# Unit prefixes

> CIE A-Level Physics · 9702
> Source: https://www.owlsprep.com/study/cie-9702-u1-unit-prefixes/

Unit prefixes are standard SI shorthand for representing very large and very small physical quantities. This guide covers required prefixes, conversion, and application to CIE A-Level Physics exam questions.

**Prerequisites:** [Standard form and scientific notation](https://www.owlsprep.com/study/cie-9702-u1-standard-form/)

## Learning objectives

- Identify all required SI unit prefixes and their corresponding powers of 10
- Convert values correctly between different unit prefixes
- Apply prefixes to standard form and calculation questions
- Avoid common unit conversion errors in exams

## 1. What are SI Unit Prefixes

The International System (SI) uses prefixes to modify the size of base and derived units, avoiding the need to write very large or small powers of 10 repeatedly. All prefixes for CIE A-Level Physics correspond to an integer power of 10.

**SI Unit Prefix** — A standard name and symbol that multiplies a unit by a fixed power of 10, to simplify expression of extreme values

*Notation:* prefix + base/derived unit

*Example:* 1 kilometre (km) = 1000 metres (m) = $10^3$ m

**Worked example:** Write 0.0005 grams using the prefix for $10^{-3}$

1. The prefix for $10^{-3}$ is milli, so $1\text{ mg} = 10^{-3}\text{ g}$. Rearrange to get $1\text{ g} = 10^3\text{ mg}$:
2. $$0.0005\text{ g} = 0.0005 \times 10^3 \text{ mg}$$
3. Simplify to get the final value:
4. $$0.0005 \times 10^3 = 0.5\text{ mg}$$

> **Exam tip:** You must memorize all prefixes from $10^{-12}$ (pico) to $10^{12}$ (tera) for CIE 9702 exams.

## 2. Converting Between Different Prefixes

To convert a quantity from one prefix to another, first write the power of 10 for each prefix, then find the conversion ratio between them. Multiply your original value by this ratio to get the converted value.

**Worked example:** Convert 2.7 megawatts (MW) to kilowatts (kW)

1. Write the power of 10 for each prefix relative to the base unit (watts, W):
2. $$1\text{ MW} = 10^6\text{ W}, \quad 1\text{ kW} = 10^3\text{ W}$$
3. Convert megawatts to base watts first:
4. $$2.7\text{ MW} = 2.7 \times 10^6\text{ W}$$
5. Convert watts to kilowatts by dividing by the power of 10 for kilo:
6. $$2.7 \times 10^6\text{ W} = \frac{2.7 \times 10^6}{10^3}\text{ kW} = 2700\text{ kW}$$

> **tip**
>
> Always check your answer makes sense: converting to a smaller prefix gives a larger numerical value, and vice versa.

## 3. Using Prefixes in Physics Calculations

For any calculation in CIE A-Level Physics, you should always convert all values to base SI units before substituting into a formula. This avoids common order of magnitude errors.

**Worked example:** Calculate the force on a 500 g mass accelerating at $2\text{ m s}^{-2}$. Use $F=ma$.

1. The base SI unit for mass is kilograms (kg), so convert 500 g to kg:
2. $$500\text{ g} = 500 \times 10^{-3}\text{ kg} = 0.5\text{ kg}$$
3. Substitute into the formula $F=ma$:
4. $$F = 0.5\text{ kg} \times 2\text{ m s}^{-2} = 1\text{ N}$$

**Check your understanding**

Test your understanding:

1. What is 1500 μm in metres?

   - $1.5 \times 10^{-3}$ m
   - $1.5 \times 10^{-6}$ m
   - $1.5 \times 10^3$ m

   *Answer:* $1.5 \times 10^{-3}$ m

   *Why:* Correct! 1 μm = $10^{-6}$ m, so 1500 μm = $1500 \times 10^{-6} = 1.5 \times 10^{-3}$ m

## Common pitfalls

- **Wrong:** Mixing up milli ($10^{-3}$) and micro ($10^{-6}$)
  - Why it fails: The prefix names sound similar, so their powers of 10 are often swapped
  - Correct: Memorize: milli = one thousandth ($10^{-3}$), micro = one millionth ($10^{-6}$)
- **Wrong:** Forgetting to convert to base units before calculation
  - Why it fails: Using grams instead of kilograms or centimetres instead of metres leads to answers that are orders of magnitude wrong
  - Correct: Convert all values to base SI units at the start of every calculation question
- **Wrong:** Flipping the conversion factor direction
  - Why it fails: When converting to a smaller prefix, you divide instead of multiplying
  - Correct: Check: smaller unit = more units for the same quantity, so numerical value should increase. If it decreases, you flipped the ratio
- **Wrong:** Using abbreviated notation like 5k instead of 5 km
  - Why it fails: Ambiguous notation can be marked wrong in exams, as k can refer to other quantities like Boltzmann's constant
  - Correct: Always write the full unit with the correct prefix attached, e.g. 5 km not 5k

## Cheatsheet

| Prefix | Symbol | Power of 10 |
| --- | --- | --- |
| pico | p | $10^{-12}$ |
| nano | n | $10^{-9}$ |
| micro | μ | $10^{-6}$ |
| milli | m | $10^{-3}$ |
| centi | c | $10^{-2}$ |
| kilo | k | $10^{3}$ |
| mega | M | $10^{6}$ |
| giga | G | $10^{9}$ |
| tera | T | $10^{12}$ |

## What's next

Unit prefixes are the foundation of all measurement in physics, and you will use them in every topic from kinematics to quantum physics. Mastering prefix conversion ensures you avoid losing easy marks in both multiple choice and structured calculation questions, where order of magnitude errors are one of the most common reasons for lost marks. You will next build on this knowledge to work with derived units and check the homogeneity of physical equations, which relies on correctly understanding unit sizes and powers of 10. Prefixes are also used constantly when working with standard form for astronomical distances and subatomic particle sizes.

- [Estimation of physical quantities](https://www.owlsprep.com/study/cie-9702-u1-estimation-of-physical-quantities/)
- [Measurement uncertainties](https://www.owlsprep.com/study/cie-9702-u1-measurement-uncertainties/)
- [Kinematics](https://www.owlsprep.com/study/cie-9702-u2-overview/)

---

From [OwlsPrep](https://www.owlsprep.com) — free study guides for A-Level, IB, AP and IGCSE, written against the official syllabus. Canonical page: https://www.owlsprep.com/study/cie-9702-u1-unit-prefixes/