📚 A-Level Physics: SI Prefixes and Unit Conversion | A-Level 物理：国际单位制词头与单位换算
In A-Level Physics, measurements range from the size of an atom to the distance between stars. To handle such extreme scales, scientists use SI prefixes — short symbols attached to base units that represent powers of ten. Mastering these prefixes and the art of converting between units is essential for every physics student.
在 A-Level 物理中，测量范围从原子大小到恒星之间的距离。为了处理如此极端的尺度，科学家使用国际单位制词头——附着在基本单位上的简短符号，表示十的幂。掌握这些词头以及单位之间的换算技巧，对每一位物理学生来说都至关重要。
1. Why Do We Need SI Prefixes? | 为什么需要国际单位制词头？
ide a clean shorthand: 1 nanometre (nm) is 1 × 10⁻⁹ m, and 1 petametre (Pm) is 1 × 10¹⁵ m.
如果我们总是用标准基本单位书写物理量，像 0.000000001 米或 6,000,000,000,000,000 米这样的数字会频繁出现。这些数字难以阅读、书写和比较。国际单位制词头提供了一种简洁的简写：1 纳米（nm）等于 1 × 10⁻⁹ 米，而 1 拍米（Pm）等于 1 × 10¹⁵ 米。
SI prefixes are not just a convenience; they are essential for avoiding errors and for communicating results clearly in scientific work.
国际单位制词头不仅是方便，更是避免错误、在科学工作中清晰交流结果所必需的。
2. SI Base Units You Must Know | 你必须知道的 SI 基本单位
Before applying prefixes, recall the core set of SI base units. In CIE A-Level Physics, you are expected to know at least the following:
在应用词头之前，先回顾一组核心的 SI 基本单位。在 CIE A-Level 物理中，你至少需要知道以下这些：
metre (m) — the unit of length.
米（m）——长度的单位。
kilogram (kg) — the unit of mass. Note that the prefix 'kilo' is built into the base unit of mass; we do not say 'megagram' for 10³ kg, we use 'tonne' informally.
千克（kg）——质量的单位。注意前缀“千”已经内置于质量基本单位中；我们不把 10³ kg 称为“兆克”，非正式场合使用“吨”。
second (s) — the unit of time.
秒（s）——时间的单位。
ampere (A) — the unit of electric current.
安培（A）——电流的单位。
kelvin (K) — the unit of thermodynamic temperature.
开尔文（K）——热力学温度的单位。
mole (mol) — the unit of amount of substance.
摩尔（mol）——物质的量的单位。
candela (cd) — the unit of luminous intensity.
坎德拉（cd）——发光强度的单位。
3. The Complete List of SI Prefixes | 国际单位制词头完整列表
The prefixes range from 10⁻¹⁸ to 10¹⁸. You should memorise the common ones in bold, as they appear most often in exams.
词头范围从 10⁻¹⁸ 到 10¹⁸。你应该记住加粗的常见词头，它们在考试中最常出现。
| Prefix | 词头 | Symbol | 符号 | Factor | 倍数 | Example | 示例 |
|---|---|---|---|
| peta 拍 | P | 10¹⁵ | 1 Pm = 10¹⁵ m |
| tera 太 | T | 10¹² | 1 THz = 10¹² Hz |
| giga 吉 | G | 10⁹ | 1 GW = 10⁹ W |
| mega 兆 | M | 10⁶ | 1 MHz = 10⁶ Hz |
| kilo 千 | k | 10³ | 1 km = 10³ m |
| hecto 百 | h | 10² | 1 hPa = 100 Pa |
| deca 十 | da | 10¹ | 1 dam = 10 m |
| deci 分 | d | 10⁻¹ | 1 dm = 0.1 m |
| centi 厘 | c | 10⁻² | 1 cm = 10⁻² m |
| milli 毫 | m | 10⁻³ | 1 mA = 10⁻³ A |
| micro 微 | μ | 10⁻⁶ | 1 μm = 10⁻⁶ m |
| nano 纳 | n | 10⁻⁹ | 1 nm = 10⁻⁹ m |
| pico 皮 | p | 10⁻¹² | 1 pF = 10⁻¹² F |
| femto 飞 | f | 10⁻¹⁵ | 1 fm = 10⁻¹⁵ m |
| atto 阿 | a | 10⁻¹⁸ | 1 as = 10⁻¹⁸ s |
4. Scientific Notation and Prefixes | 科学计数法与词头
as 2.5 × 10⁻³ A. The exponent of ten tells you how many places to move the decimal point.
带词头的量总可以改写为科学计数法。例如，2.5 mA 可以写成 2.5 × 10⁻³ A。十的指数告诉你小数点需要移动多少位。
When converting from a larger unit to a smaller unit, the numerical value increases; when converting from a smaller unit to a larger unit, the numerical value decreases. This is because the size of the unit and the number of units are inversely proportional.
从较大单位换算到较小单位时，数值变大；从较小单位换算到较大单位时，数值变小。这是因为单位的大小与单位的数量成反比。
1 nm = 10⁻⁹ m and 1 m = 10⁹ nm
5. General Method for Unit Conversion | 单位换算的一般方法
The safest technique is to replace the prefix with its power-of-ten factor, then perform the arithmetic. For example, convert 350 μs to seconds.
最安全的方法是把词头替换为对应的十的幂因子，然后进行运算。例如，将 350 μs 换算为秒。
350 μs = 350 × 10⁻⁶ s = 3.50 × 10⁻⁴ s
For multiple units, apply the conversion to each unit separately. Consider converting 72 km/h to m/s.
对于复合单位，分别对每个单位进行换算。考虑将 72 km/h 换算为 m/s。
72 km/h = 72 × (1000 m) / (3600 s) = 20 m/s
This method avoids memorising separate 'conversion factors' for every pair of units.
这种方法避免了为每一对单位单独记忆“换算系数”。
6. Square and Cube Prefix Conversions | 平方与立方单位的词头换算
A common mistake is to convert area or volume units by using the linear prefix factor directly. Remember that area uses the square of the factor, and volume uses the cube of the factor.
一个常见错误是直接用线性词头因子换算面积或体积单位。记住，面积使用因子的平方，体积使用因子的立方。
Example: Convert 1 m² to cm².
示例：将 1 m² 换算为 cm²。
1 m² = (100 cm)² = 100² cm² = 10⁴ cm²
ly, 1 m³ = (100 cm)³ = 10⁶ cm³. Notice that the exponent multiplies with the power of ten.
类似地，1 m³ = (100 cm)³ = 10⁶ cm³。注意指数与十的幂相乘。
7. Converting Composite Units | 复合单位换算
Density is a typical composite unit. Convert 1000 kg/m³ to g/cm³.
密度是典型的复合单位。将 1000 kg/m³ 换算为 g/cm³。
1000 kg/m³ = 1000 × (10³ g) / (10² cm)³ = 1000 × 10³ / 10⁶ g/cm³ = 1 g/cm³
Always write out the unit conversion in full, including powers of ten, to avoid missing a factor of 1000.
务必完整写出单位换算，包括十的幂，以避免漏掉 1000 的因子。
Another example: energy in joules can be converted to eV using the charge of an electron, but that is a physical conversion, not just a prefix change. Be careful not to mix the two.
另一个例子：焦耳为单位的能量可以转换为 eV，这需要用到电子电荷，这是物理换算，而不仅仅是词头变化。注意不要混淆两者。
8. Common Mistakes and Traps | 常见错误与陷阱
Here are the most frequent errors students make when dealing with SI prefixes:
以下是学生在处理国际单位制词头时最常犯的错误：
Forgetting that 1 cm³ = 10⁻⁶ m³, not 10⁻² m³.
忘记 1 cm³ = 10⁻⁶ m³，而不是 10⁻² m³。
Using the same symbol 'm' for metre and milli. Context matters: 'ms' is millisecond, 'm' alone is metre.
混淆米和毫的符号 'm'。需要根据语境区分：'ms' 是毫秒，单独的 'm' 是米。
Mixing up micro (μ) and nano (n); a factor of 1000 difference.
混淆微（μ）和纳（n）；它们相差 1000 倍。
Adding or subtracting prefixes directly instead of converting to base units first when adding quantities.
相加不同词头的量时，直接加减词头而没有先换算为基本单位。
Confusing 'kilo' in kg: the kilogram is the base unit, so prefixes such as 'milli' are attached to 'gram' (mg), not to 'kilogram' (mkg is wrong).
混淆千克中的“千”：千克是基本单位，所以像“毫”这样的词头应加在“克”上（mg），而不是加在“千克”上（mkg 是错的）。
9. Exam Tips and Worked Examples | 考试技巧与例题
In CIE A-Level Physics, unit conversion questions often appear in practical-based contexts, such as ruler readings or data analysis. Here is a typical question:
在 CIE A-Level 物理中，单位换算题常出现在基于实验的语境中，例如刻度尺读数或数据分析。下面是一道典型题目：
Question: The diameter of a hair is measured as 0.045 mm. Express this in μm and in m.
题目：一根头发的直径测量为 0.045 mm。请用 μm 和 m 表示。
0.045 mm = 0.045 × 10⁻³ m = 4.5 × 10⁻⁵ m
0.045 mm = 0.045 × 10⁻³ m = 45 × 10⁻⁶ m = 45 μm
When writing an answer, always include the prefix symbol with the unit. An answer of '45' without a unit is meaningless in physics.
书写答案时，一定要在单位中带上词头符号。没有单位的“45”在物理中没有意义。
a human hair should be around 50 μm, so 45 μm makes sense; 45 μm = 0.045 mm is consistent.
另一个技巧：总是检查最终答案的量级是否合理。例如，人的头发大约 50 μm，所以 45 μm 合理；45 μm = 0.045 mm 是一致的。
10. Practice Problems | 练习题
Try these yourself before checking the answers.
先自己尝试以下练习，再核对答案。
Convert 250 mA to A.
将 250 mA 换算为 A。
Convert 0.02 km to μm.
将 0.02 km 换算为 μm。
Convert 5 cm² to m².
将 5 cm² 换算为 m²。
Convert 3.6 km/h to m/s.
将 3.6 km/h 换算为 m/s。
A wavelength is 5.5 × 10⁻⁷ m. Express this in nm.
某波长为 5.5 × 10⁻⁷ m。请用 nm 表示。
Answers: 0.250 A; 2 × 10⁷ μm; 5 × 10⁻⁴ m²; 1.0 m/s; 550 nm
11. Summary | 小结
SI prefixes are a compact way to express very large and very small quantities. The key steps for unit conversion are: identify the prefix, replace it with the correct power of ten, and apply the power to every unit dimension (including squares and cubes).
国际单位制词头是表示很大和很小量的紧凑方式。单位换算的关键步骤是：识别词头，将其替换为正确的十的幂，并将该幂应用到每个单位维度（包括平方和立方）。
Remember to always carry units through your calculations and check that your final value is plausible. With practice, prefix conversions become second nature.
记住在计算中始终带上单位，并检查最终数值是否合理。通过练习，词头换算会变得自然而熟练。
Published by TutorHao | Physics Revision Series | aleveler.com
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