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Units & Measurements

The foundation of everything in Physics

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Why Measurements Matter

Every formula, every calculation, every experiment in physics depends on accurate measurement.

About 20% of your IGCSE marks come from experimental skills — and those start right here.

Think of it like cooking: if your scales are wrong, the recipe fails. In physics, wrong measurements = wrong results = lost marks.

SI Base Units

The 5 you MUST know for IGCSE

Quantity	Unit	Symbol
Length	metre	m
Mass	kilogram	kg
Time	second	s
Electric current	ampere	A
Temperature	kelvin	K

Every other unit (N, Pa, J, W) is derived from these five.

SI Prefixes

Making big & small numbers manageable

Prefix	Symbol	Multiply by	Example
giga	G	× 1,000,000,000	3 GHz
mega	M	× 1,000,000	50 MW
kilo	k	× 1,000	2.5 km
centi	c	× 0.01	30 cm
milli	m	× 0.001	250 mA
micro	μ	× 0.000001	50 μs
nano	n	× 0.000000001	550 nm

Converting Units

The Rule:
Small unit → Large unit? DIVIDE
Large unit → Small unit? MULTIPLY

Example 1: 4.5 km → m
km is larger than m → multiply by 1000
4.5 × 1000 = 4500 m

Example 2: 250 mA → A
mA is smaller than A → divide by 1000
250 ÷ 1000 = 0.25 A

Example 3: 0.035 kg → g
kg is larger than g → multiply by 1000
0.035 × 1000 = 35 g

Derived Units

Built from base units using formulae

Quantity	Formula	Unit	In base units
Speed	v = s/t	m/s	m·s⁻¹
Acceleration	a = Δv/Δt	m/s²	m·s⁻²
Force	F = ma	N	kg·m·s⁻²
Pressure	p = F/A	Pa	kg·m⁻¹·s⁻²
Energy	E = Fd	J	kg·m²·s⁻²
Power	P = E/t	W	kg·m²·s⁻³
Density	ρ = m/V	kg/m³	kg·m⁻³

If your calculated answer has wrong units, your formula or substitution is wrong!

Measuring Instruments

You need to know which instrument to use and how to read it.

Instrument	Measures	Resolution
Ruler	Length (1–100 cm)	1 mm
Vernier caliper	Length (0–15 cm)	0.01 cm (0.1 mm)
Micrometer	Small lengths (0–25 mm)	0.01 mm
Measuring cylinder	Volume of liquid	0.5–1 cm³
Electronic balance	Mass	0.01–0.1 g
Stopwatch	Time intervals	0.01 s

Reading a Vernier Caliper

Step 1: Read the main scale at the zero line of the vernier → e.g., 3.4 cm

Step 2: Find which vernier division aligns perfectly with a main scale line → e.g., 7th division

Step 3: Add: 3.4 + 0.07 = 3.47 cm

Resolution = 0.01 cm. This means a vernier is 10× more precise than a ruler.

Reading a Micrometer

Step 1: Read the sleeve (main scale) — count 0.5 mm divisions visible → e.g., 3.5 mm

Step 2: Read the thimble — which line aligns with horizontal line → e.g., 23 → 0.23 mm

Step 3: Add: 3.5 + 0.23 = 3.73 mm

True reading = Observed reading − Zero error

Zero error +0.04 mm? Subtract it: 3.73 − 0.04 = 3.69 mm
Zero error −0.03 mm? Subtract it: 3.73 − (−0.03) = 3.76 mm

Avoiding Errors

Parallax Error

Occurs when your eye is not perpendicular to the scale. Looking at an angle gives a wrong reading.

✓ Fix: Position your eye directly in line with the mark on the scale.

Reading the Meniscus

Liquids in measuring cylinders form a curved surface. For water, read from the bottom of the curve.

✓ Fix: Eye level with liquid surface, read from bottom of meniscus.

Accuracy vs Precision

Accuracy = how close to the true value

Precision = how close readings are to each other

🎯 Dart analogy:
• Accurate + Precise = all darts in the bullseye
• Precise but not Accurate = darts clustered together, but off-centre
• Accurate but not Precise = scattered around the bullseye
• Neither = scattered everywhere

Types of Error

Systematic Error
• Affects all readings the same way (all too high OR all too low)
• Example: zero error on a micrometer, a slow stopwatch
• Cannot be fixed by averaging! Must fix the instrument.

Random Error
• Causes readings to scatter above and below true value
• Example: human reaction time when using a stopwatch
• CAN be reduced by taking multiple readings and averaging.

The "Measure Many, Divide" Technique

When a single measurement is too small to measure accurately:

For the period of a pendulum:
1. Time 20 complete swings (e.g., 34.6 s)
2. Divide by 20: period = 34.6 ÷ 20 = 1.73 s

Why? Human reaction time (~0.3 s) is a tiny fraction of 34.6 s, but would be a huge fraction of a single 1.73 s swing.

For thickness of paper:
1. Stack 50 sheets and measure total (e.g., 4.2 mm)
2. Divide by 50: one sheet = 4.2 ÷ 50 = 0.084 mm

Significant Figures

How many digits to give in your answer

Number	Sig Figs	Rule
345	3	All non-zero digits count
3045	4	Zeros between digits count
0.0034	2	Leading zeros don't count
3.40	3	Trailing zeros after decimal count
2500	2 (or 4)	Ambiguous — use standard form

Exam rule: Give your answer to the same number of significant figures as the data in the question (usually 2 or 3).

Exam Tips for This Topic

✓ Always include units in your final answer. No unit = lost mark.

✓ "Describe a method" questions: State the instrument → the procedure → how you get the answer.

✓ Zero error: True = Observed − Zero error. Remember: subtract positive, which means add for negative.

⚠️ "Explain why a micrometer is better than a ruler" → Don't just say "more accurate." Say it has a higher resolution (0.01 mm vs 1 mm), so the percentage uncertainty is smaller.

✓ This topic appears on Paper 2 (MCQ), Paper 4 (Theory), and especially Paper 6 (Practical).

Key Takeaways

✅ 5 SI base units: m, kg, s, A, K

✅ Prefixes: G, M, k, c, m, μ, n

✅ Vernier = 0.01 cm, Micrometer = 0.01 mm

✅ True = Observed − Zero error

✅ Accuracy ≠ Precision

✅ Systematic vs Random errors

✅ Measure multiples and divide for small quantities

Now go ace those exam questions! 💪