Understanding Measurement and Units in Science | 理解科学中的测量与单位

📚 Understanding Measurement and Units in Science | 理解科学中的测量与单位

Measurement is a fundamental skill in all areas of science. Scientists use standardised units to describe quantities such as length, mass, time, and temperature, allowing results to be shared and compared worldwide.

测量是科学中一切领域的基本技能。科学家使用标准化的单位来描述长度、质量、时间和温度等量，从而使得结果能够在全球范围内共享和比较。

1. The International System of Units (SI) | 国际单位制

The International System of Units, abbreviated as SI, is the modern form of the metric system. SI base units are defined with fixed values and are used as the foundation for all other scientific measurements.

国际单位制，缩写为 SI，是公制在现代的形式。SI 基本单位以固定值定义，并被用作所有其他科学测量的基础。

There are seven SI base units. For IGCSE science, the most important ones are the kilogram (kg) for mass, the metre (m) for length, the second (s) for time, and the kelvin (K) for temperature.

有七个 SI 基本单位。在 IGCSE 科学中，最重要的是质量的千克（kg）、长度的米（m）、时间的秒（s）和温度的开尔文（K）。

The ampere (A) for electric current, the mole (mol) for amount of substance, and the candela (cd) for luminous intensity are also SI base units, though they are used more in advanced topics.

电流的安培（A）、物质的量的摩尔（mol）和发光强度的坎德拉（cd）也是 SI 基本单位，不过它们更多出现在高级专题中。

2. Derived Units | 导出单位

Derived units are formed by combining base units. For example, speed is measured in metres per second (m/s), which is a combination of metre and second.

导出单位由基本单位组合而成。例如，速度用米每秒（m/s）来测量，这是米和秒的组合。

Other common derived units include: area (m²), volume (m³), density (kg/m³), force (N = kg·m/s²), pressure (Pa = N/m²), and energy (J = N·m).

其他常见的导出单位包括：面积（m²）、体积（m³）、密度（kg/m³）、力（N = kg·m/s²）、压强（Pa = N/m²）和能量（J = N·m）。

density = mass ÷ volume → ρ = m ÷ V

密度 = 质量 ÷ 体积 → ρ = m ÷ V

When writing derived units, check that the algebraic combination matches the physical relationship between quantities.

在书写导出单位时，要检查单位的代数组合是否与物理量之间的关系相匹配。

3. Metric Prefixes and Converting Units | 词头与单位换算

IGCSE science often involves very large and very small quantities. Metric prefixes allow us to write these quantities in a compact form.

IGCSE 科学中经常遇到很大和很小的量。公制词头让我们能够用紧凑的形式书写这些量。

kilo (k) = 10³ → 1 km = 1000 m

千（k）= 10³ → 1 km = 1000 m
centi (c) = 10⁻² → 1 cm = 0.01 m

厘（c）= 10⁻² → 1 cm = 0.01 m
milli (m) = 10⁻³ → 1 g = 0.001 kg (strictly mass; for mass 1 g = 0.001 kg)

毫（m）= 10⁻³ → 1 g = 0.001 kg（严格来说质量；质量上 1 g = 0.001 kg）
micro (µ) = 10⁻⁶ → 1 µm = 0.000001 m

微（µ）= 10⁻⁶ → 1 µm = 0.000001 m
nano (n) = 10⁻⁹ → 1 nm = 0.000000001 m

纳（n）= 10⁻⁹ → 1 nm = 0.000000001 m

To convert from a larger unit to a smaller unit, multiply by the prefix factor. To convert from a smaller unit to a larger unit, divide by the factor.

从较大单位换算到较小单位时，乘以对应的词头倍数；从较小单位换算到较大单位时，除以对应的倍数。

Example: 2.5 cm = 2.5 × 10⁻² m = 0.025 m

示例：2.5 cm = 2.5 × 10⁻² m = 0.025 m

4. Measuring Length, Mass and Time | 测量长度、质量与时间

In the laboratory, you need to select the appropriate instrument for each measurement based on the required precision and range.

在实验室中，你需要根据所需的精确度和量程选择适当的测量仪器。

Length is often measured with a ruler, tape measure, or vernier calliper. A standard ruler typically has a precision of 1 millimetre.

长度通常用直尺、卷尺或游标卡尺测量。普通直尺的精确度通常为 1 毫米。

Mass is measured with a digital balance or a beam balance. Digital balances give readings in grams or kilograms.

质量用电子天平或托盘天平测量。电子天平以克或千克为单位给出读数。

Time is measured with a stopwatch, which can measure intervals to the nearest 0.1 s or 0.01 s, depending on the model.

时间用秒表测量，根据型号不同，秒表可以精确到 0.1 秒或 0.01 秒。

5. Accuracy, Precision and Uncertainty | 准确性、精确性与不确定性

Accuracy indicates how close a measurement is to the true value. Precision indicates how close repeated measurements are to each other.

准确性表示测量值接近真实值的程度。精确性表示重复测量结果彼此接近的程度。

A measurement can be precise but not accurate if it has a systematic error, such as a wrongly calibrated balance.

如果存在系统误差，例如天平校准错误，测量结果可能精确但并不准确。

Uncertainty is the range of values within which the true value is expected to lie. It is often quoted as ± value, for example, 25.0 mL ± 0.5 mL.

不确定度是真实值预期所在的量值范围。通常用 ± 值表示，例如 25.0 mL ± 0.5 mL。

To reduce random errors, repeat each measurement and calculate the mean.

为了减少随机误差，应重复每次测量并计算平均值。

6. Reading Scales and Significant Figures | 读刻度与有效数字

When reading a scale, you should estimate one digit beyond the smallest marked division. For example, if a ruler has millimetre divisions, you can record length to the nearest 0.5 mm or 0.1 mm by estimating.

读取刻度时，应在最小分度之后再估计一位数字。例如，如果直尺有毫米刻度，你可以通过估计记录到最接近的 0.5 毫米或 0.1 毫米。

The number of significant figures in a measurement depends on the instrument used. A digital balance that reads to two decimal places gives more significant figures than a balance reading to one decimal place.

测量中的有效数字位数取决于所用仪器。读到两位小数的电子天平比读到一位小数的天平给出的有效数字更多。

Rules for significant figures: all non-zero digits are significant; zeros between non-zero digits are significant; leading zeros are not significant; trailing zeros after a decimal point are significant.

有效数字规则：所有非零数字都是有效的；非零数字之间的零是有效的；前导零不是有效的；小数点后的末尾零是有效的。

7. Scientific Notation | 科学计数法

Scientific notation expresses a number as a value between 1 and 10 multiplied by a power of 10. This is especially useful for extremely large or small quantities.

科学计数法将一个数表示为 1 到 10 之间的数值乘以 10 的幂。这对于极大或极小的量尤其有用。

N × 10ⁿ where 1 ≤ N < 10

N × 10ⁿ 其中 1 ≤ N < 10

Examples: 0.00057 = 5.7 × 10⁻⁴; 8 300 000 = 8.3 × 10⁶.

示例：0.00057 = 5.7 × 10⁻⁴；8 300 000 = 8.3 × 10⁶。

When entering numbers in standard form on a calculator, look for the EXP or ×10ˣ key.

在计算器上输入标准形式时，使用 EXP 或 ×10ˣ 键。

8. Handling Units in Equations | 方程中的单位处理

Always include units when substituting values into an equation. If the equation is valid only for SI units, convert every quantity to SI units first.

在代入方程时始终包含单位。如果方程仅对 SI 单位有效，则应先将所有量转换为 SI 单位。

For example, in the formula for kinetic energy E = ½ mv², mass must be in kg and speed in m/s to obtain energy in joules.

例如，在动能公式 E = ½ mv² 中，质量必须以千克为单位，速度以米每秒为单位，才能得到以焦耳为单位的能量。

Using units as a check: the joule (J) is equivalent to kg·m²/s², so the product of kg and (m/s)² gives the correct unit.

用单位进行检验：焦耳（J）等效于 kg·m²/s²，因此 kg 与 (m/s)² 的乘积得到正确的单位。

When rearranging equations, remember that the unit must be transformed algebraically along with the number.

在重排方程时，记住单位必须与数值一起进行代数变换。

9. Common Errors and How to Avoid Them | 常见错误及避免方法

One common error is mixing millimetres and centimetres without converting. Write the same unit throughout a calculation.

一个常见错误是在没有换算的情况下混合使用毫米和厘米。在整个计算过程中应保持相同的单位。

Another error is using the wrong prefix when converting between grams and kilograms. Remember that 1 kg = 1000 g, so 250 g = 0.25 kg.

另一个错误是在克与千克之间换算时使用错误的倍数。记住 1 kg = 1000 g，所以 250 g = 0.25 kg。

When reading a meniscus in a measuring cylinder, keep your eye level with the bottom of the curve to avoid parallax error.

在读取量筒中的凹液面时，视线应与液体弯月面底部平齐，以避免视差误差。

For repeated readings, ignore any values that are obviously anomalous only if you have identified a valid reason; otherwise, include them and discuss the uncertainty.

对于重复读数，只有在你确定了正当理由的情况下才忽略明显异常的值；否则应将其包括在内并讨论不确定度。

10. Practice Questions | 练习题

1. Convert 3.5 mg into grams and kilograms.

1. 将 3.5 mg 换算成克和千克。

Answer: 3.5 mg = 0.0035 g = 0.0000035 kg

答案：3.5 mg = 0.0035 g = 0.0000035 kg

2. A student measures a liquid volume as 25.0 cm³ using a 50 cm³ measuring cylinder with 0.5 cm³ divisions. State the uncertainty.

2. 一名学生使用量程为 50 cm³、分度为 0.5 cm³ 的量筒测量液体体积为 25.0 cm³。给出不确定度。

Answer: ±0.25 cm³ (half the smallest division)

答案：±0.25 cm³（最小分度的一半）

3. Write 0.000 006 72 s in scientific notation.

3. 用科学计数法表示 0.000 006 72 s。

Answer: 6.72 × 10⁻⁶ s

答案：6.72 × 10⁻⁶ s

11. Summary | 总结

Using the correct units, prefixes, and measurement techniques is essential for reliable scientific results. Always record data with the appropriate uncertainty and significant figures.

正确使用单位、词头和测量技术对于获得可靠的实验结果至关重要。始终以适当的不确定度和有效数字记录数据。

Before solving problems, check that all quantities are in consistent units. After calculating, check that your answer has the correct unit and a reasonable magnitude.

在解题之前，检查所有量是否使用一致的单位。计算后，检查答案是否具有正确的单位和合理的数量级。

Mastering these core skills will help you in all IGCSE science practical exams and written papers.

掌握这些核心技能将帮助你在所有 IGCSE 科学实验考试和笔试中取得成功。

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Understanding Measurement and Units in Science | 理解科学中的测量与单位