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

تعتمد التطبيقات الهندسية بشكل كبير على العمليات الحسابية العددية ، التي يتم تمثيل نتائجها في شكل قياسي.
في الحسابات العددية ، يجب أن تكون المعادلة متجانسة الأبعاد ، ويجب التعبير عن المصطلحات بنفس الوحدات.
يتم الحفاظ على تجانس أبعاد المعادلة بغض النظر عن المعادلة التي يتم تقييمها.
يتم تقريب الأرقام إلى الأرقام المعنوية المطلوبة لدقة النتيجة ؛ ويتم التعبير عنها بمضاعفات 103. إذا كان الرقم أقل من واحد ، يتم تقريب الرقم إلى الأرقام المعنوية المطلوبة ويتم التعبير عنه بمضاعفات 10-3.
وفقا للقاعدة ، عندما ينتهي الرقم برقم أكبر من خمسة ، يتم تقريبه لأعلى ، وعندما يكون الرقم أقل من خمسة ، يظل الرقم كما هو ، حتى الأرقام المعنوية.
عندما ينتهي الرقم بقيمة الرقم خمسة ، يتم تقريبه فقط إذا كان الرقم السابق فرديا ، وإذا كان زوجيا ، فإنه يظل كما هو حتى الأرقام المعنوية.

<ol>
	<li>هيبلر ، آر سي (2016). الميكانيكا الهندسية - الإحصاء والديناميكيات. هوبوكين ، نيو جيرسي: قاعة بيرسون برنتيس. ص 10 - 111</li>
	<li>بير ، إف بي ؛ جونستون ، إي آر ؛ مازوريك ، د. إف. كرومويل ، بي جيه وسيلف ، ب. (2019). ميكانيكا المتجهات للمهندسين - الإحصاء والديناميكيات. نيويورك: ماكجرو هيل. الصفحتان 13 و 15</li>
	<li>مريم ، جي إل. كريج ، إل جي وبولتون ، ج. (2020). الميكانيكا الهندسية - الإحصاء. هوبوكين ، نيو جيرسي: جون وايلي.</li>
</ol>

الحسابات العددية.

<div style="direction:rtl">يعد التمثيل الواضح للقيم العددية أمرًا هاما في التطبيقات الهندسية. يمثل التقديم الامثل للإجابات أو التقارير احد اهم الممارسات الهندسية. يتم إجراء الحسابات العددية باستخدام آلة حاسبة محمولة يدويا أو باستخدام أجهزة الكمبيوتر وذلك للحصول على الإجابات العددية الدقيقة. يتم التعبير على حل المسائل باستخدام طرق مختلفة. في حين أن حل الرموز بشكل جبري يدوياً هو إحدى أكثر الطرق شيوعًا، إلا أن طريقة الرسم البياني غالبًا ما تكون مفضلة. يصبح الكمبيوتر مفيدًا عند حل العديد من المعادلات. يجب استخدام معادلة متجانسة الابعاد عند اجراء هذه الحسابات. يجب استخدام وحدات من نفس النظام في مثل هذه المعادلات. تعتمد دقة المسألة العددية على عدة عوامل مختلفة. عدد الأرقام المهمة الموجودة في أي قيمة عددية هي أحد هذه العوامل. نظرًا لأن الأعداد الصحيحة التي تنتهي بالأصفار تؤدي دائمًا إلى حدوث الالتباس، يتم تقديم النتيجة باستخدام التعبير الهندسي. يتم التعبير عن معظم القيم باستخدام الكلمات البادئة. تستخدم البادئات دائمًا للتعبير عن الأعداد الكبيرة أو الصغيرة. يمكن تبسيط تمثيل النتيجة إلى الأرقام المهمة المطلوبة بمضاعفات الالف . معرفة عدد الأرقام المهمة التي يجب استخدامها للتعبير عن القيمة العددية أمر ضروري. على سبيل المثال ، يمكن تبسيط العدد 34600 الى 34.6 ×103 إذا كانت هناك ثلاثة أرقام مهمة مطلوبة. إذا كانت هناك خمسة أرقام مهمة مطلوبة ، فيمكن تعبير نفس العدد عن 0.34600×106. في الكسور العشرية ، تعتبر الأصفار البادئة غير مهمة ؛ على سبيل المثال ، الكسر العشري 0.00456 لديه ثلاثة أرقام مهمة فقط. إذا بدأ العدد بالأصفار ، يتم تعبير مثل هذه الأرقام كالاتي 4.56×10-3 أو 456×10-6. يتم تقريب الأرقام الكبيرة والصغيرة إلى الأرقام المهمة المطلوبة. ومع ذلك، أثناء تقريب عدد ما، يجب أن تظل دقة النتيجة النهائية كما هي. تم تصميم معظم الآلات الحاسبة لتقريب القيمة. في حين أنه من الأفضل عدم تقريب الإجابة أثناء العديد من الخطوات حتى الخطوة الأخيرة. يجب تقريب الإجابة أو النتيجة فقط استنادًا إلى الدقة المطلوبة. يتم التعبير عن معظم الإجابات في تطبيقات الهندسة باستخدام ثلاثة أرقام مهمة.</div>

في التطبيقات الهندسية ، يعد تمثيل القيمة العددية أمرا بالغ الأهمية. يعد تقديم الإجابة أو الإبلاغ عنها أحد الأجزاء الأساسية من ...

Education

JoVE Core

Mechanical Engineering

الهندسة الميكانيكية

Unit 1

الوحدة الأولى

An Introduction to Statics

مقدمة في علم السكون (الاستاتيكا)

KEY TERMS AND CONCEPTS

المصطلحات والمفاهيم الأساسية

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

Scientific Method

The scientific method is used to solve problems and explain phenomena. The development of the scientific method coincided with changes in philosophy ...

Scientific Laws and Theories

Scientific Laws

In science, a law is defined as a concise, verbal or mathematical, statement that summarizes a vast number of experimental observations. ...

The Scientific Method

The scientific method is a detailed, empirical problem-solving process used by biologists and other scientists. This iterative approach involves ...

Chemistry is an empirical science. Scientists often pose questions to understand the chemistry in everyday life and seek answers to these questions. To ...

What is a Hypothesis?

A hypothesis can be a simple sentence or statement about a property or any phenomenon observed or predicted for a population. It is usually a claim about ...

Types of Hypothesis Testing

There are three types of hypothesis tests: right-tailed, left-tailed, and two-tailed.
When the null and alternative hypotheses are stated, it is observed ...

Hypothesis: Accept or Fail to Reject?

The outcome of any hypothesis testing leads to rejecting or not rejecting the null hypothesis. This decision is taken based on the analysis of the data, ...

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

Inductive Reasoning

Inductive reasoning is a form of logical thinking that uses related observations to arrive at a general conclusion. It is uncertain and operates in ...

Deductive Reasoning

Deductive reasoning, or deduction, is the type of logic used in hypothesis-based science. In deductive reasoning, the pattern of thinking moves in the ...

Correlation and Causation

Correlation and CausationStatistical tests can calculate whether there is a relationship, or correlation, between independent and dependent variables. A ...

Demonstrating the Scientific Method with Tree Branches
ExpandObtain branches containing a few dozen typical leaves from five different local tree species. ...

Observation and Background Research
ExpandNOTE: The first two steps in the scientific process involve studying and observing natural phenomena of ...

The student will demonstrate an understanding of scientific and engineering practices by planning and carrying out investigations
• 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

ES.1.b

Introduction to Test of Independence

In statistics, the term independence means that one can directly obtain the probability of any event involving both variables by multiplying their ...

Statistical Analysis: Overview

An analysis is usually conducted by replicated sampling or repeated measurements on the same sample. This leads to scattered results rather than a single ...

Statistical Significance

Once data is collected from both the experimental and the control groups, a statistical analysis is conducted to find out if there are meaningful ...

Review and Preview

Data are individual items of information obtained from a population or sample. Data may be classified as qualitative (categorical), quantitative ...

Data: Types and Distribution

In biostatistics, data refers to the collected observations that are subject to analysis. Data can be parametric or nonparametric.
Nonparametric data ...

Histogram

The histogram is a graphical representation in the x-y form of data distribution in a data set. The horizontal x-axis is labeled with what the data ...

Scatter Plot

The most common and easiest way to display the relationship between two variables, x and y, is a scatter plot. A scatter plot shows the direction of a ...

Bar Graph

A bar graph is also called a bar chart and consists of bars that are separated from each other. It either uses horizontal or vertical bars to show ...

Pie Chart

A pie chart (or a pie graph) is a circular graphical chart or a pictorial representation of categorical data. It is divided into slices of pie each ...

In engineering applications, the representation of the numerical value is critical. Presenting or reporting the answer is one of the essential parts of ...

Accuracy and Precision

Scientists typically make repeated measurements of a quantity to ensure the quality of their findings and to evaluate both the precision and the accuracy ...

Significant Figures in Calculations

Uncertainty in measurements can be avoided by reporting the results of a calculation with the correct number of significant figures. This can be ...

Realism in Experimentation

Source: Laboratories of Gary Lewandowski, Dave Strohmetz, and Natalie Ciarocco&#8212;Monmouth University

In an ideal world researchers would conduct ...

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

Data Collection by Observations

Data collection refers to a systematic way of obtaining, observing, measuring, and analyzing accurate information. Observational studies are one of the ...

Data Collection by Experiments

Data collection is a systematic method of obtaining, observing, measuring, and analyzing accurate information. An experimental study is a standard method ...

Data Collection by Survey

The systematic method of obtaining and analyzing accurate information of a population is called data collection. A survey is a standard method of data ...

Reliability and Validity

Reliability and validity are two important considerations that must be made with any type of data collection. Reliability refers to the ability to ...

Reasoning

Reasoning involves transforming information into conclusions, which is essential for problem-solving, decision-making, and critical thinking.
Reasoning ...

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

Using Topographic Maps to Generate Topographic Profiles

Source: Laboratory of Alan Lester - University of Colorado Boulder
Topographic maps are &#34;plan-view&#34; representations of Earth&#39;s ...

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

A data source is the origin of collected data, whether physical or digital, and includes all channels, platforms, and repositories for gathering and ...

Communication

Sharing information, concepts, and emotions to foster mutual understanding is communication. The sender, recipient, and transaction must be considered in ...

levels-of-communication-i-intrapersonal-interpersonal-and-small-group

Levels of Communication I: Intrapersonal, Interpersonal, and Small Group

Interpersonal communication focuses on the exchange of messages between two people.
We can participate in these relationships through verbal, nonverbal, ...

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

Levels of Communication II: Organizational, Public, and Group Dynamics

Effective communication is the foundation of a good organization. Communication is the lifeblood of an organization that connects the group with messages. ...

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

Description

Transcript

Tags

More videos by Standards