annual Con. -
Fundamentals of Math CHAPTER 1
© Jones and Bartlett Publishers, LLC. NOT FOR SALE OR DISTRIBUTION Fundamentals of Math CHAPTER 1 OBJECTIVES ■ Understand the difference between the Arabic and Roman numeral systems ■ Translate Arabic numerals to Roman numerals ■ Translate Roman numerals to Arabic numerals ■ Understand the metric system ■ Understand the apothecary system ■ Be able to convert metric to apothecary ■ Be able to convert apothecary to metric ARABIC NUMERALS The Arabic number system uses the numerals 1, 2, 3, 4, 5, 6, 7, 8, 9, and zero (0). It is also known as the decimal system. Depending on how these numbers are arranged determines the value of the number. For example, digits 4, 7, and 2 placed together (472) represent the number four hundred seventy-two. A decimal point (.) separates whole numbers, or units, from fractional num- bers, or fractional units. All numbers on the left side of the decimal point are considered whole numbers. All numbers placed on the right of the decimal point are considered fractional units, or less than one whole unit. The following num- ber line shows the relationship of Arabic numerals based on their position in a number. Ten-thousands hundreds ones tenths thousandths hundred-thousandths -----5------8------2-----4-----3---- . ----6------7------9------3------2-------------- thousands tens hundredths ten-thousandths The number 43.6 contains the numerals 4, 3, and 6. This represents forty-three units of one and six-tenths of one unit. Decimals will be covered in more detail in Chapter 2. 1 59612_CH01_FINAL.indd 1 8/20/09 7:38:45 PM © Jones and Bartlett Publishers, LLC. NOT FOR SALE OR DISTRIBUTION 2 Chapter 1 ■ Fundamentals of Math ROMAN NUMERALS The Roman numeral system does not utilize numerals. -
The Unified Code for Units of Measure
1 The Unified Code for Units of Measure Version 1.4b, June 6, 2002 Gunther Schadow, Clement J. McDonald Regenstrief Institute for Health Care, Indianapolis Copyright c 1998, 1999, 2000, 2001, 2002 Regenstrief Institute for Health Care. All rights reserved. Introduction The Unified Code for Units of Measures is a code system intended to include all units of measures being con- temporarily used in international science, engineering, and business. The purpose is to facilitate unambiguous electronic communication of quantities together with their units. The focus is on electronic communication, as opposed to communication between humans. A typical application of The Unified Code for Units of Measures are electronic data interchange (EDI) protocols, but there is nothing that prevents it from being used in other types of machine communication. The Unified Code for Units of Measure is inspired by and heavily based on ISO 2955-1983, ANSI X3.50-1986, and HL7’s extensions called “ISO+”. The respective ISO and ANSI standards are both entitled Representation of [...] units in systems with limited character sets where ISO 2955 refers to SI and other units provided by ISO 1000-1981, while ANSI X3.50 extends ISO 2955 to include U.S. customary units. Because these standards carry the restriction of “limited character sets” in their names they seem to be of less value today where graphical user interface and laser printers are in wide-spread use, which is why the european standard ENV 12435 in its clause 7.3 declares ISO 2955 obsolete. ENV 12435 is dedicated exclusively to the communication of measurements between humans in display and print, and does not provide codes that can be used in communication between systems. -
Dimensions and Units English Units of Measurement Units of Weight
English units of measurement Today: A system of weights and measures used in a few nations, the only major industrial one Chapter 6 continued: being the United States. It actually consists of Dimensions and Units two related systems—the U.S. Customary System of units, used in the United States and dependencies, and the British Imperial System. Units of Weight The pound (lb) is the basic unit of weight (which is proportional to mass) (how?). Within the English units of measurement there are three different systems of weights. In the avoirdupois system, the most widely used of Question: the three, the pound is divided into 16 ounces (oz) and the ounce into 16 drams. The ton, used Is there a problem? to measure large masses, is equal to 2,000 lb (short ton) or 2,240 lb (long ton). In Great Britain the stone, equal to 14 lb, is also used. “weight is proportional to mass.” Answer: You need to be aware of Force = Mass* Acceleration the law governing that proportionality: Newton’s Law Acceleration is NOT a constant, mass is. Force = Mass* Acceleration Even on earth, g = 9.81 m/s2 is NOT constant, but varies with latitude and Question: elevation. Is there a problem? “weight is proportional to mass.” “weight is proportional to mass.” 1 Another problem arises from the A mass is NEVER a “weight”. common intermingling of the terms “mass” and “weight”, as in: Force = Mass* Acceleration “How much does a pound of mass weigh?” Or: “If you don’t know whether it’s pound- “Weight” = Force mass or pound-weight, simply say pounds.” “Weight” = Force Forces in SI Units …because on earth all masses are 2 exposed to gravity. -
Metric System and Its History
Metric System and its History Following is an explanation of the Metric System and its history. This is part of a set of pages on the metric system and metric system conversion; to see the main page (and other related pages), click on Metric System Conversion Table / Chart and Converter for Metric Conversions. The metric system is an internationally agreed set of units for measurement. Since 1960, the metric system is correctly known as the SI system, which is short for Systeme International d'Unites (International System of Units). However, it is still commonly (although somewhat incorrectly) continues to be referred to as the metric system. It has only seven basic measures (known as units), listed in the following table, of which the first four are in common use and the other three are mainly for technical and scientific purposes. Type of measure Standard Unit Symbol length meter m mass (weight) kilogram kg temperature degree Kelvin K (see discussion below) time second s electric current ampere A amount of substance mole mol luminous intensity candela cd Although the kilogram is commonly used as a measure of weight, it is actually defined as a measure of mass. Weight is a measure of how heavy something is, whereas mass is a measure of the amount of matter. To illustrate, a 120 pound woman would weigh only 20 pounds on the moon (due to the moon having lower gravity than the earth), whereas a 50kg woman is 50kg on both the earth and the moon. In other words, her weight (how heavy she is) is less on the moon but her mass (how much matter she has) is unchanged. -
Systems of Measure 39
© Jones & Bartlett Learning, LLC Chapter© Jones2 & Bartlett Learning, LLC NOT FOR SALE OR DISTRIBUTION NOT FOR SALE OR DISTRIBUTION © Jones & BartlettSystems Learning, LLC of Measure© Jones & Bartlett Learning, LLC NOT FOR SALE OR DISTRIBUTION NOT FOR SALE OR DISTRIBUTION % C OBJECTIVES © Jones & Bartlett. Learning, LLC © Jones & Bartlett Learning, LLC 789NOT FOR SALE—. OR DISTRIBUTIONUpon completion of this chapter,NOT FORthe technician SALE OR student DISTRIBUTION will be able to: 4 5 6 X • Express metric measures correctly. © Jones & Bartlett Learning, LLC • Convert measures© Jones within & Bartlett the metric Learning, system LLC accurately. NOT FOR SALE OR DISTRIBUTION NOT FOR SALE OR DISTRIBUTION • Identify symbols within all systems and identify their equivalent. • State the apothecaries’ measures commonly used in the © Jones & Bartlettprac ticeLearning, of pharmacy. LLC © Jones & Bartlett Learning, LLC NOT FOR SALE OR DISTRIBUTION NOT FOR SALE OR DISTRIBUTION • Identify measures in the household system used in the practice of pharmacy. TERMS • State the common household equivalents in the © Jones & Bartlett Learning, LLC © Jones & Bartlett Learning, LLC • 24-hour time metric system. NOT FOR SALE OR DISTRIBUTION NOT FOR SALE OR DISTRIBUTION • Apothecaries’ • Convert approximate equivalents between the metric, system apothecaries’, and household systems. • Avoirdupois © Jones & Bartlettsystem Learning, LLC • Become familiar© Jones with & milliequivalents, Bartlett Learning, units, LLC and NOT FOR •SALEGram OR DISTRIBUTION internationalNOT -
Let's Use the Metric System: a Supplement to Mathematics K-6
DOCUMENT RESUME ED 086 551 SE 017 223 AUTHOR Negus, LeRoy TITLE Let's Use the Metric System: A Supplement to Mathematics K-6. INSTITUTION New York State Education Dept., Albany. Bureau of Elementary Curriculum Development. PUB DATE 73 NOTE 15p. EDRS PRICE MF-$0.65 HC-$3.29 DESCRIPTORS *Curriculum; *Elementary School Mathematics; Guides; Instruction; Instructional Materials; Learning Activities; *Measurement; *Metric System; Objectives; *Teaching Techniques ABSTRACT This bulletin proiides elementary school teachers with some information about the metric system and some suggestions for teaching it. A history of the development of the system is given followed by a grade by grade guide to objectives and activities to be used with lessons on measurement with the metric system. The activities stress the decimal character of the metric system and provide opportunities for the students to gain an intuitive feeling for the comparative size of the various units of measure. (JP) FILMED FROM BESTAVAILABLE COPY II LET'S USE THE METRIC SYSTEM asupplement to Mathematics K-6 U.S. DEPARTMENT OF HEALTH, EDUCATION & WELFARE NATIONAL INSTITUTE OF EDUCATION THIS DOCUMENT HAS BEEN REPRO DUCED EXACTLY AS RECEIVED FROM THE PERSON OR ORGANIZATION ORIGIN III ATING IT POINTS OF VIEW OR OPINIONS STATED DO NOT NECESSARILY REPRE SENT OFFICIAL NATIONAL INSTITUTE OF EDUCATION POSITION OR POLICY 9E .!,. ."/:. ...,,.7.-1.7,'"....f. 0.'. ,, ....7....,..., ...,,......, .....11, .... 14.......... .......,...,' ....,...,...,..... ...r..,..../............3t .... 0 .."-....-_.. ........!,,--Ir..",.., ....%..., The University of the State of New York THE STATE EDUCATION DEPARTMENT Bureau of Elementary Curriculum Development Albany, New York 12224 THE UNIVERSITY OF THE STATE OF NEW YORK Regents of the University (with years when terms expire) 1984 Joseph W. -
Critical Measurement Tools for the Competent Pharmacy Technician 2 Contact Hours
Chapter 1: Critical Measurement Tools for the Competent Pharmacy Technician 2 Contact Hours By Bradley Gillespie, PharmD, who has practiced in an industrial setting for the past 20+ years. Currently, he has special interests in rare diseases and developing continuing education programs for health care professionals. Author Disclosure: Bradley Gillespie and Elite Professional Questions regarding statements of credit and other customer service Education, LLC do not have any actual or potential conflicts of interest issues should be directed to 1-888-666-9053. This lesson is $10.00. in relation to this lesson. Educational Review Systems is accredited by the Universal Activity Number (UAN): 0761-9999-15-161-H04-T Accreditation Council of Pharmacy Education (ACPE) Activity Type: Knowledge-based as a provider of continuing pharmaceutical education. Initial Release Date: June 1, 2015 This program is approved for 2 hours (0.2 CEUs) of Expiration Date: May 31, 2017 continuing pharmacy education credit. Proof of Target Audience: Pharmacy Technicians in a community-based participation will be posted to your NABP CPE profile within 4 to 6 setting. weeks to participants who have successfully completed the post-test. To Obtain Credit: A minimum test score of 70 percent is needed Participants must participate in the entire presentation and complete to obtain a credit. Please submit your answers either by mail, fax, or the course evaluation to receive continuing pharmacy education credit. online at PharmacyTech.EliteCME.com. Learning objectives After the pharmacy technician has concluded this knowledge-based Recognize the simplicity with which metric units can be easily activity, he or she will be able to: manipulated and interconverted, owing to their simple decimal Examine the historical significance of the apothecary and notation. -
Brief History and Use of the ENGLISH and METRIC SYSTEMS of MEASUREMENT with a CHART of the MODERNIZED METRIC SYSTEM
AUG 13 1971 -^4 UNITED STATES DEPARTMENT OF COMMERCE 161670 C. R. SMITH, Secretary NATIONAL BUREAU OF STANDARDS / a. v. astin, Director Special Publication 304A. Issued 1968. lUj h Brief History and Use of THE ENGLISH AND METRIC SYSTEMS OF MEASUREMENT with a CHART OF THE MODERNIZED METRIC SYSTEM "Weights and measures may be ranked among the necessaries of life to every individual of human society. They enter into the eco- nomical arrangements and daily concerns of every family. They are necessary to every occupation of human industry; to the distribution and security of every species of property; to every transaction of trade and commerce ; to the labors of the husbandman ; to the in- genuity of the artificer; to the studies of the philosopher ; to the researches of the antiquarian, to the navigation of the mariner, and the marches of the soldier; to all the exchanges of peace, and all the operations of war." —JOHN QUINCY ADAMS When the American Colonies sepa- sembly of France on May 8, 1790, of the length of a great circle of the rated from the mother country to to enact a decree, sanctioned by Louis earth. This idea found favor with the assume among the nations of the XVI, which called upon the French French philosophers at the time of the earth a separate and individual sta- Academy of Sciences in concert with French Revolution, men who were tion, they retained, among other the Royal Society of London to "de- generally opposed to any vestige of things, the weights and measures duce an invariable standard for all of monarchical authority and preferred that had been used when they were the measures and all weights." Hav- a standard based on a constant of colonies, namely, the weights and ing already an adequate system of nature. -
A Brief History of Weights and Measures
Eastern Illinois University The Keep Plan B Papers Student Theses & Publications 7-8-1957 A Brief History of Weights and Measures Lynn Swango Follow this and additional works at: https://thekeep.eiu.edu/plan_b Recommended Citation Swango, Lynn, "A Brief History of Weights and Measures" (1957). Plan B Papers. 56. https://thekeep.eiu.edu/plan_b/56 This Dissertation/Thesis is brought to you for free and open access by the Student Theses & Publications at The Keep. It has been accepted for inclusion in Plan B Papers by an authorized administrator of The Keep. For more information, please contact [email protected]. A BRIEF HISTORY of WEIGHTS AND MEASURES This paper is presented to the Mathematics Department of Eastern Illinois State College in partial fulfiliment of the requirements for the degree of Master of Science in Education. by Lynn Swango EASTERN ILLINOIS STATE COLLEGE 1957 Approved Date: PREFACE In the following pages it has been the aim to present in simple and non-technical langauge, so far as possible, a comprehensive view of the evolution of weights and measures. Realizing that in the history of mankind there have been many hundreds of systems of weights and measures, no attempt is made to discuss all of these. Since in every measurement system there are dozens of different units, the discussion in this paper is limited to the most common units of linear, capacity, and weight measurement. It has been the intention to consider briefly and systematically the general history of weights and measures, the scientific methods by which units and standards have been determined, and present aspect of modern systems of weightB and measures, together with the difficulties and advantages in them. -
Not Made to Measure
Made in Britain: Not made to measure. Ronnie Cohen © 2011 Ronnie Cohen. All rights reserved. 1 Table of Contents Foreword...............................................................................................................................................5 Introduction..........................................................................................................................................6 Central Role of Measurement in Daily Life.........................................................................................7 Why Measurement Matters..................................................................................................................8 Quest for Honest Measurements since Ancient Times.........................................................................9 Measurement Facts: Did you know that....?.......................................................................................10 Description of the British Imperial System........................................................................................11 Introduction to the British Imperial System..............................................................................11 Units of Length..........................................................................................................................11 Units of Area.............................................................................................................................11 Units of Volume........................................................................................................................12