Finding the Value of an Uncertainty | 求不确定度的值

📚 Finding the Value of an Uncertainty | 求不确定度的值

Every measured quantity in physics carries a limit to its precision. In CIE A-Level Physics, ‘finding the value of an uncertainty’ means identifying that limit and expressing it as an absolute, fractional or percentage uncertainty, then carrying it through calculations. This article explains the methods you need for Paper 3, Paper 5 and practical questions, with rules, examples and common pitfalls.

在物理学中，每个被测量都带有精度的限制。在 CIE A-Level 物理中，’求不确定度的值’意味着识别这一限制，并将其表示为绝对、相对或百分不确定度，然后在计算中传递。本文解释 Paper 3、Paper 5 和实验题中所需的方法，包括规则、示例和常见错误。

1. Why Uncertainty Matters | 为什么不确定度很重要

A measured value such as 4.5 V is incomplete unless we state how confident we are in that value. The uncertainty gives the interval in which the true value is likely to lie. For example, (4.5 ± 0.1) V means the true voltage is expected between 4.4 V and 4.6 V.

像 4.5 V 这样的测量值是不完整的，除非我们说明对该值的置信程度。不确定度给出了真值很可能所在的区间。例如，(4.5 ± 0.1) V 表示真实电压预计在 4.4 V 到 4.6 V 之间。

CIE questions usually ask you to find an uncertainty from an instrument, from repeated readings, or from a derived quantity such as resistance, acceleration or density. The same rules apply in all AS and A-Level topics.

CIE 试题通常要求你从仪器、重复读数或导出量（如电阻、加速度或密度）中求不确定度。相同的规则适用于所有 AS 和 A-Level 主题。

2. Types of Uncertainty and Key Terms | 不确定度的类型与关键术语

There are three linked ways to express uncertainty. The absolute uncertainty Δx has the same unit as the quantity. The fractional uncertainty is Δx divided by the measured value x. The percentage uncertainty is the fractional uncertainty multiplied by 100.

有三种相互关联的不确定度表示方法。绝对不确定度 Δx 具有与测量量相同的单位。相对不确定度是 Δx 除以测量值 x。百分不确定度是相对不确定度乘以 100。

absolute uncertainty = Δx

fractional uncertainty = Δx / x

percentage uncertainty = (Δx / x) × 100%

For a single reading, Δx is usually the instrument reading uncertainty. For a calculated value, Δx is found by combining the uncertainties of the input quantities.

对于单次读数，Δx 通常是仪器读数不确定度。对于计算值，Δx 通过合成输入量的不确定度得到。

3. Reading Uncertainty: Analogue vs Digital Instruments | 读数不确定度：模拟与数字仪器

For an analogue scale, such as a ruler, thermometer or analogue ammeter, the reading uncertainty is usually half of the smallest scale division. For example, a thermometer with 1 °C divisions has a reading uncertainty of ±0.5 °C.

对于模拟刻度，例如直尺、温度计或模拟电流表，读数不确定度通常是最小分度值的一半。例如，分度值为 1 °C 的温度计读数不确定度为 ±0.5 °C。

For a digital instrument, such as a digital voltmeter, the reading uncertainty is normally ±1 in the last displayed digit. If the meter shows 4.50 V, the reading uncertainty is ±0.01 V.

对于数字仪器，例如数字电压表，读数不确定度通常是最后一位显示数字的 ±1。如果仪表显示 4.50 V，读数不确定度为 ±0.01 V。

When a measurement requires two readings, such as finding a length by subtracting two ruler positions, add the reading uncertainty of each end if the two ends are judged separately.

当测量需要

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