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

측정의 확실성은 두 가지 요소, 즉 측정의 자릿수와 사용된 기기의 정밀도에 따라 달라집니다.
측정된 양에서 마지막 불확실한 숫자를 포함한 모든 숫자를 유효 숫자라고 하며 특정 규칙을 사용하여 결정할 수 있습니다.
0이 아닌 숫자와 0이 아닌 두 숫자 사이에 있는 모든 캡티브 0은 중요합니다. 예를 들어, 28에는 두 개의 유효 숫자가 있고 26.25에는 4개의 유효 숫자가 있고 208에는 3개의 유효 숫자가 있습니다.
선행 0은 소수점을 찾을 뿐이므로 결코 중요하지 않습니다. 예를 들어, 0.00208에는 세 개의 유효 숫자가 있습니다. 이러한 수량은 지수 표기법을 사용하여 표현할 수 있습니다. 따라서 0.00208은 2.08 × 10−3으로 쓸 수 있습니다.
후행 0은 10진수 형식의 숫자에서만 의미가 있습니다. 2200에는 두 개의 후행 0과 두 개의 유효 숫자가 있는 반면 2200.0 및 2200.1에는 모두 5개의 유효 숫자가 있습니다.
소수점이 없는 수량의 경우 후행 0의 중요성이 모호해집니다. 따라서 2200은 두 개의 유효 숫자가 있는 2.2 × 103 또는 세 개의 유효 숫자가 있는 2.20 x 103으로 쓸 수 있습니다.

유효 숫자에 대한 규칙

모든 측정에 있어 측정 도구의 정밀도는 필수 요소입니다. 예를 들어 일반 눈금자는 길이를 가장 가까운 밀리미터까지 측정할 수 있습니다. 반면에 캘리퍼스는 길이를 가장 가까운 0.01mm까지 측정할 수 있습니다. 결과적으로 캘리퍼는 극히 미세한 길이 변화도 측정할 수 있기 때문에 더욱 정밀한 측정 도구입니다. 측정 도구가 더 정확할수록 측정값도 더 정확해집니다.

측정된 값을 나타낼 때 마지막 숫자는 측정하는 사람이 어떤 방식으로든 계산했다는 점을 강조해야 합니다. 예를 들어, 자를 사용하여 막대기의 길이를 측정하는 사람은 길이가 13.2cm에서 13.3cm 사이인 것을 알아차리고 마지막 숫자의 값을 추정해야 합니다. 유효 숫자의 규칙은 측정값에 기록된 마지막 숫자가 약간의 불확실성이 있는 첫 번째 숫자라는 것입니다. 왼쪽의 첫 번째 측정값부터 시작하여 오른쪽에 적힌 마지막 숫자까지 자릿수를 세어 값의 유효 자릿수를 결정합니다. 유효 숫자는 값을 측정하는 데 사용되는 측정 도구의 정밀도를 나타냅니다.

텍스트는 <a href="https://openstax.org/books/university-physics-volume-1/pages/1-6-significant-Figures"> 에서 채택되었습니다. Openstax, 대학 물리학 1권, 섹션: 1.6 유효 수치. </a>

모든 측정에서 측정 도구의 정밀도는 필수 요소입니다. 예를 들어, 일반 눈금자는 가장 가까운 길이를 측정 할 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

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

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 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

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...

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Dimensional Checks for Physics Equations

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solving problems in physics

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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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