Name: counting significant figures in measurements
Uploaded: 2023-09-22T11:49:39.000Z
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 значимых фигур

Rules of Significant Figures

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

Mechanical Engineering

Машиностроение

Unit 1

Раздел 1

Physics Basics

Основы физики

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

counting significant figures in measurements

Significant figures help students record measurements with the correct level of precision. They show which digits in a number are meaningful and which only help place the decimal point. In science class, this idea matters when writing and comparing measured values.

The rules for significant figures explain how to count these digits in different numbers. Some digits are always counted, while others depend on where they appear in the number. Learning the rules makes it easier to report answers clearly and consistently.

This topic is especially useful in physics and other measurement-based science work. It helps students decide how many digits to keep when writing results from lab work or calculations. That makes numerical answers easier to interpret and compare.

Counting Significant Figures in Measurements

counting-significant-figures-in-measurements

introduction to scalers

Scalar Quantities in Physics

Scalar quantities in physics have size only. They do not include direction. This makes them different from vector quantities. Common scalar examples include mass, temperature, time, and energy. Each one can be described with a number and a unit. Because direction is not part of the value, scalars are often easier to compare and measure.

vector or cross product

Cross Product of Two Vectors

The cross product of two vectors gives a new vector that is related to both original vectors. It is also called the vector product. In many physics problems, this operation helps describe quantities that depend on direction as well as size. The result of a cross product has a direction set by the two input vectors. It is not the same as ordinary multiplication. The transcript focuses on the vector or cross product as a core vector operation students use when working with vectors in science.

introduction to vectors

Vectors in Motion and Direction

Vectors describe quantities that have both size and direction. They are used in physics to show how motion, force, and other quantities act in space. A vector can be represented with an arrow. The length of the arrow shows the size, and the arrowhead shows the direction. This makes vectors useful for comparing how one quantity points relative to another. Scalars are different because they have size only and no direction. Understanding the difference between vectors and scalars is an important...

units and standards of measurement

Measurement Units, Standards, and SI Basics

Measurement units, standards, and SI basics help scientists describe physical quantities clearly. A unit gives a number meaning, while a standard provides a fixed reference for that measurement. Together, they make results easier to compare and understand. The International System of Units, or SI, is the most common measurement system in science. It uses agreed-upon base units for common quantities. These standards reduce confusion when measurements are shared across labs, classrooms, and...

accuracy and precision

Measurement Errors, Accuracy, and Precision

Measurement errors can affect how close a result is to the true value and how consistent repeated results are. Accuracy describes how close a measurement is to the accepted or true value. Precision describes how close repeated measurements are to one another. A result can be accurate, precise, both, or neither. A set of measurements may cluster tightly together and still be far from the true value. Another set may include values spread out from one another, even if one of them is close to the...

rules of significant figures

Significant figures help students record measurements with the correct level of precision. They show which digits in a number are meaningful and which only help place the decimal point. In science class, this idea matters when writing and comparing measured values. The rules for significant figures explain how to count these digits in different numbers. Some digits are always counted, while others depend on where they appear in the number. Learning the rules makes it easier to report answers...

random and systematic errors

Measuring Error in Scientific Data

Random and systematic errors affect scientific measurements. Random errors cause values to spread around the true value. They make repeated measurements less consistent. Systematic errors shift measurements in the same direction each time. Understanding both kinds of error helps students judge data quality. Random error can come from small changes during measurement. Systematic error can come from a biased tool or method. Scientists look for these patterns so they can improve results and...

position and displacement

Tracking Motion with Position and Displacement

Position and displacement are key ideas in straight-line motion. Position tells where an object is located compared with a chosen starting point, called the origin. Displacement describes how far and in what direction the object has moved from its starting position. These ideas help describe motion clearly. Position can change as an object moves. Displacement focuses on the change in position, not just the path taken. That makes it useful for comparing motion in a simple and precise way.

position and displacement vectors

Using Vectors to Describe Motion

Position and displacement vectors describe motion in physics. A position vector shows where an object is located relative to a chosen origin. A displacement vector shows how far and in what direction the object moves from one point to another. These vectors are useful because they give a clear way to track movement in space. The video connects position and displacement to the idea of a reference point and shows how direction matters as much as distance. That makes them important for describing...

mass and weight

How Mass Differs from Weight

Mass and weight are related, but they are not the same. Mass is the amount of matter in an object. Weight is the force of gravity acting on that object. This difference matters because mass stays the same even when gravity changes. Weight can change if the gravitational pull changes. A person or object therefore has the same mass, but not always the same weight. The terms are often used in everyday speech as if they mean the same thing. In physics, they describe two different ideas.

acceleration due to gravity on earth

Free-Fall Acceleration on Earth

Free-fall acceleration on Earth describes how fast an object speeds up when gravity is the only force acting on it. Near Earth’s surface, this acceleration is nearly constant for many everyday situations. Gravity pulls objects toward Earth and gives them downward acceleration. This motion is often written as g, and it helps explain why falling objects gain speed as they move downward. The value of g is commonly used in physics to predict the motion of objects dropped or released near the...

tension

Tension in Ropes and Strings

Tension is the pulling force carried by a rope, string, or cable when it is stretched by a load. In physics, this force acts along the length of the object and pulls away from the objects at each end. A stretched rope can support a hanging mass because the tension in the rope balances the weight of the load. The same idea appears in many everyday situations, such as a cable holding a sign or a string lifting an object. Understanding tension helps students connect force diagrams to real motion.

gravitational force

How Gravity Acts Between Objects

Gravity is a force that pulls objects toward one another. On Earth, this force gives objects weight and keeps people, water, and other materials from drifting away. It also helps explain why planets and moons stay in motion around larger bodies. The strength of gravitational force depends on the masses of the objects involved. Larger masses create a stronger pull, while smaller masses create a weaker one. The distance between objects also matters, because gravity becomes weaker as objects move...

key terms and concepts

Learn how to count significant figures in measurements and report scientific values with the right precision for high school science and lab work.

Counting Significant Figures in Measurements | 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

Counting Significant Figures in Measurements

Description

Transcript