Name: rounding rules for significant figures
Uploaded: 2023-04-30T12:12:11.000Z
Duration: 58 s
Channel: JoVE

K12 Standards

Virginia  Standards of Learning

HIgh School

Earth Science

ES.1

ES.1.c

Significant Figures in Calculations

נתונים משמעותיים מסייעים להשיג ודאות גם בפעולות מתמטיות. בנוסף או חיסור, יש לעגל את התוצאה כך שמספר המקומות העשרוניים יהיה זהה למספר המקומות העשרוניים כמו המדידה עם המקומות העשרוניים המעטים ביותר.
עיגול כלפי מטה צריך להתבצע כאשר הספרה האחרונה נמוכה מ-5, ועיגול כלפי מעלה מתבצע כאשר היא 5 ומעלה. שיטות עיגול אחרות משמשות לעתים כאשר הספרה האחרונה היא 5.
לדוגמה, הסכום של 2.052 ו- 1.2 מעוגל כ- 3.3.
עם זאת, בעת הכפלה או חלוקה, יש לעגל את התוצאה כך שתהיה לה אותו מספר דמויות משמעותיות כמו המדידה עם המספרים המשמעותיים המעטים ביותר. לפיכך, המכפלה של 2.052 ו- 1.2 מעוגלת כ- 2.5.

נתונים משמעותיים בחישובים

<div style="direction:rtl">ניתן למנוע אי ודאות במדידות על ידי דיווח על תוצאות חישוב עם המספר הנכון של נתונים משמעותיים. ניתן לקבוע זאת לפי הכללים הבאים לעיגול מספרים: <ol style="padding-right: 35px; margin: 0;"> <li style="text-align: right;">בעת הוספה או חיסור של מספרים, עגל את התוצאה לאותו מספר מקומות עשרוניים כמו המספר בעל המספר הקטן ביותר של מקומות עשרוניים.</li> <li style="text-align: right;">כאשר מכפלים או מחלקים מספרים, עגל את התוצאה לאותו מספר ספרות כמו המספר בעל המספר הנמוך ביותר של מספרים משמעותיים.</li> <li style="text-align: right;">אם הספרה שיש להוריד (הספרה שמיד מימין לספרה שיש לשמור) היא פחות מ-5, "עגל כלפי מטה" והשאירו את הספרה שנשמרה ללא שינוי.</li> <li style="text-align: right;">אם הספרה שיש להוריד (הספרה שמיד מימין לספרה שיש לשמור) היא 5 או יותר, "עגל כלפי מעלה" והגדל את הספרה שנשמרה ב-1. חלופה ניתן להשתמש בשיטות עיגול גם אם הספרה שירדה היא 5. הספרה שנשמרה מעוגלת כלפי מעלה או למטה, לפי מה שמניב ערך זוגי.</li> </ol> הערה חשובה היא שעדיף עיגול של נתונים משמעותיים להיעשות בסוף חישוב רב-שלבי כדי למנוע הצטברות של שגיאות בכל שלב עקב עיגול. לפיכך, נתונים ועיגול משמעותיים מקלים על ייצוג נכון של הוודאות של הערכים הנמדדים שדווחו. טקסט זה מותאם מ <a href="https://openstax.org/books/chemistry-2e/pages/1-5-measurement-uncertainty-accuracy-and-precision">Openstax, Chemistry 2e, Section 1.5: Measurement Uncertainty, Accuracy, and Precision</a>.</div>

אי ודאות במדידות ניתן למנוע על ידי דיווח על תוצאות חישוב עם המספר הנכון של נתונים משמעותיים. זה יכול להיות ...

Education

JoVE Core

Physics

פיזיקה

Unit 1

יחידה 1

Units, Dimensions, and Measurements

יחידות, ממדים ומדידות

KEY TERMS AND CONCEPTS

מונחים ומושגים מרכזיים

rounding rules for significant figures

Rounding rules for significant figures help show the right level of certainty in measured results. When a calculation is reported with the correct number of significant figures, it better matches the uncertainty in the measurements.

The rounding rule depends on the type of math being done. For addition and subtraction, the result should have the same number of decimal places as the number with the fewest decimal places. For multiplication and division, the result should have the same number of significant figures as the number with the fewest significant figures.

The digit to be dropped also matters. If that digit is less than 5, round down and keep the retained digit the same. If it is 5 or greater, round up and increase the retained digit by 1.

An alternative method may be used when the dropped digit is 5. In that case, the retained digit is rounded up or down, whichever gives an even value. In multistep calculations, rounding should preferably be done at the end. This helps avoid extra error from rounding at each step.

Rounding Rules for Significant Figures

the scope of physics

How Physics Shapes Science and Technology

Physics studies the interactions of energy, matter, space, and time. It looks for the basic mechanisms that explain natural phenomena. The word physics comes from the Greek word physis, which means nature. Physics helps us understand the natural world at its most fundamental level. It relies on quantitative laws, or rules written in numbers and measurements, to describe how things behave. That approach can also help other fields improve the limits of current technology. Physics matters in...

orders of magnitude

Estimating Scale with Powers of 10

Orders of magnitude help estimate the scale of a number using powers of 10. It is a simple way to round values to the nearest power of 10. This makes it easier to compare very large and very small numbers. To find the order of magnitude of a number, take its base-10 logarithm and round to the nearest integer. The result gives the power of 10 that most closely matches the original value. This method gives a consistent estimate of size without using exact digits. Orders of magnitude are useful...

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models, theories, and laws

Scientific Models, Theories, and Laws

Scientific models, theories, and laws help physicists describe natural phenomena. A model is a simplified version of a physical system that is too complex to study in full. It acts as a rough mental or visual picture of what may be happening. Good models keep the important parts and simplify the rest so the problem becomes workable. The light wave model is one example. Light waves are usually invisible, so they cannot be seen in the same way as water waves. Even so, it is useful to think of...

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units and standards of measurement

SI Units for Physical Quantities

SI units give a standard way to measure physical quantities. A physical quantity can be defined by how it is measured or by how it is calculated from other measurements. For example, the mass and dimensions of a metallic cube can be found with a weighing machine and a meter scale. Some quantities are built from others. The volume of a cube is the cube of its side length. The density of the cube is then found by dividing mass by volume. Measurements are written in units, which are standardized...

estimation of the physical quantities

Fermi Estimation for Physical Quantities

Fermi estimation helps physicists, scientists, and engineers make rough calculations for physical quantities. These estimates are also called guesstimates, order-of-magnitude approximations, back-of-the-envelope calculations, or Fermi calculations. Enrico Fermi was known for making these kinds of estimates with surprising precision. Estimation is not random guessing. It uses prior experience and sound physical reasoning to get a rough value for a quantity. This kind of reasoning helps build...

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base quantities and derived quantities

SI Base Units Behind Measured Quantities

SI base units are the starting point for measuring physical quantities. In any system of units, some quantities must be defined through direct measurement. These are called base quantities, and their units are base units. Other physical quantities are built from these base values by algebraic combinations. These are called derived quantities, and their units are derived units. For example, area comes from two lengths multiplied together. It is a derived quantity and is written in SI base units...

conversion of units

Unit Conversion Steps and Real-World Errors

Unit conversion lets you change a measurement from one unit to another. It is useful in everyday life, such as when a cookbook gives amounts in liters or ounces and you need cups instead. It also helps when directions use feet or meters, but you want to know the distance in miles. The first step is to list the given unit and the unit you need. The second step is to choose a conversion factor, which is a ratio that shows how many of one unit equal another unit. For example, 1,000 meters equal 1...

accuracy and precision

Repeated Measurements in Science

Repeated measurements help scientists check the quality of their results. They are used to judge both precision and accuracy. These two ideas are related, but they do not mean the same thing. Measurements are precise when repeated trials give very similar results. Precision shows how closely the values agree with one another. Measurements are accurate when the result is very close to the true value or the accepted value. Accuracy shows how closely the values agree with the real target. High...

random and systematic errors

How Measurement Errors Affect Results

Measurement errors can change how accurate and precise a result appears. Scientists try to record measurements as carefully as possible, but errors can still happen. These errors are usually random or systematic. Random errors come from inconsistency or fluctuation in the measuring process. They can also come from changes in the quantity being measured. In repeated measurements, random error may make a value appear greater than the true value one time and less than it the next. A simple...

rules for significant figures

Measurement Precision and Significant Figures

Measurement precision depends on the tool used, and significant figures show that precision. A ruler can measure length to the closest millimeter. A caliper can measure length to the nearest 0.01 mm, so it gives a more precise measurement because it can detect very small changes in length. When a value is written from a measurement, the last digit is not exact. The person making the measurement must estimate that digit. For example, a stick that seems to fall between 13.2 cm and 13.3 cm must...

significant figures in calculations

Rounding rules for significant figures help show the right level of certainty in measured results. When a calculation is reported with the correct number of significant figures, it better matches the uncertainty in the measurements. The rounding rule depends on the type of math being done. For addition and subtraction, the result should have the same number of decimal places as the number with the fewest decimal places. For multiplication and division, the result should have the same number of...

dimensional analysis

Dimensional Checks in Physics Equations

Dimensional consistency is a key check in physics equations. It means the dimensions on both sides of an equation must match. The idea helps show whether an equation can represent a real physical law. The first rule is simple: expressions on each side of the equal sign must have the same dimensions. That makes sense because you can only add or subtract quantities of the same type. The second rule says that the input to a standard mathematical function, such as a trigonometric function, a...

problem solving: dimensional analysis

Dimensional Checks for Physics Equations

Dimensional analysis helps check whether physics equations make sense. It compares the dimensions on each side of an equation and shows whether the units are consistent. This method is useful for spotting algebra errors, typos, and for remembering physical laws. A valid equation must follow two rules. First, both sides of an equality must have the same dimension, so only quantities with matching dimensions can be added or subtracted. Second, common math functions such as exponential,...

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solving problems in physics

Physics Problem Solving: Strategy to Check

Physics problem solving uses general physical principles to work out specific situations. It is a key skill in physics, and it can also help with everyday life. The same analytical skills can be used in new situations, while a list of facts can never cover every possible case. Solving physics problems also takes creativity and insight. These skills grow with experience and practice. There is no simple step-by-step method that works for every problem, but a three-stage process can guide the...

key terms and concepts

Learn how to round significant figures in addition, subtraction, multiplication, and division, and why rounding at the end helps reduce error.

Rounding Rules for Significant Figures | JoVE K12

physics

JoVE Core Physics introduces the theory and application of fundamental physics topics, including kinematics, dynamics, fluid mechanics, statics, waves, and acoustics, with concise and easy-to-understand animated videos. Additionally, the scientist-in-action videos demonstrate the application of related concepts in classical and original research experiments performed in today's laboratories worldwide.

Life Science

LS.1

LS.1.b

LS.1.c

Texas Essential Knowledge and Skills

High School

Specialised Topic in Science

112.51.c.1.

112.51.c.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

Inductive Reasoning

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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
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

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

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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

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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

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Nonparametric data ...

Histogram

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Scatter Plot

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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

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Numerical Calculations

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Accuracy and Precision

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Realism in Experimentation

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

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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

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

ES.1.e

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

Rounding Rules for Significant Figures

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