CSEC Essential Skill: SI prefixes are used to express multiples or fractions of units, making measurements more manageable. You must know how to convert between prefixes (like km to m, mg to kg) for CSEC Physics calculations. This skill appears in almost every topic—from mechanics (km to m) to electricity (mA to A) to atomic physics (nm to m).
Why We Need Prefixes in Physics
Imagine measuring these without prefixes:
- The distance to school: 3,000 m (instead of 3 km)
- The diameter of a wire: 0.0015 m (instead of 1.5 mm)
- The mass of a paperclip: 0.001 kg (instead of 1 g)
- The wavelength of green light: 0.00000055 m (instead of 550 nm)
Prefixes make measurements easier to write, read, and comprehend. They’re essential for working with the enormous range of values encountered in physics—from subatomic scales to astronomical distances.
CSEC Insight: “It is easier to visualise the size of the thickness if the student uses a rather large fraction (two-fifths) of a tiny unit, the millimetre, than it is to judge the size of a tiny fraction (two ten thousandths) of a much larger unit, the metre.” This explains why prefixes are so useful!
The Complete SI Prefix Table (CSEC Focus)
| Prefix | Symbol | Power of 10 | Decimal Value | Example in Physics |
|---|---|---|---|---|
| tera | T | 1012 | 1,000,000,000,000 | Terawatt (TW) – large power stations |
| giga | G | 109 | 1,000,000,000 | Gigahertz (GHz) – processor speeds |
| mega | M | 106 | 1,000,000 | Megawatt (MW) – power output |
| kilo | k | 103 | 1,000 | Kilogram (kg), kilometer (km) |
| hecto | h | 102 | 100 | Hectopascal (hPa) – atmospheric pressure |
| deca | da | 101 | 10 | Decametre (dam) – rarely used |
| deci | d | 10-1 | 0.1 | Decimetre (dm) – sometimes used |
| centi | c | 10-2 | 0.01 | Centimetre (cm), centigrade (old term) |
| milli | m | 10-3 | 0.001 | Millimetre (mm), milliampere (mA) |
| micro | μ | 10-6 | 0.000001 | Micrometre (μm), microampere (μA) |
| nano | n | 10-9 | 0.000000001 | Nanometre (nm) – light wavelengths |
| pico | p | 10-12 | 0.000000000001 | Picofarad (pF) – small capacitors |
⚠️ Most Important Prefixes for CSEC
Focus on mastering these prefixes, as they appear most frequently:
- kilo (k) = 10³ = 1,000 (e.g., km, kg, kJ)
- centi (c) = 10⁻² = 0.01 (e.g., cm, cN)
- milli (m) = 10⁻³ = 0.001 (e.g., mm, mL, mA)
- micro (μ) = 10⁻⁶ = 0.000001 (e.g., μm, μA)
- nano (n) = 10⁻⁹ = 0.000000001 (e.g., nm)
Special Note: The prefix “micro” uses the Greek letter mu (μ), not the letter “u”. In handwriting, be careful to distinguish μ from m (milli). Also note: 1 dm³ = 1 liter (L) = 0.001 m³ – an important conversion in volume measurements.
How to Convert Between Prefixes: The 3-Step Method
Determine how many of the smaller unit make one of the larger unit, or vice versa.
Multiply by a fraction that equals 1, with the desired unit in the numerator and original unit in denominator.
Cancel the original units and perform the arithmetic.
Step 1: 1 km = 1,000 m (kilo = 10³)
Step 2: 2.5 km × (1,000 m / 1 km)
Step 3: km cancels: 2.5 × 1,000 m = 2,500 m
Step 1: Need two conversions: mg → g → kg
1 mg = 0.001 g (milli = 10⁻³) and 1,000 g = 1 kg
Step 2: 450 mg × (0.001 g / 1 mg) × (1 kg / 1,000 g)
Step 3: mg and g cancel: 450 × 0.001 × 1/1000 kg = 0.00045 kg or 4.5 × 10⁻⁴ kg
The Power of 10 Method (Recommended for CSEC)
Since all prefixes are powers of 10, you can convert by simply moving the decimal point:
When converting to a smaller unit (e.g., km → m, kg → g), the number gets larger, so move the decimal point to the right.
Example: 3.5 km = 3,500 m (kilo to base: move decimal 3 places right)
When converting to a larger unit (e.g., mm → m, mg → kg), the number gets smaller, so move the decimal point to the left.
Example: 2,500 mm = 2.5 m (milli to base: move decimal 3 places left)
🎯 Memory Trick: “King Henry Died By Drinking Chocolate Milk”
This mnemonic helps remember the order of prefixes from largest to smallest:
Kilo – Hecto – Deca – Base – Deci – Centi – Milli
Each step represents moving the decimal one place. Moving to the right (to smaller units) moves decimal right. Moving to the left (to larger units) moves decimal left.
Common CSEC Physics Conversions
| Conversion | Factor | Example | Application |
|---|---|---|---|
| km → m | × 1,000 | 5 km = 5,000 m | Distance, displacement |
| cm → m | ÷ 100 or × 0.01 | 150 cm = 1.50 m | Length, height measurements |
| mm → m | ÷ 1,000 or × 0.001 | 2.5 mm = 0.0025 m | Wire diameter, small lengths |
| g → kg | ÷ 1,000 | 250 g = 0.250 kg | Mass measurements |
| mg → kg | ÷ 1,000,000 | 500 mg = 0.0005 kg | Small masses (tablets, chemicals) |
| mA → A | ÷ 1,000 | 20 mA = 0.020 A | Electric current |
| kV → V | × 1,000 | 0.5 kV = 500 V | Potential difference |
| cm³ → m³ | ÷ 1,000,000 | 100 cm³ = 0.0001 m³ | Volume (careful: cubed conversion!) |
🚨 Critical Warning: Area and Volume Conversions
When converting squared or cubed units, you must square or cube the conversion factor!
- Area: 1 cm² = (0.01 m)² = 0.0001 m² (NOT 0.01 m²!)
- Volume: 1 cm³ = (0.01 m)³ = 0.000001 m³ (NOT 0.001 m³!)
- Volume: 1 dm³ = (0.1 m)³ = 0.001 m³ = 1 liter (L)
This is a common CSEC exam trap! Many students forget to square/cube the conversion factor.
Incorrect: 150 cm² = 150 × 0.01 = 1.5 m² ✗
Correct: 1 cm = 0.01 m, so 1 cm² = (0.01 m)² = 0.0001 m²
150 cm² = 150 × 0.0001 m² = 0.0150 m² ✓
Prefixes in Real Physics Measurements
- Nanometre (nm): Wavelength of visible light (400-700 nm)
- Micrometre (μm): Diameter of human hair (50-100 μm)
- Millimetre (mm): Thickness of a coin (1-3 mm)
- Microampere (μA): Small electronic currents
- Centimetre (cm): Height of a book (20-30 cm)
- Metre (m): Height of a person (1.5-2.0 m)
- Kilogram (kg): Mass of a textbook (1-2 kg)
- Kilometre (km): Distance to school (1-5 km)
- Megametre (Mm): Earth’s diameter (12.7 Mm)
- Gigametre (Gm): Earth-Sun distance (150 Gm)
- Megawatt (MW): Power output of a wind turbine (2-3 MW)
- Gigawatt (GW): Large power station output (1-2 GW)
CSEC Exam Strategy: When you see a measurement with a prefix in an exam question, immediately consider: “Do I need to convert this to base units (m, kg, s, A) for the calculation?” Often, you’ll need everything in consistent units before calculating.
CSEC Exam Practice
Explanation: kilo = 10³ = 1,000. So 3.6 km = 3.6 × 1,000 = 3,600 m. Remember: km → m is converting to a smaller unit, so the number gets larger.
Explanation: milli = 10⁻³ = 0.001. So 0.5 mm = 0.5 × 0.001 = 0.0005 m. Alternatively, move decimal 3 places left: 0.5 → 0.0005.
Explanation: 1 cm = 0.01 m, so 1 cm² = (0.01 m)² = 0.0001 m².
250 cm² = 250 × 0.0001 m² = 0.0250 m².
Common mistake: Forgetting to square the conversion factor would give 250 × 0.01 = 2.5 m² (incorrect!).
Explanation: milli = 10⁻³ = 0.001. So 15 mA = 15 × 0.001 A = 0.015 A.
In electricity problems, you’ll often need to convert mA to A before using formulas like V = IR or P = IV.
Explanation: nano = 10⁻⁹. So 550 nm = 550 × 10⁻⁹ m = 5.50 × 10⁻⁷ m (since 550 = 5.50 × 10², and 10² × 10⁻⁹ = 10⁻⁷).
Light wavelengths are typically in the nanometre range (400-700 nm for visible light).
Explanation:
First find area in m²: 250 m × 150 m = 37,500 m²
Now convert m² to km²: 1 km = 1,000 m, so 1 km² = (1,000 m)² = 1,000,000 m²
37,500 m² = 37,500 ÷ 1,000,000 = 0.0375 km²
Final CSEC Tips:
- Always check the units in your final answer match what the question asks for
- When in doubt, convert everything to base SI units (m, kg, s, A) before calculating
- Remember that area conversions use the square of the conversion factor, volume uses the cube
- Practice mental conversions for common prefixes (kilo, centi, milli, micro)
- Write units at every step of your calculation to avoid confusion
Quick Reference: Most Common Prefix Conversions
- k → base: Multiply by 1,000 (move decimal 3 places right)
- base → k: Divide by 1,000 (move decimal 3 places left)
- c → base: Divide by 100 (move decimal 2 places left)
- m → base: Divide by 1,000 (move decimal 3 places left)
- μ → base: Divide by 1,000,000 (move decimal 6 places left)
- n → base: Divide by 1,000,000,000 (move decimal 9 places left)