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

Значащие цифры помогают достичь определенности и в математических операциях. В дополнение или вычитание результат должен быть округлен в меньшую сторону, чтобы иметь такое же количество знаков после запятой, как и измерение с наименьшим количеством знаков после запятой.
Округление в меньшую сторону следует выполнять, когда последняя цифра меньше 5, а округление в большую сторону, когда она равна 5 или выше. Другие методы округления иногда используются, когда последняя цифра равна 5.
Например, сумма чисел 2,052 и 1,2 округляется как 3,3.
Однако при умножении или делении результат должен быть округлен так, чтобы получить такое же количество значащих цифр, как и при измерении с наименьшим числом значащих цифр. Таким образом, произведение 2,052 на 1,2 округляется как 2,5.

Важные фигуры в вычислениях

Погрешность измерений можно избежать, представляя результаты вычислений с правильным количеством значащих цифр. Это можно определить с помощью следующих правил округления чисел:

<ol>
	<li>При сложении или вычитании чисел округлите результат до того же количества десятичных знаков, что и число с наименьшим количеством десятичных знаков.</li>
	<li>При умножении или делении чисел округлите результат до того же количества цифр, что и число с наименьшим количеством значащих цифр.</li>
	<li>Если цифра, которая будет отброшена (непосредственно справа от цифры, которую нужно сохранить), меньше 5, "округлите вниз" и оставьте сохранённую цифру неизменной.</li>
	<li>Если цифра, которую нужно отбросить (непосредственно справа от сохраняемой цифры), равна 5 или больше, производится "округление вверх", а сохраняемая цифра увеличивается на 1. Если отбрасываемая цифра равна 5, могут также использоваться альтернативные методы округления. В таком случае сохраняемая цифра округляется вверх или вниз, в зависимости от того, что приводит к чётному значению.</li>
</ol>

Важно отметить, что округление значащих цифр следует предпочтительно выполнять в конце многошагового вычисления, чтобы избежать накопления ошибок на каждом этапе из-за округления. Таким образом, значащие цифры и округление облегчают правильное представление уверенности в отчётных измеренных значениях.

Этот текст адаптирован из <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>

Погрешности в измерениях можно избежать, сообщив результаты расчета с правильным числом значащих цифр. Это может быть...

Education

JoVE Core

Physics

Физика

Unit 1

Раздел 1

Units, Dimensions, and Measurements

Единицы, размерности и измерения

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

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

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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...

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units and standards of measurement

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rules for significant figures

Measurement Precision and Significant Figures

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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

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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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ES.1.b

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• evaluate the merits and limitations of models
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• read and interpret topographic and basic geologic maps and globes, including location by latitude and longitude

ES.1.e

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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
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• 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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