Overview
What you’ll learn
- State that physical quantities consist of a numerical magnitude and a unit.
- Recall the base quantities and their units: mass (kg), length (m), time (s), current (A), temperature (K), amount of substance (mol).
- Use the prefixes nano, micro, milli, centi, deci, kilo, mega, giga and tera with SI units.
- Show an understanding of the orders of magnitude of the sizes of common objects from a typical atom to the Earth.
- Select and explain the use of appropriate measuring instruments, taking into account range and precision.
- State what is meant by scalar and vector quantities and give common examples of each.
Key points
- 1Every physical quantity = a number (magnitude) with a unit — "3.5" alone is not a measurement.
- 2Base quantities: mass (kg), length (m), time (s), current (A), temperature (K), amount of substance (mol).
- 3Prefixes scale units: n 10⁻⁹, µ 10⁻⁶, m 10⁻³, c 10⁻², d 10⁻¹, k 10³, M 10⁶, G 10⁹, T 10¹².
- 4Orders of magnitude: atom 10⁻¹⁰ m, molecule ≈10⁻⁹ m, hair width ≈10⁻⁴ m, person ≈10⁰ m, tall building ≈10² m, Earth's diameter ≈10⁷ m.
- 5Range = the largest value an instrument can measure; precision = the smallest change it can show. Match both to the job.
- 6Scalars have magnitude only (mass, time, speed, energy); vectors have magnitude and direction (force, velocity, displacement).
Notes · 1 of 5
Quantities and units
A number without a unit is only half a measurement.
A physical quantity is anything you can measure, and every measurement has two parts: the numerical magnitude and the unit. "The rope is 3.5" says nothing — 3.5 centimetres, metres or kilometres are three different ropes. In equations the unit travels with the number, and a final answer without a unit is an incomplete answer.
The SI system builds every unit from a small set of base quantities. The ones this course uses daily: mass in kilograms (kg), length in metres (m), time in seconds (s), electric current in amperes (A), temperature in kelvin (K), and amount of substance in moles (mol). Derived quantities — speed in m/s, force in newtons — are assembled from these.
| Base quantity | Unit | Measures |
|---|---|---|
| mass | kilogram (kg) | amount of matter |
| length | metre (m) | distance in one dimension |
| time | second (s) | duration |
| electric current | ampere (A) | rate of charge flow |
| temperature | kelvin (K) | hotness (degree Celsius in lab work) |
| amount of substance | mole (mol) | number of particles |
Notes · 2 of 5
Prefixes: stretching the unit
Nano to tera — nine prefixes that cover the whole course.
Writing the diameter of an atom as 0.000 000 000 1 m is correct and unreadable. Prefixes multiply a unit by a fixed power of ten so the number stays friendly. Nine prefixes matter in this course:
| Prefix | Symbol | Meaning |
|---|---|---|
| nano | n | 10⁻⁹ (a thousand-millionth) |
| micro | µ | 10⁻⁶ (a millionth) |
| milli | m | 10⁻³ (a thousandth) |
| centi | c | 10⁻² (a hundredth) |
| deci | d | 10⁻¹ (a tenth) |
| kilo | k | 10³ (a thousand) |
| mega | M | 10⁶ (a million) |
| giga | G | 10⁹ (a thousand million) |
| tera | T | 10¹² (a million million) |
Notes · 3 of 5
Orders of magnitude
From an atom to the Earth in powers of ten.
An order of magnitude is the power of ten that best matches a size — how many zeroes, not the exact digits. Physicists sanity-check answers this way: if a calculation makes an atom 10⁻² m across, something has gone badly wrong. The staircase from small to large: a typical atom ≈10⁻¹⁰ m; a molecule ≈10⁻⁹ m; the width of a human hair ≈10⁻⁴ m; a person ≈10⁰ m (about 1–2 m); a tall building ≈10² m; and the Earth's diameter ≈1.3 × 10⁷ m.
| Object | Typical size | Order |
|---|---|---|
| atom | 0.1 nm | 10⁻¹⁰ m |
| DNA helix width | about 2 nm | 10⁻⁹ m |
| red blood cell | about 8 µm | 10⁻⁵ m |
| human hair width | about 0.1 mm | 10⁻⁴ m |
| person | 1–2 m | 10⁰ m |
| skyscraper | about 300 m | 10² m |
| Earth diameter | 12 700 km | 10⁷ m |
Notes · 4 of 5
Choosing an instrument
Range first, precision second.
Two questions pick the right instrument. First, range: can it measure the whole value at all? A thermometer marked to 50 °C cannot read an 80 °C water bath; a 30 cm ruler cannot reach across a 2 m table in one measurement. Second, precision: does it show the smallest change that matters? A metre rule reads to 1 mm; a measuring cylinder to about 1 cm³; a digital stopwatch to 0.01 s (though human reaction time makes timing the real limit); a thermometer to 1 °C or 0.5 °C; an electronic balance to 0.01 g or better.
Precision is the smallest change the instrument can display — the value of one smallest division (for analogue instruments) or one unit of the last digit (digital). The instrument with the smaller precision resolves finer differences: measuring 2.5 cm needs a rule (millimetre marks), not a tape measure marked in centimetres. But precision without range is useless — you cannot measure a football pitch with a micrometer-scale rule however precisely it reads.
Notes · 5 of 5
Scalars and vectors
Some quantities carry a direction — and it matters.
A scalar is fully specified by a magnitude with a unit: mass 5 kg, time 12 s, speed 8 m/s, energy 300 J, temperature 20 °C. A vector also needs a direction: force 20 N downwards, velocity 8 m/s north, displacement 50 m east. Same size, different direction = different vector.
| Scalars | Vectors |
|---|---|
| distance, speed, mass, time, energy, temperature, current | displacement, velocity, acceleration, force, weight |
The distinction changes how quantities combine. Scalars add arithmetically: 30 J + 40 J = 70 J. Vectors add allowing for direction — two 5 N forces pulling the same way give 10 N; pulling against each other they give zero. In this course you handle this directly for vectors along the same line (choose a positive direction, add with signs); graphical addition of vectors at angles is not required.
Revise
Key terms
The words examiners expect you to use precisely.
- physical quantity
- Anything that can be measured, stated as a numerical magnitude with a unit."3.5 m" is a quantity; "3.5" is not.
- base quantity
- One of the small set of quantities from which all others are built: mass, length, time, current, temperature, amount of substance.Each has one agreed SI unit: kg, m, s, A, K, mol.
- prefix
- A symbol that multiplies a unit by a power of ten, such as milli (10⁻³) or kilo (10³).m means milli and M means mega — case matters, a factor of 10⁹.
- order of magnitude
- The nearest power of ten to a size or value.An atom is of order 10⁻¹⁰ m; the Earth of order 10⁷ m.
- range
- The largest value an instrument can measure.A 0–50 °C thermometer cannot follow water to boiling.
- precision
- The smallest change in value an instrument can show.A millimetre rule is precise to 1 mm; a 2-d.p. balance to 0.01 g.
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- scalar
- A quantity with magnitude only.Mass, time, speed, energy, temperature.
- vector
- A quantity with magnitude and direction.Force, weight, velocity, acceleration, displacement.
Revise
Common mistakes
Where students most often lose marks in this chapter — and what to do instead.
Mistake: Quoting a measurement without a unit.
The magnitude alone does not define the quantity.
Instead: Always pair the number with its unit: 3.5 m, 12 s, 250 mA.
Mistake: Mixing up m (milli) and M (mega).
They differ by 10⁹ — a billion times.
Instead: Lowercase m = 10⁻³; capital M = 10⁶. Same for µ (10⁻⁶) versus none.
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Mistake: Treating centi and deci as prefixes only chemists use.
Centimetres and decimetres appear constantly in lab measurements.
Instead: c = 10⁻², d = 10⁻¹ — the everyday middle steps between milli and the base unit.
Mistake: Saying a red blood cell is about 10⁻³ m across.
That is a millimetre — a hundred times too big.
Instead: A red blood cell is about 8 µm, order 10⁻⁵ m; 10⁻³ m is hair-thick at most.
Mistake: Choosing an instrument by precision alone.
A precise instrument with too small a range cannot do the job at all.
Instead: Check range first (can it measure the value?), then precision (is it fine enough?).
Mistake: Reporting a stopwatch reading as exact to 0.01 s.
Human reaction time is around 0.2 s — the display is not the limit.
Instead: For hand timing, the reaction time dominates; quote sensibly and time longer intervals where possible.
Mistake: Calling speed a vector.
Speed has no direction attached.
Instead: Speed is scalar; velocity is speed with a direction — the vector version.
Mistake: Adding vector magnitudes without directions.
Two 5 N forces can add to anything from 0 to 10 N depending on direction.
Instead: Choose a positive direction and add with signs for same-line vectors: (+5) + (−5) = 0.
Mistake: Confusing mass (kg) with weight (N).
Mass is scalar amount of matter; weight is a vector force.
Instead: Mass in kg never changes with location; weight in N is a gravitational force on that mass.
Mistake: Writing kelvin temperatures with a degree sign.
The unit is kelvin, not "degrees kelvin".
Instead: K alone: 273 K, not 273 °K. Lab work usually quotes °C for temperature differences both work identically.
Mistake: Thinking precision improves by writing extra digits.
Quoting beyond what the instrument shows fakes certainty.
Instead: Quote to the precision of the instrument — one smallest division or one last digit.
Mistake: Saying distance and displacement are always equal.
Distance ignores direction; displacement is the straight-line change in position.
Instead: On a straight line without turning they match; a full lap of a track gives large distance, zero displacement.
Check yourself
Quick quiz
20 questions with instant explanations. About 5 minutes.
Question 1 of 3
- Question 1: current question
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- Question 3: not answered
State that physical quantities consist of a numerical magnitude and a unit.
A complete measurement of a physical quantity always consists of
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Practise
Topical questions
Exam-style practice in three tiers, from recall to data questions.
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12 questions worth 58 marks, each with a model answer, mark scheme and examiner tips.
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Chapter 1 Practice Paper
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5 multiple-choice questions and structured questions with answer lines. Chapter 1 (quantities and base units, prefixes, orders of magnitude, range and precision, scalars and vectors).
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Chapter 1 Practice Paper — mark scheme
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Questions
Frequently asked questions
Which units do I actually have to memorise?
The six base pairings: mass kg, length m, time s, current A, temperature K, amount of substance mol — plus the nine prefixes. Everything else in the course is built from these.
How do I convert 45 nm to metres quickly?
Replace nano with 10⁻⁹: 45 nm = 45 × 10⁻⁹ m = 4.5 × 10⁻⁸ m. Always swap the prefix for its power of ten before doing anything else.
Range or precision — which comes first when choosing an instrument?
Range first: the instrument must be able to measure the value at all. Then precision: it must show the smallest change that matters. A precise instrument with the wrong range is useless.
Why is speed a scalar but velocity a vector?
They use different inputs: speed comes from total distance (no direction), velocity from displacement (which has direction). Going round a circle at steady speed still changes your velocity, because direction keeps changing.