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

測定の確実性は、測定の桁数と使用する機器の精度という2つの要素に依存します。
測定された量では、最後の不確定な数字を含むすべての数字は有効数字と呼ばれ、特定のルールを使用して決定できます。
ゼロ以外の数字とすべてのキャプティブ ゼロ (ゼロ以外の 2 桁の間にある) は重要です。たとえば、28 には 2 つの有効数字があり、26.25 には 4 つ、208 には 3 つの有効数字があります。
先行ゼロは小数点を特定するだけなので、決して重要ではありません。たとえば、0.00208 には 3 つの有効数字があります。このような量は、指数表記を使用して表すことができます。したがって、0.00208は10−3×2.08と書くことができます。
末尾のゼロは、10 進数形式の数値でのみ有効です。2200 には 2 つの末尾のゼロと 2 つの有効数字がありますが、2200.0 と 2200.1 にはどちらも 5 つの有効数字があります。
小数点のない数量の場合、末尾のゼロの意味はあいまいになります。したがって、2200 は、有効数字が 2 つの場合は 2.2 × 103、有効数字は 3 つの場合は 2.20 x 103 と記述できます。

有効数字の規則

いかなる測定においても、測定ツールの精度は重要な要素です。 たとえば、通常の定規は、最も近いミリメートルまで長さを測定できます。 一方、ノギスは 0.01 mm 単位で長さを測定できます。 その結果、ノギスは非常に微細な長さの変化を測定できるため、より正確な測定ツールとなります。 測定ツールの精度が高ければ、測定値もより正確になります。

測定値を表す場合、最後の桁は測定者によって何らかの方法で計算されていることを強調しておく必要があります。 たとえば、棒の長さを定規で測っている人は、それが 13.2 cm から 13.3 cm の間にあることに気づき、最後の桁の値を推定する必要があります。 有効数字の規則は、測定値に記録される最後の桁が、ある程度の不確実性を伴う最初の桁であるということです。 左側の最初の測定値から始めて、右側に書かれた最後の桁までの桁数を数えて、値の有効桁数を決定します。 有効数字は、値の測定に使用される測定ツールの精度を表します。

本文は <a href="https://openstax.org/books/university-physics-volume-1/pages/1-6-significant-figures">< から引用しています。 Openstax、University Physics Volume 1, Section: 1.6 Significant Figures. </a>

どのような測定においても、測定ツールの精度は重要な要素です。たとえば、通常の定規は、最も近い長さを測定できます...

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

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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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 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。

Measurement Precision and Significant Figures

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