The National Measurement System for Mass, Volume and Density
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The Metric System: America Measures Up. 1979 Edition. INSTITUTION Naval Education and Training Command, Washington, D.C
DOCONENT RESUME ED 191 707 031 '926 AUTHOR Andersonv.Glen: Gallagher, Paul TITLE The Metric System: America Measures Up. 1979 Edition. INSTITUTION Naval Education and Training Command, Washington, D.C. REPORT NO NAVEDTRA,.475-01-00-79 PUB CATE 1 79 NOTE 101p. .AVAILABLE FROM Superintendent of Documents, U.S. Government Printing .Office, Washington, DC 2040Z (Stock Number 0507-LP-4.75-0010; No prise quoted). E'DES PRICE MF01/PC05 Plus Postage. DESCRIPTORS Cartoons; Decimal Fractions: Mathematical Concepts; *Mathematic Education: Mathem'atics Instruction,: Mathematics Materials; *Measurement; *Metric System; Postsecondary Education; *Resource Materials; *Science Education; Student Attitudes: *Textbooks; Visual Aids' ABSTRACT This training manual is designed to introduce and assist naval personnel it the conversion from theEnglish system of measurement to the metric system of measurement. The bcokteliswhat the "move to metrics" is all,about, and details why the changeto the metric system is necessary. Individual chaPtersare devoted to how the metric system will affect the average person, how the five basic units of the system work, and additional informationon technical applications of metric measurement. The publication alsocontains conversion tables, a glcssary of metric system terms,andguides proper usage in spelling, punctuation, and pronunciation, of the language of the metric, system. (MP) ************************************.******i**************************** * Reproductions supplied by EDRS are the best thatcan be made * * from -
Variables in Mathematics Education
Variables in Mathematics Education Susanna S. Epp DePaul University, Department of Mathematical Sciences, Chicago, IL 60614, USA http://www.springer.com/lncs Abstract. This paper suggests that consistently referring to variables as placeholders is an effective countermeasure for addressing a number of the difficulties students’ encounter in learning mathematics. The sug- gestion is supported by examples discussing ways in which variables are used to express unknown quantities, define functions and express other universal statements, and serve as generic elements in mathematical dis- course. In addition, making greater use of the term “dummy variable” and phrasing statements both with and without variables may help stu- dents avoid mistakes that result from misinterpreting the scope of a bound variable. Keywords: variable, bound variable, mathematics education, placeholder. 1 Introduction Variables are of critical importance in mathematics. For instance, Felix Klein wrote in 1908 that “one may well declare that real mathematics begins with operations with letters,”[3] and Alfred Tarski wrote in 1941 that “the invention of variables constitutes a turning point in the history of mathematics.”[5] In 1911, A. N. Whitehead expressly linked the concepts of variables and quantification to their expressions in informal English when he wrote: “The ideas of ‘any’ and ‘some’ are introduced to algebra by the use of letters. it was not till within the last few years that it has been realized how fundamental any and some are to the very nature of mathematics.”[6] There is a question, however, about how to describe the use of variables in mathematics instruction and even what word to use for them. -
Metric System Units of Length
Math 0300 METRIC SYSTEM UNITS OF LENGTH Þ To convert units of length in the metric system of measurement The basic unit of length in the metric system is the meter. All units of length in the metric system are derived from the meter. The prefix “centi-“means one hundredth. 1 centimeter=1 one-hundredth of a meter kilo- = 1000 1 kilometer (km) = 1000 meters (m) hecto- = 100 1 hectometer (hm) = 100 m deca- = 10 1 decameter (dam) = 10 m 1 meter (m) = 1 m deci- = 0.1 1 decimeter (dm) = 0.1 m centi- = 0.01 1 centimeter (cm) = 0.01 m milli- = 0.001 1 millimeter (mm) = 0.001 m Conversion between units of length in the metric system involves moving the decimal point to the right or to the left. Listing the units in order from largest to smallest will indicate how many places to move the decimal point and in which direction. Example 1: To convert 4200 cm to meters, write the units in order from largest to smallest. km hm dam m dm cm mm Converting cm to m requires moving 4 2 . 0 0 2 positions to the left. Move the decimal point the same number of places and in the same direction (to the left). So 4200 cm = 42.00 m A metric measurement involving two units is customarily written in terms of one unit. Convert the smaller unit to the larger unit and then add. Example 2: To convert 8 km 32 m to kilometers First convert 32 m to kilometers. km hm dam m dm cm mm Converting m to km requires moving 0 . -
Kind of Quantity’
NIST Technical Note 2034 Defning ‘kind of quantity’ David Flater This publication is available free of charge from: https://doi.org/10.6028/NIST.TN.2034 NIST Technical Note 2034 Defning ‘kind of quantity’ David Flater Software and Systems Division Information Technology Laboratory This publication is available free of charge from: https://doi.org/10.6028/NIST.TN.2034 February 2019 U.S. Department of Commerce Wilbur L. Ross, Jr., Secretary National Institute of Standards and Technology Walter Copan, NIST Director and Undersecretary of Commerce for Standards and Technology Certain commercial entities, equipment, or materials may be identifed in this document in order to describe an experimental procedure or concept adequately. Such identifcation is not intended to imply recommendation or endorsement by the National Institute of Standards and Technology, nor is it intended to imply that the entities, materials, or equipment are necessarily the best available for the purpose. National Institute of Standards and Technology Technical Note 2034 Natl. Inst. Stand. Technol. Tech. Note 2034, 7 pages (February 2019) CODEN: NTNOEF This publication is available free of charge from: https://doi.org/10.6028/NIST.TN.2034 NIST Technical Note 2034 1 Defning ‘kind of quantity’ David Flater 2019-02-06 This publication is available free of charge from: https://doi.org/10.6028/NIST.TN.2034 Abstract The defnition of ‘kind of quantity’ given in the International Vocabulary of Metrology (VIM), 3rd edition, does not cover the historical meaning of the term as it is most commonly used in metrology. Most of its historical meaning has been merged into ‘quantity,’ which is polysemic across two layers of abstraction. -
Forestry Commission Booklet: Forest Mensuration Handbook
Forestry Commission ARCHIVE Forest Mensuration Handbook Forestry Commission Booklet 39 KEY TO PROCEDURES (weight) (weight) page 36 page 36 STANDING TIMBER STANDS SINGLE TREES Procedure 7 page 44 SALE INVENTORY PIECE-WORK THINNING Procedure 8 VALUATION PAYMENT CONTROL page 65 Procedure 9 Procedure 10 Procedure 11 page 81 page 108 page 114 N.B. See page 14 for further details Forestry Commission Booklet No. 39 FOREST MENSURATION HANDBOOK by G. J. Hamilton, m sc FORESTRY COMMISSION London: Her Majesty’s Stationery Office © Crown copyright 1975 First published 1975 Third impression 1988 ISBN 0 11 710023 4 ODC 5:(021) K eyw ords: Forestry, Mensuration ACKNOWLEDGEMENTS The production of the various tables and charts contained in this publication has been very much a team effort by members of the Mensuration Section of the Forestry Commission’s Research & Development Division. J. M. Christie has been largely responsible for initiating and co-ordinating the development and production of the tables and charts. A. C. Miller undertook most of the computer programming required to produce the tables and was responsible for establishing some formheight/top height and tariff number/top height relationships, and for development work in connection with assortment tables and the measurement of stacked timber. R. O. Hendrie prepared the single tree tariff charts and analysed various data concerning timber density, stacked timber, and bark. M. D. Witts established most of the form height/top height and tariff number/top height relationships and investigated bark thickness in the major conifers. Assistance in checking data was given by Miss D. Porchet, Mrs N. -
Guide for the Use of the International System of Units (SI)
Guide for the Use of the International System of Units (SI) m kg s cd SI mol K A NIST Special Publication 811 2008 Edition Ambler Thompson and Barry N. Taylor NIST Special Publication 811 2008 Edition Guide for the Use of the International System of Units (SI) Ambler Thompson Technology Services and Barry N. Taylor Physics Laboratory National Institute of Standards and Technology Gaithersburg, MD 20899 (Supersedes NIST Special Publication 811, 1995 Edition, April 1995) March 2008 U.S. Department of Commerce Carlos M. Gutierrez, Secretary National Institute of Standards and Technology James M. Turner, Acting Director National Institute of Standards and Technology Special Publication 811, 2008 Edition (Supersedes NIST Special Publication 811, April 1995 Edition) Natl. Inst. Stand. Technol. Spec. Publ. 811, 2008 Ed., 85 pages (March 2008; 2nd printing November 2008) CODEN: NSPUE3 Note on 2nd printing: This 2nd printing dated November 2008 of NIST SP811 corrects a number of minor typographical errors present in the 1st printing dated March 2008. Guide for the Use of the International System of Units (SI) Preface The International System of Units, universally abbreviated SI (from the French Le Système International d’Unités), is the modern metric system of measurement. Long the dominant measurement system used in science, the SI is becoming the dominant measurement system used in international commerce. The Omnibus Trade and Competitiveness Act of August 1988 [Public Law (PL) 100-418] changed the name of the National Bureau of Standards (NBS) to the National Institute of Standards and Technology (NIST) and gave to NIST the added task of helping U.S. -
Measuring in Metric Units BEFORE Now WHY? You Used Metric Units
Measuring in Metric Units BEFORE Now WHY? You used metric units. You’ll measure and estimate So you can estimate the mass using metric units. of a bike, as in Ex. 20. Themetric system is a decimal system of measurement. The metric Word Watch system has units for length, mass, and capacity. metric system, p. 80 Length Themeter (m) is the basic unit of length in the metric system. length: meter, millimeter, centimeter, kilometer, Three other metric units of length are themillimeter (mm) , p. 80 centimeter (cm) , andkilometer (km) . mass: gram, milligram, kilogram, p. 81 You can use the following benchmarks to estimate length. capacity: liter, milliliter, kiloliter, p. 82 1 millimeter 1 centimeter 1 meter thickness of width of a large height of the a dime paper clip back of a chair 1 kilometer combined length of 9 football fields EXAMPLE 1 Using Metric Units of Length Estimate the length of the bandage by imagining paper clips laid next to it. Then measure the bandage with a metric ruler to check your estimate. 1 Estimate using paper clips. About 5 large paper clips fit next to the bandage, so it is about 5 centimeters long. ch O at ut! W 2 Measure using a ruler. A typical metric ruler allows you to measure Each centimeter is divided only to the nearest tenth of into tenths, so the bandage cm 12345 a centimeter. is 4.8 centimeters long. 80 Chapter 2 Decimal Operations Mass Mass is the amount of matter that an object has. The gram (g) is the basic metric unit of mass. -
Maße & Gewichte
Maße & Gewichte Die Geschichte der Maße und Gewichte Inhaltsverzeichnis 0.1 Geschichte der Maße und Gewichte .................................. 1 0.1.1 Überblick ........................................... 1 0.1.2 Längeneinheiten ....................................... 1 0.1.3 Gewichtseinheiten ...................................... 1 0.1.4 Beispiel der Vielfalt ..................................... 1 0.1.5 Einheiten für Zeit und Winkel ................................ 2 0.1.6 Angelsächsische Maßeinheiten ................................ 2 0.1.7 Das metrische System .................................... 3 0.1.8 Typografische Maßeinheiten ................................. 3 0.1.9 Listen von historischen Maßen und Gewichten ........................ 3 0.1.10 Gebräuchliche Masseeinheiten ................................ 4 0.1.11 Siehe auch .......................................... 4 0.1.12 Literatur ........................................... 4 0.1.13 Weblinks ........................................... 4 0.1.14 Einzelnachweise ....................................... 5 1 Die Anfänge des Messens in der Frühzeit des Menschen 6 1.1 Kognitive Archäologie ......................................... 6 1.1.1 Entstehung .......................................... 6 1.1.2 Kognitive Archäologie heute ................................. 6 1.1.3 Kognitive Archäologie im deutschsprachigen Raum ..................... 7 1.1.4 Kognitive Archäologie in der Diskussion ........................... 7 1.1.5 Literatur ........................................... 7 1.1.6 -
Scalars and Vectors
1 CHAPTER ONE VECTOR GEOMETRY 1.1 INTRODUCTION In this chapter vectors are first introduced as geometric objects, namely as directed line segments, or arrows. The operations of addition, subtraction, and multiplication by a scalar (real number) are defined for these directed line segments. Two and three dimensional Rectangular Cartesian coordinate systems are then introduced and used to give an algebraic representation for the directed line segments (or vectors). Two new operations on vectors called the dot product and the cross product are introduced. Some familiar theorems from Euclidean geometry are proved using vector methods. 1.2 SCALARS AND VECTORS Some physical quantities such as length, area, volume and mass can be completely described by a single real number. Because these quantities are describable by giving only a magnitude, they are called scalars. [The word scalar means representable by position on a line; having only magnitude.] On the other hand physical quantities such as displacement, velocity, force and acceleration require both a magnitude and a direction to completely describe them. Such quantities are called vectors. If you say that a car is traveling at 90 km/hr, you are using a scalar quantity, namely the number 90 with no direction attached, to describe the speed of the car. On the other hand, if you say that the car is traveling due north at 90 km/hr, your description of the car©s velocity is a vector quantity since it includes both magnitude and direction. To distinguish between scalars and vectors we will denote scalars by lower case italic type such as a, b, c etc. -
Outline of Mathematics
Outline of mathematics The following outline is provided as an overview of and 1.2.2 Reference databases topical guide to mathematics: • Mathematical Reviews – journal and online database Mathematics is a field of study that investigates topics published by the American Mathematical Society such as number, space, structure, and change. For more (AMS) that contains brief synopses (and occasion- on the relationship between mathematics and science, re- ally evaluations) of many articles in mathematics, fer to the article on science. statistics and theoretical computer science. • Zentralblatt MATH – service providing reviews and 1 Nature of mathematics abstracts for articles in pure and applied mathemat- ics, published by Springer Science+Business Media. • Definitions of mathematics – Mathematics has no It is a major international reviewing service which generally accepted definition. Different schools of covers the entire field of mathematics. It uses the thought, particularly in philosophy, have put forth Mathematics Subject Classification codes for orga- radically different definitions, all of which are con- nizing their reviews by topic. troversial. • Philosophy of mathematics – its aim is to provide an account of the nature and methodology of math- 2 Subjects ematics and to understand the place of mathematics in people’s lives. 2.1 Quantity Quantity – 1.1 Mathematics is • an academic discipline – branch of knowledge that • Arithmetic – is taught at all levels of education and researched • Natural numbers – typically at the college or university level. Disci- plines are defined (in part), and recognized by the • Integers – academic journals in which research is published, and the learned societies and academic departments • Rational numbers – or faculties to which their practitioners belong. -
The International System of Units (SI)
NAT'L INST. OF STAND & TECH NIST National Institute of Standards and Technology Technology Administration, U.S. Department of Commerce NIST Special Publication 330 2001 Edition The International System of Units (SI) 4. Barry N. Taylor, Editor r A o o L57 330 2oOI rhe National Institute of Standards and Technology was established in 1988 by Congress to "assist industry in the development of technology . needed to improve product quality, to modernize manufacturing processes, to ensure product reliability . and to facilitate rapid commercialization ... of products based on new scientific discoveries." NIST, originally founded as the National Bureau of Standards in 1901, works to strengthen U.S. industry's competitiveness; advance science and engineering; and improve public health, safety, and the environment. One of the agency's basic functions is to develop, maintain, and retain custody of the national standards of measurement, and provide the means and methods for comparing standards used in science, engineering, manufacturing, commerce, industry, and education with the standards adopted or recognized by the Federal Government. As an agency of the U.S. Commerce Department's Technology Administration, NIST conducts basic and applied research in the physical sciences and engineering, and develops measurement techniques, test methods, standards, and related services. The Institute does generic and precompetitive work on new and advanced technologies. NIST's research facilities are located at Gaithersburg, MD 20899, and at Boulder, CO 80303. -
Euclidean Spaces and Vectors
EUCLIDEAN SPACES AND VECTORS PAUL L. BAILEY 1. Introduction Our ultimate goal is to apply the techniques of calculus to higher dimensions. We begin by discussing what mathematical concepts describe these higher dimensions. Around 300 B.C. in ancient Greece, Euclid set down the fundamental laws of synthetic geometry. Geometric figures such as triangles and circles resided on an abstract notion of plane, which stretched indefinitely in two dimensions; the Greeks also analysed solids such as regular tetrahedra, which resided in space which stretched indefinitely in three dimensions. The ancient Greeks had very little algebra, so their mathematics was performed using pictures; no coordinate system which gave positions to points was used as an aid in their calculations. We shall refer to the uncoordinatized spaces of synthetic geometry as affine spaces. The word affine is used in mathematics to indicate lack of a specific preferred origin. The notion of coordinate system arose in the analytic geometry of Fermat and Descartes after the European Renaissance (circa 1630). This technique connected the algebra which was florishing at the time to the ancient Greek geometric notions. We refer to coordinatized lines, planes, and spaces as cartesian spaces; these are composed of ordered n-tuples of real numbers. Since affine spaces and cartesian spaces have essentially the same geometric properties, we refer to either of these types of spaces as euclidean spaces. Just as coordinatizing affine space yields a powerful technique in the under- standing of geometric objects, so geometric intuition and the theorems of synthetic geometry aid in the analysis of sets of n-tuples of real numbers.