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

엔지니어링 응용 프로그램은 결과가 표준 형식으로 표현되는 수치 계산에 크게 의존합니다.
수치 계산에서 방정식은 차원이 동질적이어야 하며 항은 동일한 단위로 표현되어야 합니다.
방정식의 차원 균질성은 평가되는 방정식에 관계없이 유지됩니다.
숫자는 결과의 정확성을 위해 필요한 유효 숫자로 반올림되며 103의 배수로 표현됩니다. 숫자가 1보다 작으면 숫자는 필요한 유효 숫자로 반올림되고 10-3의 배수로 표현됩니다.
규칙에 따르면 숫자가 5보다 큰 숫자로 끝나면 반올림되고 숫자가 5보다 작으면 유효 숫자까지 숫자가 동일하게 유지됩니다.
숫자가 숫자 값 5로 끝나면 이전 숫자가 홀수인 경우에만 반올림되고 짝수인 경우 유효 숫자까지 동일하게 유지됩니다.

<ol>
	<li>히벨러, R.C. (2016). Engineering Mechanics \u2012 정역학 및 동역학. 뉴저지 호보켄: 피어슨 프렌티스 홀. 10쪽\u201211</li>
	<li>맥주, F.P.; 존스턴, ER; 마주렉, D.F; 크롬웰, PJ 및 셀프, BP (2019). 엔지니어를 위한 벡터 역학 \u2012 Statics and Dynamics. 뉴욕 : McGraw-Hill. 13, 15쪽</li>
	<li>메리암, J.L.; Kraige, L.G. 및 Bolton, J.N. (2020). 엔지니어링 역학 \u2012 정역학. 뉴저지 호보켄: 존 와일리.</li>
</ol>

수치 값 계산

공학 응용 분야에서는 수치 값의 표현이 매우 중요합니다. 답변을 제시하거나 보고하는 것은 공학 실무의 필수적인 부분 중 하나입니다. 수치적으로 정확한 답이 항상 선호되기 때문에 수치 계산은 휴대용 계산기나 컴퓨터를 사용하여 수행됩니다.
문제에 대한 해답은 다양한 방법을 사용하여 얻습니다. 대수 기호를 수동으로 푸는 것이 가장 일반적인 방법 중 하나이지만 그래픽 방법이 선호되는 경우도 많습니다. 많은 방정식을 풀어야 할 때애는 컴퓨터가 유용합니다. 이러한 계산을 수행할 때는 차원적으로 균일한 방정식을 사용해야 합니다. 이러한 방정식에 사용되는 단위는 동일한 시스템이어야 합니다.
수치 문제의 정확도은 여러 요인에 따라 달라집니다. 수치에 얼마나 많은 유효 숫자가 포함되어 있는지도 그러한 요인 중 하나입니다. 0으로 끝나는 정수는 항상 혼란을 야기를 함으로 결과는 공학표기법을 사용하여 보고됩니다. 대부분의 값은 접두사를 사용하여 표현됩니다.
접두사는 항상 큰 숫자나 작은 숫자를 표현하는 데 사용됩니다. 결과는 필요한 유효 숫자로 반올림되어 (103)의 배수로 표시됩니다.
숫자를 표현하려면 유효 숫자를 몇 개나 사용해야 하는지 아는 것이 중요합니다. 예를 들어 유효 숫자 3개가 필요한 경우 34,600은 34.6(103)으로 표현될 수 있습니다.
유효숫자 5개가 필요한 경우, 같은 숫자는 0.34600(106)으로 표현할 수 있습니다.
소수에서 시작하는 0은 중요하지 않습니다. 예를 들어, 소수 0.00456에는 유효 숫자가 3개만 있습니다. 숫자가 0으로 시작하는 경우 해당 숫자는 4.56(10-3) 또는 456(10-6)으로 표시됩니다.
너무 크거나 작은 숫자는 필요한 유효 숫자로 반올림됩니다. 그러나 숫자를 반올림하는 동안 최종 결과의 정확도는 동일하게 유지되어야 합니다. 거의 모든 계산기는 값을 반올림하도록 설계되었습니다. 여러 단계를 수행하는 동안 마지막 단계까지 답을 반올림하지 않는 것이 좋습니다. 답변이나 결과만 필요한 정확도에 따라 반올림해야 합니다. 공학 응용 분야의 답은 대부분 유효 숫자 3개를 사용하여 표현됩니다.

엔지니어링 응용 프로그램에서는 숫자 값의 표현이 중요합니다. 답변을 제시하거나 보고하는 것은 의 필수 부분 중 하나입니다.

Education

교육

JoVE Core

Mechanical Engineering

기계공학

Unit 1

제1단원

An Introduction to Statics

정역학 입문

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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

Engineering mechanics begins with four basic quantities: length, time, mass, and force. These ideas help describe how objects move and how they respond to loads. They also support many other engineering fields. Length measures the distance traveled by an object. Engineers describe this distance with coordinates relative to a reference point. Length is also useful for showing the geometry of physical systems. Time measures the succession of an event. A bus traveling from city X to city Y is a...

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

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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
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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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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 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

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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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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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