Name: estimating scale with powers of 10
Uploaded: 2023-05-16T08:18:39.000Z
Duration: 1 min 15 s
Channel: JoVE

物理学では、宇宙に存在する最小のものであるクォークから、私たちが見ることができる最大のものである太陽まで、さまざまなオブジェクトに出くわします。
そういった物体の大きさや小ささを感じるのは難しいものです。このような量を表現するために、桁数、または10の累乗法の概念を使用します。
ここでは、すべての数値は、指定された数量に最も近い 10 の累乗に近似されます。たとえば、鉄の原子核の半径は4.6フェムトメートルです。これは半径の正確な値ではなく、単なる桁数の近似値です。
4.6フェムトメータは、10の4.6倍を負の15の累乗として書くことができるので、原子核の半径はマイナス15の桁になります。
桁違いにすると、特定の仮定を立て、計算を簡略化するのに役立ちます。
たとえば、建物から落下する物体の重力による加速度を計算する場合、建物の高さは地球の半径よりも数桁小さいため、無視されます。

<ol>
	<li>OpenStaxです。(2019). 大学物理学 Vol.1.【Web版】。10ページから取得 <a href="https://openstax.org/books/university-physics-volume-1/pages/1-1-the-scope-and-scale-of-physics">https://openstax.org/books/university-physics-volume-1/pages/1-1-the-scope-and-scale-of-physics</a></li>
</ol>

物理学の範囲

Orders of Magnitude

物理学は、すべての現象の根底にあるメカニズムを発見するために、エネルギー、物質、空間、時間の相互作用に関係します。 「物理学」という言葉は、 自然を意味するギリシャ語「phúsis」に由来します。 物理学は、私たちの周りの自然界を最も基本的なレベルで理解しようとします。 これを行うために定量的な法則を使用することを強調しています。これは、現在のテクノロジーのパフォーマンスの限界を押し広げたいと考えている他の分野でも役立つ可能性があります。

物理学の知識は、科学者のキャリアだけでなく、日常の場面でも不可欠です。 たとえば、物理学は、電子レンジがどのように機能するのか、そしてなぜ電子レンジがペースメーカーに影響を与えるのかを理解するのに役立ちます。 多くの分野が物理学に依存しており、物理学はさらにいくつかの分野に直接貢献しています。 たとえば、化学は原子と分子の相互作用を扱うため、原子物理学および分子物理学と密接な関係があります。 同様に、工学のほとんどの分野は、物理法則によって設定された制約内で新しいテクノロジー、プロセス、または構造を設計することに関係しています。

物理学のすべての応用を正式に学ぶ必要はありません。 基本的なルールを知り、それを適用する分析スキルを持つことが最も価値のあることです。 物理学は問題解決能力を高めるのにも役立ちます。 さらに、物理学は科学の最も基本的な要素を保存しているため、あらゆる科学で使用されています。

このテキストは <a href="https://openstax.org/books/university-physics-volume-1/pages/1-introduction">Openstax, University Physics Volume 1, Introduction</a> から改変されたものです。

数値の大きさのオーダーは、その数値に最も近い 10 の累乗です。したがって、大きさのオーダーは、そのスケール(またはサイズ)を推定します...

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Education

JoVE Core

Physics

物理学

Unit 1

ユニット1

Units, Dimensions, and Measurements

単位、次元、および測定

KEY TERMS AND CONCEPTS

主要用語と概念

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 for rough mental math. For example, the diameter of a hydrogen atom is on the order of 10^-10 m. The diameter of the Sun is on the order of 10^9 m, so about 10^19 hydrogen atoms would stretch across the Sun’s diameter.

That estimate is much easier to work out in your head than the precise values. Using 1.06×10^-10 m for a hydrogen atom and 1.39×10^9 m for the Sun gives 1.31×10^19 atoms. The rough estimate is still nearly as informative as the exact calculation.

Estimating Scale with Powers of 10

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

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...

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 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

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

Dimensional analysis helps check whether physics equations make sense. It compares the dimensions on each side of an equation and shows whether the units are consistent. This method is useful for spotting algebra errors, typos, and for remembering physical laws. A valid equation must follow two rules. First, both sides of an equality must have the same dimension, so only quantities with matching dimensions can be added or subtracted. Second, common math functions such as exponential,...

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solving problems in physics

Physics Problem Solving: Strategy to Check

Physics problem solving uses general physical principles to work out specific situations. It is a key skill in physics, and it can also help with everyday life. The same analytical skills can be used in new situations, while a list of facts can never cover every possible case. Solving physics problems also takes creativity and insight. These skills grow with experience and practice. There is no simple step-by-step method that works for every problem, but a three-stage process can guide the...

key terms and concepts

Learn how orders of magnitude use powers of 10 to estimate size, compare huge and tiny numbers, and make rough mental math easier.

Estimating Scale with Powers of 10 | JoVE K12

physics

JoVE Core 物理学は、運動学、力学、流体力学、静力学、波動、音響などの基礎的な物理学の理論と応用を、簡潔でわかりやすいアニメーション ビデオで紹介します。さらに、科学者の実際のビデオでは、世界中の今日の研究所で行われている古典的および独自の研究実験における関連概念の適用を示しています。

Estimating Scale with Powers of 10

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