Name: measurement precision and significant figures
Uploaded: 2023-04-30T10:48:20.000Z
Duration: 1 min 44 s
Channel: JoVE

Достоверность измерения зависит от двух факторов: количества цифр в измерении и точности используемого прибора.
В измеряемой величине все цифры, включая последнюю неопределенную цифру, называются значащими цифрами и могут быть определены с помощью определенных правил.
Любые ненулевые цифры и все зависимые нули, которые лежат между двумя ненулевыми цифрами, имеют значение. Например, у 28 две значащие фигуры, у 26,25 — четыре, а у 208 — три.
Ведущие нули никогда не являются значимыми, так как они просто определяют местоположение десятичной запятой. Например, 0,00208 имеет три значащие фигуры. Такие величины могут быть выражены с помощью экспоненциальных обозначений. Таким образом, 0.00208 можно записать как 2.08 × 10−3.
Конечные нули имеют значение только в десятичных числах. 2200 имеет два незначащих нуля и две значащие цифры, тогда как 2200.0 и 2200.1 имеют по 5 значащих цифр.
Для величин без десятичных знаков значение нулей в конце становится неоднозначным. Таким образом, 2200 можно записать как 2.2 × 103 с двумя значащими цифрами или 2.20 x 103 с тремя значащими цифрами.

Правила для значащих цифр

В любом измерении точность измерительного инструмента играет важную роль. Например, обычная линейка может измерять длину с точностью до ближайшего миллиметра; тем временем, штангенциркуль может измерять длину до ближайших 0,01 мм. В результате, штангенциркуль является более точным инструментом измерения, потому что он может измерить крайне маленькие изменения в длине. Измерения будут более точными, если измерительный инструмент более точный.

Следует подчеркнуть, что при представлении измеренных значений последняя цифра была вычислена каким-то образом человеком, производящим измерение. Например, человек, измеряющий длину палки линейкой, замечает, что она находится между 13,2 см и 13,3 см, и поэтому ему необходимо оценить значение последней цифры. Правило значащих цифр заключается в том, что последняя записанная цифра в измерении является первой цифрой с некоторой неопредёленностью. Начните с первого измеренного значения слева и просчитайте количество цифр до последней записанной цифры справа, чтобы определить количество значащих цифр в значении. Значащие цифры представляют точность используемого инструмента для измерения значения.

Этот текст адаптирован из <a href="https://openstax.org/books/university-physics-volume-1/pages/1-6-significant-figures">Openstax, University Physics Volume 1, Section: 1.6 Significant Figures.</a>

При любом измерении точность измерительного инструмента является важным фактором. Обычная линейка, например, может измерять длину с точностью до ближайшего...

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

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 be recorded with a guessed last digit.

The last digit in a measurement is the first digit with some uncertainty. To find the number of significant figures, start with the first measured value on the left and count through the last digit written on the right. Significant figures show how precise the measuring tool was when the value was recorded.

Measurement Precision and Significant Figures

measurement-precision-and-significant-figures

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accuracy and precision

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rules for 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...

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key terms and concepts

Learn how ruler and caliper precision affects measurements and how to count significant figures from the first measured digit to the uncertain last digit.

Measurement Precision and 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.

Measurement Precision and Significant Figures

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