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

Aplikacje inżynierskie w dużej mierze opierają się na obliczeniach numerycznych, których wyniki są przedstawiane w standardowym formacie.
W obliczeniach numerycznych równanie musi być jednorodne wymiarowo, a wyrazy muszą być wyrażone w tych samych jednostkach.
Jednorodność wymiarowa równania jest zachowana niezależnie od ocenianego równania.
Liczby są zaokrąglane do liczb znaczących wymaganych dla dokładności wyniku i są wyrażane jako wielokrotności 103. Jeśli liczba jest mniejsza niż jeden, liczba jest zaokrąglana do wymaganych cyfr znaczących i wyrażana w wielokrotnościach 10-3.
Zgodnie z zasadą, gdy liczba kończy się cyfrą większą niż pięć, jest ona zaokrąglana w górę, a gdy cyfra jest mniejsza niż pięć, liczba pozostaje taka sama, aż do cyfr znaczących.
Gdy liczba kończy się cyfrą o wartości pięć, jest zaokrąglana w górę tylko wtedy, gdy poprzednia liczba jest nieparzysta, a jeśli jest parzysta, pozostaje taka sama aż do cyfr znaczących.

<ol>
	<li>Hibbeler, R.C. (2016). Mechanika inżynierska \u2012 Statyka i dynamika. Hoboken, New Jersey: Pearson Prentice Hall. str. 10\u201211</li>
	<li>Piwo, F.P.; Johnston, E.R.; Mazurek, D.F.; Cromwell, PJ i Self, BP (2019). Mechanika wektorowa dla inżynierów \u2012 Statyka i dynamika. Nowy Jork: McGraw-Hill. str. 13 i 15</li>
	<li>Meriam, J.L.; Kraige, L.G. i Bolton, J.N. (2020). Mechanika inżynierska \u2012 Statyka. Hoboken, New Jersey: John Wiley.</li>
</ol>

metoda numeryczna

W pracach inżynieryjnych reprezentacja wartości liczbowej ma kluczowe znaczenie. Przedstawianie lub raportowanie wartości stanowi jedną z podstawowych części praktyk inżynieryjnych. Obliczenia numeryczne są wykonywane przy użyciu kalkulatorów przenośnych lub komputerów, ponieważ preferowane są zawsze dokładne odpowiedzi oparte na liczbach.

Rozwiązanie problemu uzyskuje się za pomocą różnych metod. Ręczne rozwiązywanie symboli algebraicznych to jedna z najczęściej stosowanych metod, ale preferowana jest metoda graficzna. Komputery są przydatne, gdy należy rozwiązywać wiele równań jednocześnie. Podczas wykonywania tych obliczeń należy używać równań homogenicznych wymiarowo. Jednostki użyte w takich równaniach muszą być z tego samego typu.

Dokładność metody numerycznej zależy od kilku czynników. Jednym z takich czynników jest liczba ważnych cyfr zawartych w jakiejkolwiek wartości liczbowej. Ponieważ liczba całkowita kończąca się zerami zawsze prowadzi do zamieszania, wynik jest podawany w notacji wykładniczej. Większość wartości jest wyrażana za pomocą przedrostków.

Przedrostki są zawsze używane do wyrażania dużych lub małych wartości. Wynik jest zaokrąglany do wymaganej liczby ważnych cyfr i wyrażany w wielokrotnościach (103).

Znajomość liczby ważnych cyfr, które powinny być używane do wyrażenia wartości liczbowej, jest istotna. Na przykład, liczba 34 600 może być wyrażona jako 34,6(103), jeśli wymagane są trzy ważne cyfry.

Jeśli wymagane jest pięć ważnych cyfr, ta sama liczba może być wyrażona jako 0,34600(106).

W przypadku liczb dziesiętnych zera na początku są nieistotne; na przykład dziesiętna 0,00456 ma tylko trzy ważne cyfry. Jeśli liczba zaczyna się od zer, takie liczby są wyrażane jako 4,56(10-3) lub 456(10-6).

Zbyt duże i małe liczby są zaokrąglane do wymaganych ważnych cyfr. Jednak podczas zaokrąglania liczby, dokładność ostatecznego wyniku powinna pozostać taka sama. Wszystkie kalkulatory są zazwyczaj zaprojektowane do zaokrąglania wartości. Podczas wykonywania wielu kroków lepiej nie zaokrąglać odpowiedzi, aż do ostatniego kroku. Jedynie odpowiedź lub wynik powinny być zaokrąglone zgodnie z wymaganą dokładnością. Większość odpowiedzi w pracach inżynieryjnych jest wyrażana z trzema ważnymi cyframi.

Metoda numeryczna

W zastosowaniach inżynierskich odwzorowanie wartości liczbowej ma kluczowe znaczenie. Przedstawienie lub zrelacjonowanie odpowiedzi jest jedną z istotnych części ...

Education

JoVE Core

Mechanical Engineering

Inżynieria mechaniczna

Unit 1

Jednostka 1

An Introduction to Statics

Wstęp do statyki

KEY TERMS AND CONCEPTS

Kluczowe terminy i pojęcia

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

Fundamental Quantities in Engineering Mechanics

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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

SI Units and Metric Prefixes

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

PHYS.2.C

Chemistry and Physics

IPC.2

IPC.2.C

Scientific Method

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Scientific Laws and Theories

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When the null and alternative hypotheses are stated, it is observed ...

Hypothesis: Accept or Fail to Reject?

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The student will demonstrate an understanding of scientific and engineering practices by asking questions and defining problems
• 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
• plan and conduct investigations to test design solutions in a safe and ethical manner including considerations of environmental, social and personal effects
• select and use appropriate tools and technology to collect, record, analyze, and evaluate data

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Pie Chart

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Accuracy and Precision

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The student will demonstrate an understanding of scientific and engineering practices by pnterpreting, analyzing, and evaluating data
• 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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Data Collection by Experiments

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Data Collection by Survey

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Reliability and Validity

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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

using-topographic-maps-to-generate-topographic-profiles

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The student will demonstrate an understanding of scientific and engineering practices by developing and using models
• 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

Data Source

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levels-of-communication-ii-organizational-public-and-group-dynamics

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The student will demonstrate an understanding of scientific and engineering practices by obtaining, evaluating, and communicating information
• 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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