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

יישומים הנדסיים מסתמכים במידה רבה על חישובים מספריים, שתוצאותיהם מיוצגות בפורמט סטנדרטי.
בחישובים נומריים, המשוואה חייבת להיות הומוגנית מבחינה ממדית, והמונחים חייבים לבוא לידי ביטוי באותן יחידות.
ההומוגניות הממדית של המשוואה נשמרת ללא קשר למשוואה המוערכת.
המספרים מעוגלים למספרים המשמעותיים הנדרשים לדיוק התוצאה; ומבוטאים בכפולות של 103. אם המספר קטן מאחד, המספר מעוגל למספרים המשמעותיים הנדרשים ומתבטא בכפולות של 10-3.
על פי הכלל, כאשר מספר מסתיים בספרה גדולה מחמש, הוא מעוגל כלפי מעלה, וכאשר הספרה קטנה מחמש, המספר נשאר זהה, עד למספרים המשמעותיים.
כאשר המספר מסתיים בערך הספרה חמש, הוא מעוגל כלפי מעלה רק אם המספר הקודם הוא אי-זוגי, ואם הוא זוגי, הוא נשאר זהה עד למספרים המשמעותיים.

<ol>
	<li>היבלר, R.C. (2016). מכניקה הנדסית - סטטיקה ודינמיקה. הובוקן, ניו ג'רזי: אולם פירסון פרנטיס. עמ' 10\u201211</li>
	<li>באר, פ"פ; ג'ונסטון, א.ר.; מזורק, ד"ו; קרומוול, פי ג'יי ועצמי, ב. (2019). מכניקה וקטורית למהנדסים - סטטיקה ודינמיקה. ניו יורק: מקגרו-היל. עמ' 13 ו-15</li>
	<li>מרים, י"ל; Kraige, L.G. ובולטון, J.N. (2020). מכניקה הנדסית - סטטיקה. הובוקן, ניו ג'רזי: ג'ון ווילי.</li>
</ol>

חישובים מספריים

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ביישומים תעשייתיים, הייצוג של ערך המספרי מאוד חשוב. הצגת או דיווח התשובה הם אחד מהחלקים החיוניים ביישומים ההנדסיים. חישובים מספריים מתבצעים באמצעות מחשבונים ידניים או מחשבים, מאחר ותשובות מדויקות נומרית נדרשות תמיד. 

פתרון של בעיה נמצא בעזרת שיטות שונות. בנוסף לפתרון ידני של סמלים אלגבריים, שיטת הגרפים נמצאת בשימוש נרחב. מחשבים מוציאים מכך תועלת כאשר יש לפתור מספר משוואות. עליהן יש להשתמש במשוואה הדימנציונית. יחידות המידה שבשימוש בכזו משוואה צריכות להיות באותו מערכת. 

הדיוק של חישוב מספרי תלוי במספר גורמים. מספר ספרות סימנטיביות הכלולות בערך מספרי הוא גורם כזה. מאחר ומספר שלם שמסתיים באפסים יכול להוביל תמיד לבלבול, התוצאה מדווחת באמצעות ריווח הנדסי. רוב הערכים מובאים בעזרת תחיליות. 

תחיליות תמיד משמשות לביטוי של מספרים גדולים או קטנים. התוצאה מגורעת לספרות החשובות הנדרשות ונמצאת במרובעים של (103).


ידע על כמה ספרות חשובות יש להשתמש כדי לבטא את הערך המספרי הוא חיוני. לדוגמה, 34,600 ניתן להביע כ-34.6 (103) אם נדרשות שלוש ספרות חשובות.

אם נדרשות חמישה ספרות חשובות, אותו מספר ניתן להביע כ-0.34600 (106). 

במספרים עשרוניים, האפסים התחלה הם לא משמעותיים; לדוגמה, העשרוני 0.00456 יש לו שלוש ספרות חשובות בלבד. אם המספר מתחיל באפסים, מספרים כאלה מובאים כמו 4.56 (10-3) או 456 (10-6).

מספרים גדולים מדי או קטנים מדי מסובכים לסיבוב כדי להגיע לספרות חשובות הנדרשות. אך, בעת סיבוב מספר, דיוק התוצאה הסופית צריך להישמר אותו דבר. רוב המחשבונים עוצבו כך שיסבירו את הערך. כאשר עוברים בין כמה שלבים, כדאי שלא לסבוב את התשובה עד מלוא השלב האחרון. רק התשובה או התוצאה צריכה להיסבב בהתאם לדיוק המובטח. רוב התשובות ביישומים ההנדסיים מובאות בעזרת שלוש ספרות חשובות.

</div>

ביישומים הנדסיים, ייצוג הערך המספרי הוא קריטי. הצגה או דיווח של התשובה היא אחד החלקים החיוניים של ...

Education

JoVE Core

Mechanical Engineering

הנדסת מכונות

Unit 1

יחידה 1

An Introduction to Statics

מבוא לסטטיקה

KEY TERMS AND CONCEPTS

מונחים ומושגים מרכזיים

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

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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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Deductive Reasoning

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Demonstrating the Scientific Method with Tree Branches
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Observation and Background Research
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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

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Nonparametric data ...

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Scatter Plot

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Bar Graph

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Pie Chart

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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

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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

Data Collection by Observations

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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

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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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