📚 Prefixes in A-Level Physics | A-Level 物理中的单位前缀
In A-Level Physics, very large and very small quantities appear constantly - from the wavelength of visible light to the power output of a national grid. SI prefixes allow us to write these values compactly, compare them quickly, and convert safely between units without losing a factor of a thousand.
在 A-Level 物理中，极大和极小的量随处可见——从可见光的波长到国家电网的输出功率。国际单位制前缀让我们能够紧凑地书写这些数值、快速进行比较，并在不丢失一千倍因子的前提下安全地在单位之间换算。
This article covers every prefix on the CIE A-Level Physics syllabus, the conversions you must be able to do without a calculator error, the compound-unit traps in area and volume, and the mistakes that cost marks most often in Paper 1, Paper 2 and practical work.
本文覆盖 CIE A-Level 物理大纲中的全部前缀、你必须做到零计算器错误的换算、面积与体积中的复合单位陷阱，以及在 Paper 1、Paper 2 和实验题中最常丢分的错误。
1. What Are SI Prefixes? | 什么是国际单位制前缀
m = 10³ m and 1 kW = 10³ W. The prefix is never a separate quantity - it is part of the unit itself.
国际单位制前缀是放在单位前面的字母或符号，用来将该单位乘以固定的十的幂。例如，前缀 kilo (k) 表示 10³，因此 1 km = 10³ m，1 kW = 10³ W。前缀本身不是独立的物理量，它是单位的一部分。
tten in different units. The same is true of 4.7 kΩ and 4700 Ω, or 500 nm and 5.0 × 10⁻⁷ m.
前缀不会改变被测量的物理量，它们只是重新标度单位。这意味着 25 mm 与 0.025 m 是完全相同的长度，只是用不同单位书写。4.7 kΩ 与 4700 Ω、500 nm 与 5.0 × 10⁻⁷ m 也是如此。
The seven SI base units (m, kg, s, A, K, mol, cd) are all prefixable, and so is every derived unit such as N, J, W, Pa, V, Ω, F, T and Hz. Learning the prefix system therefore multiplies your fluency across the whole specification.
七个国际单位制基本单位（m、kg、s、A、K、mol、cd）都可以加前缀，所有导出单位如 N、J、W、Pa、V、Ω、F、T、Hz 也一样。因此掌握前缀体系会让你的整体应试熟练度成倍提升。
2. Why Prefixes Matter in Physics | 为什么前缀在物理中很重要
o wave (10⁸ Hz). Prefixes reduce the chance of copying errors when you transfer numbers from a question to your working.
大多数 A-Level 物理问题都涉及极大或极小的量，例如电子的电荷（1.6 × 10⁻¹⁹ C）或无线电波的频率（10⁸ Hz）。前缀能减少你在把数据从题目抄到解题步骤时出错的机会。
avelength around 5 × 10⁻⁷ m, which is normally written as 500 nm. The Planck constant is usually quoted as 6.63 × 10⁻³⁴ J s rather than in any prefixed form, because no prefix is convenient there.
在考试中，你应当能用正确的前缀引用标准数值，并快速在不同前缀之间换算。例如，可见光的波长约为 5 × 10⁻⁷ m，通常写作 500 nm。普朗克常数通常写作 6.63 × 10⁻³⁴ J s，而不是任何带前缀的形式，因为那里没有方便的前缀。
Prefixes also keep significant figures honest. Writing 0.000 000 000 47 F is both ugly and error-prone; writing 470 pF is unambiguous, and the three significant figures are immediately visible.
前缀还能保证有效数字的诚实性。写出 0.000 000 000 47 F 既难看又容易出错；写成 470 pF 则毫不含糊，且三位有效数字一目了然。
3. The Core Prefix Table for CIE A-Level | CIE A-Level 核心前缀表
The table below lists the prefixes you must know for the CIE A-Level Physics syllabus. Learn the exact symbol, the power of ten, and one familiar example for each entry.
下表列出了 CIE A-Level 物理大纲中你必须掌握的前缀。请记住每个前缀的准确符号、十的幂以及一个熟悉的例子。
| Prefix | Symbol | Power of ten | Example |
|---|---|---|---|
| tera | T | 10¹² | 1 THz = 10¹² Hz |
| giga | G | 10⁹ | 1 GHz = 10⁹ Hz |
| mega | M | 10⁶ | 1 MW = 10⁶ W |
| kilo | k | 10³ | 1 km = 10³ m |
| deci | d | 10⁻¹ | 1 dm = 10⁻¹ m |
| centi | c | 10⁻² | 1 cm = 10⁻² m |
| milli | m | 10⁻³ | 1 mm = 10⁻³ m |
| micro | μ | 10⁻⁶ | 1 μm = 10⁻⁶ m |
| nano | n | 10⁻⁹ | 1 nm = 10⁻⁹ m |
| pico | p | 10⁻¹² | 1 pF = 10⁻¹² F |
Notice that each step of three powers of ten gets its own prefix, which is why the gaps between k, M, G and T are all a factor of 1000. The small side follows the same pattern: m, μ, n and p are separated by 10³ each.
注意每三个十的幂为一档，各有自己的前缀，这就是为什么 k、M、G、T 之间都相隔 1000 倍。小数一侧遵循同样的规律：m、μ、n、p 彼此相隔 10³。
4. Large Prefixes: tera, giga, mega, kilo | 大数前缀：tera、giga、mega、kilo
Large prefixes appear whenever you describe power stations, radio frequencies or astronomical distances. A typical power station generates 2 GW, a microwave oven operates at 2.45 GHz, and a student experiment might use a 12 kΩ resistor.
大数前缀出现在你描述发电站、射电频率或天文距离的时候。典型的发电站输出 2 GW，微波炉工作在 2.45 GHz，而学生实验可能使用 12 kΩ 的电阻。
Useful anchors to memorise:
值得记忆的锚点：
- 1 kW = 1000 W - a domestic heater; 1 kW h = 3.6 × 10⁶ J.
- 1 MW = 10⁶ W - a small wind turbine or a large engine.
- 1 GW = 10⁹ W - a national grid power station unit.
- 1 GHz = 10⁹ Hz - WiFi and mobile phone bands.
- 1 THz = 10¹² Hz - far-infrared and submillimetre astronomy.
在一个 2.45 GHz 的微波炉中，频率写作 2.45 × 10⁹ Hz；在一个 2 GW 的电站中，功率写作 2 × 10⁹ W。看到 GW 时立刻想到 10⁹ W，可以省去一次换算错误。
he output is 2 × 10⁹ W. Reading GW and instantly thinking 10⁹ W saves one conversion slip.
A common exam pattern is to give the answer in a prefixed unit and ask you to justify it. The justification is always the same: the number becomes between 1 and 1000, so it is easier to read and less likely to be misread.
常见的考题模式是要求你把答案写成带前缀的单位并说明理由。理由总是相同的：数值落在 1 到 1000 之间，因此更易读、更不容易看错。
5. Small Prefixes: centi, milli, micro, nano, pico | 小数前缀：centi、milli、micro、nano、pico
Small prefixes dominate microscopy, electronics and atomic physics. The wavelength of red light is about 650 nm, the diameter of a human hair is roughly 70 μm, and a small capacitor might be rated 470 pF.
小数前缀在显微、电子学和原子物理中占主导地位。红光的波长约为 650 nm，人类头发的直径大约是 70 μm，而一个小电容器可能标称 470 pF。
The centimetre is the only centi-prefixed unit you will use routinely. It survives because rulers are marked in centimetres, but almost every calculation should be done in metres, so convert before substituting into a formula.
厘米是你日常唯一常用的 centi 前缀单位。它能存活下来是因为尺子以厘米刻度，但几乎所有计算都应当在米制下进行，所以代入公式前先换算。
- 1 mm = 10⁻³ m - the pitch of a steel rule; 1 mA = 10⁻³ A.
- 1 μm = 10⁻⁶ m - bacterial cell; 1 μF = 10⁻⁶ F.
- 1 nm = 10⁻⁹ m - visible light; 1 nF = 10⁻⁹ F.
- 1 ps = 10⁻¹² s - laser pulse durations; 1 pF = 10⁻¹² F.
1 mm = 10⁻³ m 是钢尺的刻度间距；1 mA = 10⁻³ A。1 μm = 10⁻⁶ m 是细菌细胞尺度；1 μF = 10⁻⁶ F。1 nm = 10⁻⁹ m 对应可见光；1 nF = 10⁻⁹ F。1 ps = 10⁻¹² s 是激光脉冲时长；1 pF = 10⁻¹² F。
A useful sanity check: the smaller the prefix power, the larger the number in front of it. So 5 μF is much bigger than 5 pF, because 10⁻⁶ F is a million times larger than 10⁻¹² F.
一个实用的量级检查：前缀的幂越小，前面的数字就应当越大。所以 5 μF 远大于 5 pF，因为 10⁻⁶ F 是 10⁻¹² F 的一百万倍。
6. Converting Between Prefixes Step by Step | 前缀之间换算的步骤
Conversion is always a multiplication or division by a power of ten. The only reliable method is to write the power explicitly and let the indices do the work.
换算永远是乘以或除以一个十的幂。唯一可靠的方法是明确写出幂次，让指数替你完成工作。
Step 1: write the value with its prefix as a number times a power of ten.
第一步：把带前缀的数值写成"数字 × 十的幂"。
Step 2: change the power of ten to the target power, adjusting the number by the same factor in the opposite direction.
第二步：把十的幂改为目标幂，同时把数字朝相反方向调整相同的倍数。
Step 3: check the order of magnitude. If a quantity should be around 10⁻⁷ m and you get 10⁻⁴ m, you have slipped by 10³.
第三步：检查数量级。如果某量应在 10⁻⁷ m 左右而你得到 10⁻⁴ m，说明你差了 10³。
3.5 GHz = 3.5 × 10⁹ Hz = 3.5 × 10⁶ kHz
0.047 μF = 0.047 × 10⁻⁶ F = 4.7 × 10⁻⁸ F = 47 nF
Another efficient trick is the "power difference" rule: to go from prefix A (power a) to prefix B (power b), multiply by 10a − b. Going from MHz (10⁶) to kHz (10³) means multiplying by 10³, so 12 MHz = 12 000 kHz.
另一个高效技巧是"幂差"规则：从幂为 a 的前缀 A 换到幂为 b 的前缀 B，就乘以 10a − b。从 MHz（10⁶）换到 kHz（10³）要乘以 10³，所以 12 MHz = 12 000 kHz。
7. Prefixes, Standard Form and Significant Figures | 前缀、科学计数法与有效数字
Prefixes and standard form are two ways of expressing the same idea. A prefix is more compact for reading; standard form is more reliable for calculation. Convert to standard form before you substitute into any equation.
前缀和科学计数法是同一思想的两种表达方式。前缀更便于阅读，科学计数法更便于计算。在代入任何方程之前，先换算成科学计数法。
igures - the original data only supports two. Write 2.2 × 10³ Ω and keep two significant figures.
有效数字在换算中保持不变。如果某电阻标称为 2.2 kΩ，你不能写成 2200 Ω 然后声称有四位有效数字——原始数据只支持两位。应写成 2.2 × 10³ Ω，保留两位有效数字。
| Prefixed form | Standard form | Significant figures |
|---|---|---|
| 2.2 kΩ | 2.2 × 10³ Ω | 2 |
| 470 pF | 4.70 × 10⁻¹⁰ F | 3 |
| 650 nm | 6.50 × 10⁻⁷ m | 3 |
| 1.5 MW | 1.5 × 10⁶ W | 2 |
Examiners often award a mark for a correctly prefixed final answer with consistent significant figures, and deduct the final mark for an answer such as 8800000.0 Pa when the data was given to two significant figures.
考官常常给"前缀正确且有效数字一致"的最终答案分数，而对诸如数据只给两位有效数字却答成 8800000.0 Pa 的情况扣掉最后一分。
8. Prefixes in Compound and Derived Units | 复合单位与导出单位中的前缀
This is where most marks are lost. When a prefix is attached to a unit that is squared or cubed, the conversion factor is also squared or cubed, not simply multiplied.
这是最容易丢分的地方。当前缀附着在带平方或立方的单位上时，换算因子也要平方或立方，而不是简单相乘。
1 cm² = (10⁻² m)² = 10⁻⁴ m²
1 cm³ = (10⁻² m)³ = 10⁻⁶ m³
1 mm³ = (10⁻³ m)³ = 10⁻⁹ m³
m⁻³ by 1000 to obtain kg m⁻³. Water at 1000 kg m⁻³ is 1.0 g cm⁻³; aluminium at 2.7 g cm⁻³ is 2700 kg m⁻³.
密度换算遵循同样的逻辑。由于 1 g cm⁻³ = 10⁻³ kg ÷ 10⁻⁶ m³ = 10³ kg m⁻³，把以 g cm⁻³ 为单位的值乘以 1000 就得到 kg m⁻³。水为 1000 kg m⁻³，即 1.0 g cm⁻³；铝为 2.7 g cm⁻³，即 2700 kg m⁻³。
For rates, the prefix attaches to one part only. A speed of 72 km h⁻¹ must be converted using 1000 m km⁻¹ and 3600 s h⁻¹:
对于速率类量，前缀只附着在其中一个部分上。72 km h⁻¹ 的速度必须用 1000 m km⁻¹ 和 3600 s h⁻¹ 换算：
72 km h⁻¹ = 72 × 1000 ÷ 3600 = 20 m s⁻¹
Pa. Young modulus values are usually quoted in GPa, so steel at 200 GPa is 2.0 × 10¹¹ Pa.
压强把前缀与复合单位结合起来：1 kN m⁻² = 10³ Pa，1 MPa = 10⁶ Pa。杨氏模量通常以 GPa 引用，所以钢的 200 GPa 即 2.0 × 10¹¹ Pa。
9. Prefixes in Electricity, Energy and Waves | 电学、能量与波动中的前缀
pF for capacitance. Always convert to base SI units before using V = IR, P = VI or Q = CV.
电学题目充满前缀：电阻用 kΩ 和 MΩ，电流用 mA 和 μA，电势差用 mV 和
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