📚 Measurement and Experimental Error in Science | 科学中的测量与实验误差
Science is built on observation and measurement. In the Edexcel IGCSE Science course, you must understand how to measure physical quantities correctly, how to handle errors, and how to present data with appropriate precision. This article explains the core ideas of measurement and experimental error in a bilingual, revision-friendly way.
科学建立在观察和测量之上。在 Edexcel IGCSE 科学课程中，你必须理解如何正确测量物理量、如何处理误差，以及如何以适当的精度呈现数据。本文以双语、便于复习的方式解释测量与实验误差的核心概念。
1. The International System of Units | 国际单位制
Scientists around the world use the International System of Units (SI). The base units you need to know include the metre (m) for length, the kilogram (kg) for mass, the second (s) for time, the ampere (A) for electric current, the kelvin (K) for temperature, and the mole (mol) for amount of substance.
全世界的科学家都使用国际单位制（SI）。你需要知道的基本单位包括：米（m）表示长度，千克（kg）表示质量，秒（s）表示时间，安培（A）表示电流，开尔文（K）表示温度，摩尔（mol）表示物质的量。
When quantities are very large or very small, prefixes are used. For example, 1 mm = 10⁻³ m, 1 μm = 10⁻⁶ m, 1 nm = 10⁻⁹ m, and 1 km = 10³ m. You must be able to convert between these prefixes in calculations.
当物理量非常大或非常小时，会使用词头。例如，1 mm = 10⁻³ m，1 μm = 10⁻⁶ m，1 nm = 10⁻⁹ m，1 km = 10³ m。你必须能够在计算中进行这些单位换算。
2. Choosing the Right Measuring Instrument | 选择合适的测量仪器
Every measurement requires a suitable instrument. For length, a ruler or tape measure gives readings to the nearest millimetre, while a micrometer screw gauge can measure to the nearest 0.01 mm. For volume, a measuring cylinder is less precise than a burette or a pipette. For time, a stopwatch is common, but a light gate connected to a data logger is more accurate.
每次测量都需要合适的仪器。对于长度，直尺或卷尺可以精确到毫米，而千分尺（螺旋测微器）可以精确到 0.01 mm。对于体积，量筒的精度低于滴定管或移液管。对于时间，秒表很常用，但连接数据记录器的光门更加准确。
The rule is: choose the instrument with the smallest scale division that is practical for the measurement. A 30 cm ruler is not suitable for measuring the thickness of a single coin, because the scale division is too large relative to the quantity being measured.
规则是：选择在测量中实际可行的、最小分度值最小的仪器。30 cm 的直尺不适合测量一枚硬币的厚度，因为与待测物相比，它的分度值太大了。
3. Accuracy and Precision | 准确度与精密度
Accuracy describes how close a measured value is to the true value. Precision describes how close repeated measurements are to each other. A measurement can be precise but not accurate if there is a systematic error. For example, a balance that is not zeroed correctly may give very consistent readings that are all 0.2 g too high.
准确度描述测量值与真实值之间的接近程度。精密度描述重复测量值之间的接近程度。如果存在系统误差，测量结果可能精密度很高但准确度不高。例如，未正确调零的天平可能给出非常一致但都偏高 0.2 g 的读数。
You should always make repeated readings and calculate a mean to reduce the effect of random errors. The mean value is usually the best estimate of the true value.
你应该总是进行重复测量并计算平均值，以减小随机误差的影响。平均值通常是对真实值的最佳估计。
4. Random and Systematic Errors | 随机误差与系统误差
Random errors cause readings to be scattered around the true value. They are caused by unpredictable changes in the environment, by human reaction time, or by parallax when reading a scale. Random errors can be reduced by repeating measurements and taking an average.
随机误差使读数围绕真实值散布。它们由环境中的不可预测变化、人的反应时间或读取刻度时的视差引起。随机误差可以通过重复测量并取平均值来减小。
Systematic errors cause readings to be consistently too high or too low. They are caused by faulty equipment, zero errors, or an incorrect experimental method. Systematic errors cannot be reduced by averaging; you must change the equipment or method.
系统误差使读数一致地偏高或偏低。它们由故障设备、零误差或错误的实验方法引起。系统误差不能通过求平均来减小；你必须更换设备或改进方法。
Systematic error = accuracy problem; Random error = precision problem
系统误差 = 准确度问题；随机误差 = 精密度问题
5. Calculating Uncertainty | 计算不确定度
Every measurement has an uncertainty. For a single reading with a ruler marked in millimetres, the uncertainty is usually ±0.5 mm, because you can estimate to half a scale division. For a repeated measurement, you can estimate the uncertainty as half the range of the readings.
每次测量都有不确定度。对于毫米刻度直尺的单次读数，不确定度通常为 ±0.5 mm，因为你可以估读到半个分度。对于重复测量，你可以将读数极差的一半估计为不确定度。
For example, if three readings of a length are 12.1 cm, 12.2 cm and 12.3 cm, the range is 0.2 cm, so the uncertainty is ±0.1 cm. The mean is 12.2 cm, so the final result can be written as 12.2 ± 0.1 cm.
例如，如果三次长度读数分别为 12.1 cm、12.2 cm 和 12.3 cm，极差为 0.2 cm，因此不确定度为 ±0.1 cm。平均值为 12.2 cm，所以最终结果可写成 12.2 ± 0.1 cm。
When you combine measurements, uncertainties add. If you measure two lengths as 5.0 ± 0.1 cm and 3.0 ± 0.1 cm and add them, the total is 8.0 ± 0.2 cm.
当你组合测量时，不确定度会叠加。如果你测量两个长度分别为 5.0 ± 0.1 cm 和 3.0 ± 0.1 cm，相加后总和为 8.0 ± 0.2 cm。
6. Significant Figures and Rounding | 有效数字与舍入
The number of significant figures in a measurement reflects its precision. A measurement of 12.30 g has four significant figures, while 12.3 g has three. When calculating, you should give your final answer to the same number of significant figures as the least precise value used in the calculation.
测量中的有效数字位数反映其精密度。12.30 g 有四位有效数字，而 12.3 g 有三位。在计算时，你的最终答案应保留与计算中使用的最不精确数值相同位数的有效数字。
For example, if you divide 10.0 cm by 3.0 s, the calculator shows 3.333… cm/s. Since both values have three significant figures, the answer should be written as 3.33 cm/s.
例如，如果你用 10.0 cm 除以 3.0 s，计算器显示 3.333… cm/s。因为两个数值都有三位有效数字，答案应写成 3.33 cm/s。
Be careful with zeros. Leading zeros are not significant: 0.025 has two significant figures. Trailing zeros after a decimal point are significant: 2.50 has three significant figures.
注意零的处理。前导零不是有效数字：0.025 有两位有效数字。小数点后的末尾零是有效数字：2.50 有三位有效数字。
7. Recording and Presenting Data | 记录和呈现数据
In IGCSE Science, you must record raw data in a clear table. Each column should have a heading, the quantity, the unit in brackets, and all readings should be given with the same precision. Do not write units in every cell of the table.
在 IGCSE 科学中，你必须将原始数据记录在清晰的表格中。每一列应有表头、物理量、带括号的单位，并且所有读数应具有相同的精度。不要在表格的每个单元格中重复写单位。
When presenting data, you should include repeated readings and the calculated mean. This shows that you have considered random errors and gives the examiner a chance to see your working.
呈现数据时，你应该包含重复读数和计算出的平均值。这表明你考虑了随机误差，也让考官有机会看到你的计算过程。
| Length / cm | Reading 1 | Reading 2 | Reading 3 | Mean / cm |
| Block A | 5.12 | 5.14 | 5.13 | 5.13 |
The table above shows a good format: consistent decimal places, units in the heading, and a mean calculated from three readings.
上面的表格展示了一种良好的格式：一致的小数位数、单位放在表头、平均值由三次读数计算得出。
8. Drawing Graphs and Interpreting Slopes | 绘制图表并解读斜率
A graph is a powerful tool for analysing data. The independent variable goes on the x-axis and the dependent variable goes on the y-axis. You should label both axes with the quantity and the unit, and choose a scale that uses at least half of the graph paper. The points should be plotted carefully with small crosses or dots.
图表是分析数据的强大工具。自变量放在 x 轴，因变量放在 y 轴。你应该标记两个轴上的物理量和单位，并选择至少使用图纸一半的标度。数据点应用小叉号或小圆点仔细标出。
If the relationship is linear, draw a best-fit straight line. The line should pass through as many points as possible, with roughly equal numbers of points above and below the line. Points that are far from the line are called anomalies and should be identified and ignored when drawing the line.
如果关系是线性的，画一条最佳拟合直线。直线应尽可能多地穿过数据点，且上方和下方点的数量大致相等。远离直线的点称为异常值，在画线时应识别并忽略它们。
The slope (gradient) of a straight line is calculated as the change in y divided by the change in x. Use two points on the line that are far apart, not data points, to calculate the gradient.
直线的斜率（梯度）等于 y 的变化量除以 x 的变化量。使用直线上相距较远的两个点（而不是数据点）来计算斜率。
Gradient = Δy / Δx = (y₂ − y₁) / (x₂ − x₁)
斜率 = Δy / Δx = (y₂ − y₁) / (x₂ − x₁)
9. Evaluating Experiments | 评估实验
An evaluation asks you to judge how reliable and valid the experiment is. Reliability refers to whether the results are trusted and reproducible. Valid conclusions must be supported by a method that tests the hypothesis without other variables interfering.
评估要求你判断实验的可靠性和有效性。可靠性指结果是否可信且可重复。有效的结论必须由能够检验假设且不受其他变量干扰的方法来支持。
You should consider the following questions in an evaluation:
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Did I repeat the experiment enough times? | 我是否进行了足够次数的重复实验？
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Were there any anomalous results? | 是否存在异常结果？
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Were all other variables kept constant? | 是否控制所有其他变量保持恒定？
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Is the measuring equipment appropriate and accurate? | 测量设备是否合适且准确？
Write a paragraph that states a limitation of the experiment and explains how it could be reduced. For example, “The stopwatch was started manually, causing random errors. This could be improved by using light gates connected to a computer.”
写一段话，说明实验的局限性并解释如何减小它。例如：“秒表由手动启动，会引起随机误差。可以通过使用连接到计算机的光门来改进。”
10. Improving Experimental Design | 改进实验设计
To improve an experiment, you can reduce errors, increase precision, or change the method to obtain more data. Using a sensor and data logger removes human reaction time and parallax errors. Increasing the number of repeated readings reduces the effect of random errors on the mean. Changing the range of the independent variable gives a wider set of data and a more reliable graph.
要改进实验，你可以减小误差、提高精密度，或改变方法以获得更多数据。使用传感器和数据记录器可以消除人的反应时间和视差误差。增加重复读数的次数可以减小随机误差对平均值的影响。改变自变量的范围可以提供更广泛的数据集和更可靠的图表。
Another improvement is to control the environment more strictly. For example, in a cooling experiment, you could use a lid to prevent heat loss by convection, or place the setup in a draught-free room. This reduces systematic errors caused by uncontrolled external factors.
另一个改进是更严格地控制环境。例如，在冷却实验中，你可以使用盖子防止对流散热，或将装置放在无风处。这可以减小由不受控制的外部因素引起的系统误差。
Always state a specific improvement and link it to the error it reduces. Do not write vague phrases like “take more readings” without explaining why.
始终说明具体的改进措施，并把它与它减小的误差联系起来。不要写“多读几次”这样的模糊短语而不解释原因。
11. Conclusion | 结论
Measuring is not just about reading numbers; it is about understanding limitations and uncertainties. In IGCSE Science practical papers, you are assessed on your ability to record data accurately, identify errors, and suggest improvements. Mastering these skills will help you in physics, chemistry and biology experiments.
测量不仅仅是读取数字，而是理解局限性和不确定度。在 IGCSE 科学实验卷中，你的评估内容包括准确记录数据、识别误差和提出改进建议的能力。掌握这些技能将帮助你在物理、化学和生物实验中取得好成绩。
Remember the key words: accuracy, precision, random error, systematic error, uncertainty, significant figures, and best-fit line. Use them confidently in your answers.
记住关键词：准确度、精密度、随机误差、系统误差、不确定度、有效数字和最佳拟合线。在答题中自信地使用它们。
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