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

유효 숫자는 수학 연산에서도 확실성을 달성하는 데 도움이 됩니다. 더하기 또는 빼기, 결과는 소수점 이하 자릿수가 가장 적은 측정값과 동일한 소수점 이하 자릿수를 갖도록 반올림해야 합니다.
마지막 숫자가 5 미만일 때 반올림을 수행하고 5 이상일 때 반올림을 수행해야 합니다. 마지막 숫자가 5일 때 다른 반올림 방법이 사용되는 경우가 있습니다.
예를 들어 2.052와 1.2의 합은 3.3으로 반올림됩니다.
그러나 곱하거나 나누는 동안 결과는 가장 적은 유효 숫자를 가진 측정값과 동일한 수의 유효 숫자를 갖도록 반올림되어야 합니다. 따라서 2.052와 1.2의 곱은 2.5로 반올림됩니다.

계산의 유효 숫자

정확한 유효 숫자 수를 사용하여 계산 결과를 보고하면 측정의 불확실성을 피할 수 있습니다. 이는 숫자 반올림에 대한 다음 규칙에 따라 결정될 수 있습니다:

<ol>
	<li>숫자를 더하거나 뺄 때 소수점 이하 자릿수가 가장 작은 숫자와 동일한 소수점 이하 자릿수로 결과를 반올림하세요.</li>
	<li>숫자를 곱하거나 나눌 때는 유효 숫자가 가장 작은 숫자와 동일한 자릿수로 결과를 반올림하세요.</li>
	<li>삭제할 숫자(보존할 숫자 바로 오른쪽에 있는 숫자)가 5보다 작은 경우 '내림'하고 유지한 숫자는 변경하지 않고 그대로 둡니다.</li>
	<li>삭제할 숫자(유지할 숫자 바로 오른쪽에 있는 숫자)가 5 이상인 경우 '반올림'하고 유지된 숫자를 1만큼 늘립니다. 삭제된 숫자가 5인 경우 반올림 방법을 사용할 수도 있습니다. 유지된 숫자는 반올림 또는 내림 중 짝수 값을 산출합니다.</li>
</ol>

중요한 점은 반올림으로 인해 각 단계에서 오류가 누적되는 것을 피하기 위해 다단계 계산이 끝날 때 유효 숫자의 반올림을 수행하는 것이 바람직하다는 것입니다. 따라서 유효 숫자와 반올림을 통해 보고된 측정 값의 확실성을 정확하게 표현할 수 있습니다.

이 텍스트는 <a .="" href="https://openstax.org/books/chemistry-2e/pages/1-5-measurement-uncertainty-accuracy-and-precision">Openstax, Chemistry 2e, 섹션 1.5: 측정 불확실성, 정확성 및 정밀도</a>.

측정의 불확실성은 정확한 수의 유효 숫자와 함께 계산 결과를 보고함으로써 피할 수 있습니다. 이것은 될 수 있습니다 ...

Education

교육

JoVE Core

Physics

물리학

Unit 1

제1단원

Units, Dimensions, and Measurements

단위, 차원 및 측정

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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

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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

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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

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solving problems in physics

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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.

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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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Observation and Background Research
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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

ES.1.b

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Histogram

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Scatter Plot

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Bar Graph

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Pie Chart

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• 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
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Reliability and Validity

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Reasoning

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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
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• 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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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

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Communication

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

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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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