Study Guide

Unit prefixes

CIE A-Level PhysicsΒ· Unit 1: Physical quantities and unitsΒ· 10 min read

1. 1. What are SI Unit Prefixesβ˜…β˜†β˜†β˜†β˜†β± 3 min

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.

πŸ“˜ Definition

SI Unit Prefix

prefix+base/derivedunitprefix + base/derived unit

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

Example:

1 kilometre (km) = 1000 metres (m) = m

πŸ“ Worked Example

Write 0.0005 grams using the prefix for

  1. 1

    The prefix for is milli, so . Rearrange to get :

  2. 2
    0.0005extg=0.0005Γ—103 mg0.0005 ext{ g} = 0.0005 \times 10^3 \text{ mg}
  3. 3

    Simplify to get the final value:

  4. 4
    0.0005Γ—103=0.5 mg0.0005 \times 10^3 = 0.5\text{ mg}

Exam tip:

You must memorize all prefixes from (pico) to (tera) for CIE 9702 exams.

2. 2. Converting Between Different Prefixesβ˜…β˜…β˜†β˜†β˜†β± 4 min

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.

πŸ“ Worked Example

Convert 2.7 megawatts (MW) to kilowatts (kW)

  1. 1

    Write the power of 10 for each prefix relative to the base unit (watts, W):

  2. 2
    1 MW=106 W,1 kW=103 W1\text{ MW} = 10^6\text{ W}, \quad 1\text{ kW} = 10^3\text{ W}
  3. 3

    Convert megawatts to base watts first:

  4. 4
    2.7 MW=2.7Γ—106 W2.7\text{ MW} = 2.7 \times 10^6\text{ W}
  5. 5

    Convert watts to kilowatts by dividing by the power of 10 for kilo:

  6. 6
    2.7Γ—106 W=2.7Γ—106103 kW=2700 kW2.7 \times 10^6\text{ W} = \frac{2.7 \times 10^6}{10^3}\text{ kW} = 2700\text{ kW}

3. 3. Using Prefixes in Physics Calculationsβ˜…β˜…β˜†β˜†β˜†β± 3 min

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.

πŸ“ Worked Example

Calculate the force on a 500 g mass accelerating at . Use .

  1. 1

    The base SI unit for mass is kilograms (kg), so convert 500 g to kg:

  2. 2
    500 g=500Γ—10βˆ’3 kg=0.5 kg500\text{ g} = 500 \times 10^{-3}\text{ kg} = 0.5\text{ kg}
  3. 3

    Substitute into the formula :

  4. 4
    F=0.5 kgΓ—2 m sβˆ’2=1 NF = 0.5\text{ kg} \times 2\text{ m s}^{-2} = 1\text{ N}
βœ“ Quick check

Test your understanding:

  1. What is 1500 ΞΌm in metres?

    • m

    • m

    • m

4. Common Pitfalls

Wrong move:

Mixing up milli () and micro ()

Why:

The prefix names sound similar, so their powers of 10 are often swapped

Correct move:

Memorize: milli = one thousandth (), micro = one millionth ()

Wrong move:

Forgetting to convert to base units before calculation

Why:

Using grams instead of kilograms or centimetres instead of metres leads to answers that are orders of magnitude wrong

Correct move:

Convert all values to base SI units at the start of every calculation question

Wrong move:

Flipping the conversion factor direction

Why:

When converting to a smaller prefix, you divide instead of multiplying

Correct move:

Check: smaller unit = more units for the same quantity, so numerical value should increase. If it decreases, you flipped the ratio

Wrong move:

Using abbreviated notation like 5k instead of 5 km

Why:

Ambiguous notation can be marked wrong in exams, as k can refer to other quantities like Boltzmann's constant

Correct move:

Always write the full unit with the correct prefix attached, e.g. 5 km not 5k

5. Quick Reference Cheatsheet

Prefix

Symbol

Power of 10

pico

p

nano

n

micro

ΞΌ

milli

m

centi

c

kilo

k

mega

M

giga

G

tera

T

When this came up on past exams

AI-estimated based on syllabus patterns β€” cross-check with official past papers for accuracy. Use only as revision-focus signals.

  • 2022 Β· 1

    Multiple choice prefix conversion

  • 2023 Β· 2

    Unit conversion for force calculation

Going deeper

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.