Name: engineering notation and significant figures
Uploaded: 2023-09-22T11:49:19.000Z
Duration: 1 min 24 s
Channel: JoVE

K12 Standards

Virginia  Standards of Learning

HIgh School

Earth Science

ES.1

ES.1.c

Numerical Calculations

Technische Anwendungen sind stark auf numerische Berechnungen angewiesen, deren Ergebnisse in einem Standardformat dargestellt werden.
Bei numerischen Berechnungen muss die Gleichung dimensional homogen sein, und die Terme müssen in den gleichen Einheiten ausgedrückt werden.
Die dimensionale Homogenität der Gleichung bleibt unabhängig von der zu bewertenden Gleichung erhalten.
Die Zahlen werden auf die für die Genauigkeit des Ergebnisses erforderlichen signifikanten Zahlen gerundet und in Vielfachen von 103 ausgedrückt. Wenn die Zahl kleiner als eins ist, wird die Zahl auf die erforderlichen signifikanten Stellen gerundet und in den Vielfachen von 10-3 ausgedrückt.
Nach der Regel wird eine Zahl, die mit einer Ziffer größer als fünf endet, aufgerundet, und wenn die Zahl kleiner als fünf ist, bleibt die Zahl bis zu den signifikanten Ziffern gleich.
Wenn die Zahl mit dem Ziffernwert fünf endet, wird sie nur aufgerundet, wenn die vorhergehende Zahl ungerade ist, und wenn sie gerade ist, bleibt sie bis zu den signifikanten Zahlen gleich.

<ol>
	<li>Hibbeler, R.C. (2016). Technische Mechanik \u2012 Statik und Dynamik. Hoboken, New Jersey: Pearson Prentice Hall. Seite 10\u201211</li>
	<li>Bier, F.P.; Johnston, E.R.; Mazurek, D.F.; Cromwell, P.J. und Self, B.P. (2019). Vektormechanik für Ingenieure \u2012 Statik und Dynamik. New York: McGraw-Hill. Seiten 13 und 15</li>
	<li>Meriam, J.L.; Kraige, L.G. und Bolton, J.N. (2020). Technische Mechanik \u2012 Statik. Hoboken, New Jersey: John Wiley.</li>
</ol>

numerische berechnungen

In ingenieurtechnischen Anwendungen ist die Darstellung des numerischen Werts entscheidend. Das Präsentieren oder Berichten der Antwort ist einer der wesentlichen Teile der Ingenieurpraxis. Numerische Berechnungen werden mit Taschenrechnern oder Computern durchgeführt, da numerisch genaue Antworten immer bevorzugt werden. Die Lösung eines Problems wird mit verschiedenen Methoden erzielt. Während das manuelle Lösen algebraischer Symbole eine der häufigsten Methoden ist, wird oft die grafische Methode bevorzugt. Computer sind nützlich, wenn viele Gleichungen gelöst werden müssen. Eine dimensionshomogene Gleichung sollte bei diesen Berechnungen verwendet werden. Die in solchen Gleichungen verwendeten Einheiten sollten demselben System angehören. Die Genauigkeit eines numerischen Problems hängt von mehreren Faktoren ab. Wie viele signifikante Ziffern ein numerischer Wert enthält, ist ein solcher Faktor. Da eine ganze Zahl, die mit Nullen endet, immer zu Verwirrung führt, wird das Ergebnis unter Verwendung der Ingenieursnotation berichtet. Die meisten Werte werden unter Verwendung von Präfixen ausgedrückt. Präfixe werden immer verwendet, um große oder kleine Zahlen auszudrücken. Das Ergebnis wird auf die erforderlichen signifikanten Zahlen gerundet und in Vielfachen von (103) ausgedrückt. Zu wissen, wie viele signifikante Ziffern verwendet werden sollten, um den numerischen Wert auszudrücken, ist wesentlich. Zum Beispiel kann 34,600 als 34,6(103) ausgedrückt werden, wenn drei signifikante Ziffern erforderlich sind. Wenn fünf signifikante Ziffern erforderlich sind, kann dieselbe Zahl als 0,34600(106) ausgedrückt werden. Bei Dezimalzahlen sind die führenden Nullen nicht signifikant; zum Beispiel hat die Dezimalzahl 0,00456 nur drei signifikante Ziffern. Wenn die Zahl mit Nullen beginnt, werden solche Zahlen als 4,56 (10-3) oder 456(10-6) ausgedrückt. Zu große und zu kleine Zahlen werden auf die erforderlichen signifikanten Ziffern gerundet. Beim Runden einer Zahl sollte jedoch die Genauigkeit des Endergebnisses gleich bleiben. Fast alle Taschenrechner sind so konzipiert, dass sie den Wert runden. Während der verschiedenen Schritte ist es besser, die Antwort nicht zu runden, bis zum letzten Schritt. Nur die Antwort oder das Ergebnis sollte basierend auf der erforderlichen Genauigkeit gerundet werden. Die meisten Antworten in ingenieurtechnischen Anwendungen werden mit drei signifikanten Ziffern ausgedrückt.

Numerische Berechnungen

In technischen Anwendungen ist die Darstellung des Zahlenwerts entscheidend. Die Antwort zu präsentieren oder zu berichten ist einer der wesentlichen Bestandteile ...

Education

Lehre

JoVE Core

Mechanical Engineering

Maschinenbau

Unit 1

Einheit 1

An Introduction to Statics

Einführung in die Statik

KEY TERMS AND CONCEPTS

KERNBEGRIFFE UND KONZEPTE

engineering notation and significant figures

Numerical calculations in engineering depend on clear values, correct units, and careful rounding. Presenting the answer is an important part of engineering practice, so numerically accurate results are preferred. Handheld calculators and computers are often used because they help produce accurate answers.

Problems can be solved in several ways. Solving algebraic symbols by hand is common, and the graphical method is often preferred in some cases. Computers are especially useful when many equations must be solved. In every case, the equation should be dimensionally homogeneous, which means the units must belong to the same system.

The accuracy of a numerical result depends on several factors, including the number of significant figures. Significant figures are the digits in a value that carry meaning, and they matter when reporting answers. Whole numbers that end in zeroes can be confusing, so results are often written in engineering notation. This format uses prefixes and expresses values as multiples of 10^3.

Engineering notation also helps show very large or very small numbers clearly. For example, 34,600 can be written as 34.6(10^3) when three significant figures are needed. If five significant figures are needed, the same number can be written as 0.34600(10^6). In decimals, leading zeroes are not significant, so 0.00456 has three significant figures. Values with leading zeroes can also be written as 4.56(10^-3) or 456(10^-6).

Rounding must be done carefully so the final accuracy is preserved. Very large or very small numbers are rounded to the required number of significant figures. During multi-step work, it is better not to round until the last step. Only the final answer should be rounded to the required accuracy, and in many engineering problems, three significant figures are used.

Engineering Notation and Significant Figures

an introduction to mechanics

Mechanics in Physics and Engineering

Mechanics is a key branch of physics that explains how objects stay at rest or move when forces act on them. It also has major uses in engineering and science. The topic helps students understand everyday motion, machine behavior, and the way many systems work. The recorded history of mechanics begins with Aristotle, who lived from 384 to 322 BC. He linked mechanics with physical theory and looked for a broad universal explanation. Later, Newton defined mechanics as the study of objects at...

basic concept

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newton's law of motion

Newton's Laws and Everyday Motion

Newton's laws explain everyday motion and the forces that change it. These three laws describe why objects move, stay still, or speed up. They also show how force and mass affect motion. Newton's first law is the law of inertia. It says an object at rest stays at rest, and an object in motion keeps moving at a constant speed and direction unless an external force acts on it. A sliding box that slows down on its own is a good example. In that case, friction is the net external force that works...

newton's law of gravitational attraction

Gravity Between Masses and Distance

Newton’s law of gravitational attraction describes how gravity acts between two objects. Sir Isaac Newton built this law from empirical evidence and inductive reasoning. He published it in Philosophiae Naturalis Principia Mathematica, or the Principia, on July 5, 1687. The law says that the gravitational force between any two objects depends on their masses and their distance apart. The force is proportional to mass and inversely proportional to the square of the distance between the objects.

units of measurement

SI and Customary Measurement Systems

Mechanical engineering depends on units of measurement for precise and accurate calculations. These units give engineers a standard way to express and compare physical quantities. They are essential when designing and analyzing machines and mechanical systems. Many historical measurement systems have been used over time. Examples include the Babylonian system, the Roman system, the Egyptian system, the Olympian system, the British system, and the Indus Valley system. Today, the International...

international system of units

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SI units and metric prefixes provide a standard way to measure size, mass, and time. The International System of Units, or SI system, is used worldwide because it gives scientists a common language for measurement. Its values do not change with location, which helps keep results consistent. The SI system is built on three base units: meter, kilogram, and second. These are the core units for length, mass, and time. The kilogram is the only base unit that already includes a prefix. Prefixes...

numerical calculations

Numerical calculations in engineering depend on clear values, correct units, and careful rounding. Presenting the answer is an important part of engineering practice, so numerically accurate results are preferred. Handheld calculators and computers are often used because they help produce accurate answers. Problems can be solved in several ways. Solving algebraic symbols by hand is common, and the graphical method is often preferred in some cases. Computers are especially useful when many...

accuracy, limits, and approximation

Accuracy and Approximation in Calculations

Accuracy and approximation are important in calculations, especially in engineering. Accuracy means how close a measured value is to the true or actual value. Repeated measurements are often used in engineering mechanics to help make results more precise and accurate. The accuracy of a solution depends on empirical data and the results from different calculations or measurements. A cylindrical container filled with liquid is a simple example. Its volume can be found from the measured...

dimensional analysis

Using Dimensions to Check Physics Equations

Dimensional analysis is a useful way to check physics and engineering equations. It works by writing physical quantities in terms of basic dimensions such as mass, length, and time. Quantities like velocity, acceleration, and force are derived from these basic dimensions. This method helps compare measurements even when the units are different. It also checks whether an equation is dimensionally homogeneous. That means the powers of the fundamental dimensions must match on both sides of the...

problem solving in statics

Statics Problem-Solving Steps for Beams

Statics problem-solving uses a step-by-step method to analyze bodies in equilibrium, especially beams. It is an important part of physics and engineering because the goal is to find practical and accurate answers for real situations. The process usually starts with a physical situation and then turns it into a mathematical model. That model often needs approximations and assumptions. Very small distances can be ignored when they are much smaller than the main dimensions, such as beam width...

key terms and concepts

Learn how engineers use calculators, dimensionally homogeneous equations, engineering notation, and significant figures to report accurate numerical results.

Engineering Notation and Significant Figures | JoVE K12

JoVE Core Mechanical Engineering offers concise, easy-to-understand animated videos covering key topics such as equilibrium, forces, truss analysis, and structural mechanics. Explore their real-world applications, and witness these concepts in action through scientist-led experiments.

mechanical engineering

ES.1.e

Life Science

LS.1

LS.1.c

LS.1.e

Texas Essential Knowledge and Skills

High School

Specialised Topic in Science

112.51.c.1.

112.51.c.2.C.

Biology

BIO.2

BIO.2.C

Physics

PHYS.2

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Chemistry and Physics

IPC.2

IPC.2.C

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Scientific Laws and Theories

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• ask questions that arise from careful observation of phenomena, examination of a model or theory, or unexpected results, and/or to seek additional information
• determine which questions can be investigated within the scope of the school laboratory or field experience
• generate hypotheses based on research and scientific principles
• make hypotheses that specify what happens to a dependent variable when an independent variable is manipulated
• define design problems that involve the development of a process or system with multiple components and criteria

ES.1.a

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• individually and collaboratively plan and conduct observational and experimental investigations
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• select and use appropriate tools and technology to collect, record, analyze, and evaluate data

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• construct and interpret data tables showing independent and dependent variables, repeated trials, and means
• construct, analyze, and interpret graphical displays of data and consider limitations of data analysis
• apply mathematical concepts and processes to scientific questions
• use data in building and revising models, supporting explanations of phenomena, or testing solutions to problems
• analyze data using tools, technologies, and/or models in order to make valid and reliable scientific claims or determine an optimal design solution

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Reasoning

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The student will demonstrate an understanding of scientific and engineering practices by constructing and critiquing conclusions and explanations
• make quantitative and/or qualitative claims based on data
• construct and revise explanations based on valid and reliable evidence obtained from a variety of sources, including students' own investigations, models, theories, simulations, and peer review
• apply scientific ideas, principles, and/or evidence to provide an explanation of phenomena or design solutions
• construct arguments or counterarguments based on data and evidence
• differentiate between a scientific hypothesis, theory, and law

ES.1.d

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• evaluate the merits and limitations of models
• develop, revise, and/or use models based on evidence to illustrate or predict relationships
• construct and interpret scales, diagrams, classification charts, graphs, tables, imagery, models, including geologic cross sections and topographic profiles
• read and interpret topographic and basic geologic maps and globes, including location by latitude and longitude

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• compare, integrate, and evaluate sources of information presented in different media or formats to address a scientific question or solve a problem
• gather, read, and evaluate scientific and/or technical information from multiple sources, assessing the evidence and credibility of each source
• communicate scientific and/or technical information about phenomena and/or a design process in multiple formats

ES.1.f

Engineering Notation and Significant Figures

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