1.1 Units & Measurements
What are Units?
A unit is a standard amount used to measure a physical quantity. We need units for almost everything, from measuring a dose of medicine to building rockets.
A unit is a standard amount used to measure a physical quantity. We need units for almost everything, from measuring a dose of medicine to building rockets.
⚡ Key Concept:
• Units give meaning to numbers: "5" means nothing, but "5 metres" tells us a length
• Units must match: You can't add 5 kg to 3 metres.
• Units must match: You can't add 5 kg to 3 metres.
💡 Why Standard Units Matter:
There are hundreds of units. For example, we can measure mass in:
• Kilograms (kg)
• Grams (g)
• Pounds (lb)
• Stones
Using different units causes confusion. In science, we use the SI system (Système International)
• Kilograms (kg)
• Grams (g)
• Pounds (lb)
• Stones
Using different units causes confusion. In science, we use the SI system (Système International)
⚠️ Mars Climate Orbiter (1999)
NASA lost a $125 million orbiter because one team used pounds (imperial) while another used newtons (SI). The probe crashed into Mars because of a simple error that could have been avoided using the same unit system.
The Seven SI Base Units
The SI system is built on seven base units. All other units can be derived from these seven.
The SI system is built on seven base units. All other units can be derived from these seven.
⚡ The 7 SI Base Units:
These are the fundamental building blocks of all measurements in science.
Length
metre
m
Mass
kilogram
kg
Time
second
s
Current
ampere
A
Temperature
kelvin
K
Amount
mole
mol
Light Intensity
candela
cd
| Quantity | Unit Name | Symbol |
|---|---|---|
| Length | metre | m |
| Mass | kilogram | kg |
| Time | second | s |
| Electric Current | ampere | A |
| Temperature | kelvin | K |
| Amount of Substance | mole | mol |
| Luminous Intensity | candela | cd |
💡 Remember:
Remember the 7 quantities with: "Long Mass Times Current Temperature And Light"
Length, Mass, Time, Current, Temperature, Amount, Light intensity
Length, Mass, Time, Current, Temperature, Amount, Light intensity
🎯 SI Base Units Practice
Building New Units from Base Units
All other units can be built from the seven base units. These are called derived units.
• The 7 fundamental units
• e.g., m, kg, s, A, K, mol, cd
• Use formulas to combine
• e.g., m/s, N, J, m²
All other units can be built from the seven base units. These are called derived units.
⚡ How Derived Units Work:
Derived units come from combining base units using formulas.
For example, speed = distance ÷ time
$$\text{speed} = \frac{\text{distance}}{\text{time}} = \frac{\text{m}}{\text{s}} = \text{m/s}$$
For example, speed = distance ÷ time
$$\text{speed} = \frac{\text{distance}}{\text{time}} = \frac{\text{m}}{\text{s}} = \text{m/s}$$
Example 1: Finding the Unit for Speed
Step 1: Write the formula
speed = distance ÷ time
Step 2: Substitute the base units
speed = metres ÷ seconds
Step 3: Write the derived unit
speed = m/s (or m s⁻¹)
speed = distance ÷ time
Step 2: Substitute the base units
speed = metres ÷ seconds
Step 3: Write the derived unit
speed = m/s (or m s⁻¹)
distance (m)
÷
time (s)
=
speed (m/s)
Example 2: Finding the Unit for Force
Step 1: Write the formula
force = mass × acceleration
Step 2: Find the unit for acceleration first
acceleration = velocity ÷ time = (m/s) ÷ s = m/s²
Step 3: Substitute into force formula
force = kg × m/s² = kg·m/s²
This is called a Newton (N): 1 N = 1 kg·m/s²
force = mass × acceleration
Step 2: Find the unit for acceleration first
acceleration = velocity ÷ time = (m/s) ÷ s = m/s²
Step 3: Substitute into force formula
force = kg × m/s² = kg·m/s²
This is called a Newton (N): 1 N = 1 kg·m/s²
| Quantity | Formula | Derived Unit | Special Name |
|---|---|---|---|
| Speed | distance ÷ time | m/s | — |
| Acceleration | velocity ÷ time | m/s² | — |
| Force | mass × acceleration | kg·m/s² | Newton (N) |
| Energy | force × distance | kg·m²/s² | Joule (J) |
| Area | length × length | m² | — |
| Volume | length³ | m³ | — |
Base Units
• Cannot be broken down further• The 7 fundamental units
• e.g., m, kg, s, A, K, mol, cd
Derived Units
• Built from base units• Use formulas to combine
• e.g., m/s, N, J, m²
🎯 Derived Units Practice
Making Units Bigger or Smaller
SI units can be very large or very small. We use prefixes to make them easier to write and understand.
SI units can be very large or very small. We use prefixes to make them easier to write and understand.
⚡ Key Concept:
Prefixes multiply the base unit by powers of 10:
• kilo (k) means × 1000 (10³)
• milli (m) means × 0.001 (10⁻³)
So 1 km = 1000 m and 1 mm = 0.001 m
• kilo (k) means × 1000 (10³)
• milli (m) means × 0.001 (10⁻³)
So 1 km = 1000 m and 1 mm = 0.001 m
giga (G)
10⁹
mega (M)
10⁶
kilo (k)
10³
BASE
10⁰
centi (c)
10⁻²
milli (m)
10⁻³
micro (μ)
10⁻⁶
nano (n)
10⁻⁹
| Prefix | Symbol | Multiplier | Example |
|---|---|---|---|
| giga | G | 10⁹ (1,000,000,000) | 1 GHz = 1,000,000,000 Hz |
| mega | M | 10⁶ (1,000,000) | 1 MW = 1,000,000 W |
| kilo | k | 10³ (1,000) | 1 km = 1,000 m |
| centi | c | 10⁻² (0.01) | 1 cm = 0.01 m |
| milli | m | 10⁻³ (0.001) | 1 mm = 0.001 m |
| micro | μ | 10⁻⁶ (0.000001) | 1 μm = 0.000001 m |
| nano | n | 10⁻⁹ | 1 nm = 0.000000001 m |
Example 1: Converting km to m
Convert 5.2 km to metres
Step 1: Identify the prefix
kilo (k) means × 1000
Step 2: Multiply
5.2 km = 5.2 × 1000 m = 5200 m
Step 1: Identify the prefix
kilo (k) means × 1000
Step 2: Multiply
5.2 km = 5.2 × 1000 m = 5200 m
Example 2: Converting mm to m
Convert 450 mm to metres
Step 1: Identify the prefix
milli (m) means × 0.001
Step 2: Multiply
450 mm = 450 × 0.001 m = 0.45 m
Step 1: Identify the prefix
milli (m) means × 0.001
Step 2: Multiply
450 mm = 450 × 0.001 m = 0.45 m
💡 Conversion:
• Going to a smaller unit → number gets bigger
• Going to a larger unit → number gets smaller
Example: 2 km = 2000 m (smaller unit, bigger number)
• Going to a larger unit → number gets smaller
Example: 2 km = 2000 m (smaller unit, bigger number)
🧮 Unit Converter:
→
1 kilo
=
1000 base units
🎯 Prefix Conversion Practice
Real Life Uses:
• Medicine: Dosages in mg, μg — mistakes can cause deaths
• Technology: Processors (GHz), storage (GB/TB), components (μF)
• Construction: Length in mm, cm, m — wrong units = structural failure
• Science: Experiments require precise SI units for reproducibility
• Cooking: Recipes in g, ml — wrong conversions ruin dishes
• Travel: Distance (km/miles), speed (km/h, mph)
• Medicine: Dosages in mg, μg — mistakes can cause deaths
• Technology: Processors (GHz), storage (GB/TB), components (μF)
• Construction: Length in mm, cm, m — wrong units = structural failure
• Science: Experiments require precise SI units for reproducibility
• Cooking: Recipes in g, ml — wrong conversions ruin dishes
• Travel: Distance (km/miles), speed (km/h, mph)