JEE/NEET Physics · Units & Measurements series · Part 1 of 6 · All parts →
- A physical quantity = number × unit; the number is meaningless without the unit
- Seven SI base units: metre (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol), candela (cd)
- Everything else (speed, force, energy…) is a DERIVED unit built from these seven
- Prefixes are powers of ten: kilo = 10³, milli = 10⁻³, micro = 10⁻⁶, nano = 10⁻⁹
- Check any equation: units on the left must match units on the right (homogeneity)
Say ‘I weigh 60’ to a physicist and they’ll ask: 60 what? Kilograms? Pounds? Stones? The number alone carries zero information. Part 1 of the Units & Measurements series — the foundation card on which every other chapter in physics stands.
- Quantity = number × unit
- The seven base units: physics’s alphabet
- Derived units: words built from letters
- Prefixes: the powers-of-ten ladder
- Homogeneity: the free error-check
- Solved examples
- Common mistakes
- This physics in your daily life
- Practice set
- Recap
Quantity = Number × Unit
Every measurement is a marriage of two things: a pure number and a unit that tells you what was counted. Write it as Q = n × u. The same length is 1 m, or 100 cm, or 0.001 km — the quantity never changed, only the divorce settlement between number and unit. All of unit-conversion is just keeping the quantity fixed while trading number against unit.
The Seven Base Units: Physics’s Alphabet
Physics chose seven quantities that cannot be built from each other, and defined one unit for each — the alphabet of measurement:
| Quantity | Unit | Symbol | Everyday anchor |
|---|---|---|---|
| Length | metre | m | a big stride |
| Mass | kilogram | kg | a litre bottle of water |
| Time | second | s | one heartbeat |
| Electric current | ampere | A | phone charger ~1–3 A |
| Temperature | kelvin | K | room = ~300 K |
| Amount of substance | mole | mol | 12 g of carbon |
| Luminous intensity | candela | cd | one candle |
Derived Units: Words Built From Letters
Every other quantity is a combination of these seven — like words built from an alphabet. Speed = m/s. Force = kg·m/s², which physics nicknames the newton (N). Energy = kg·m²/s² = the joule (J). You never memorise derived units; you assemble them from the base seven.
Prefixes: the Powers-of-Ten Ladder
| Prefix | Symbol | Power | Everyday anchor |
|---|---|---|---|
| giga | G | 10⁹ | GB of storage |
| mega | M | 10⁶ | MB, megaphone |
| kilo | k | 10³ | kilogram, kilometre |
| centi | c | 10⁻² | centimetre |
| milli | m | 10⁻³ | millilitre |
| micro | μ | 10⁻⁶ | micrometre (cell size) |
| nano | n | 10⁻⁹ | nanometre (atom scale) |
Homogeneity: The Free Error-Check
Any correct equation must have matching units on both sides — you cannot add apples to volts. Before trusting any formula in an exam, strip it to units and check. It costs five seconds and catches a stunning share of algebra mistakes.
| Letter | What it means (plain words) | Value / unit |
|---|---|---|
| Q | any physical quantity — the thing being measured | number × unit |
| n | the pure number in front of the unit | dimensionless |
| u | the unit chosen | m, kg, s, … |
| N (unit) | newton — the unit of force | kg·m/s² (from F = ma) |
| J (unit) | joule — the unit of energy | kg·m²/s² (from W = F×d) |
Solved Examples
Multiply by the conversion fraction: 72 km/h × (1000 m / 1 km) × (1 h / 3600 s).
= 72 × 1000/3600 = 20 m/s.
Sanity check: 20 m each second — highway speed. ✔
Answer: 20 m/s
Assemble from base units: Force = kg·m/s²; divide by area m².
P → kg/(m·s²) — which physics names the pascal (Pa).
No memorisation, pure assembly. ✔
Answer: kg·m⁻¹·s⁻² = pascal (Pa)
Left: (m/s)² = m²/s². Right: 2 (m/s²) (m²) = m³/s².
m²/s² ≠ m³/s² — NOT homogeneous, so the formula is definitely wrong.
This check never proves a formula RIGHT, but reliably proves it WRONG — the cheapest error-filter in physics. ✔
Answer: Invalid — dimensions don’t match
- Converting km/h to m/s by dividing by 60. The chain is ×1000 then ÷3600 → net ÷3.6. Memorise: km/h ÷ 3.6 = m/s.
- Confusing the unit ‘newton’ with other N’s. Context decides; read the sentence, not just the letter.
- Treating ‘kilogram’ as if ‘kilo’ were separate. The base unit is the KILOgram, not the gram.
- Writing 1 h = 60 s in a chain. Hours → minutes → seconds; the 3600 trips everyone exactly once. Let it trip you here, now, forever.
This Physics in Your Daily Life
- Your electricity bill is in units (kWh) — a derived unit (kilowatt-hour) built from base units; 1 unit = 3.6 million joules of energy.
- Phone storage (GB), processor sizes (nm), drink labels (ml, kcal) — the prefix ladder runs your shopping: giga down to nano, powers of ten everywhere.
- NASA lost the $125-million Mars Climate Orbiter in 1999 to a pounds-vs-newtons mixup: units are money. The ₹500-crore Mars Orbiter Mission works because every engineer used the same units.
- Nutrition labels (kcal), medicine doses (mg), speed limits (km/h) — daily life is a running unit-conversion exam you already pass.
- 5G, Wi-Fi bands (GHz) and screen sizes (inches → cm) — the same seven-unit alphabet scaled by prefixes.
Two shopkeepers sell ‘rice for 60’. One means rupees per kilo, the other per pound — the same number, wildly different deals. A number without a unit is a cheque without a bank: impressive-looking, legally worthless. Units are the shared promise that 60 means the same thing to everyone.
A litre of milk is 1000 ml or 0.001 m³ — same milk, three settlements of number vs unit. Your charger: 5 V, 2 A → 10 W. Swap the unit (mA instead of A) and the number must move 1000× to keep the physics fixed: 2000 mA. Number × unit = the only invariant.
Draw a ladder of prefixes: each rung a power of ten — nano at the bottom, giga at the top. Any quantity can sit on any rung; climbing one rung divides the number by 1000 exactly. The ladder is the whole map of unit conversion.
Practice set (answers hidden — try first)
(NEET-level) 90 km/h in m/s:
(JEE Main-level) The SI unit of work in base units:
(NEET-level) Which is NOT a base quantity: mass, current, force, temperature?
(Concept) v² = u² + 2as is checked for homogeneity. Both sides have:
(JEE Main-level) 1 joule expressed using prefixes: 1 J = ? μJ
- quantity = number × unit; conversions keep the product fixed
- 7 base units: m, kg, s, A, K, mol, cd
- derived units are assembled, not memorised (N = kg·m/s²)
- km/h → m/s: divide by 3.6
- homogeneity check: units must match on both sides
- 🔁 quantity = number × unit
- 🔁 7 SI base units (m kg s A K mol cd)
- 🔁 km/h ÷ 3.6 = m/s
- 🧠 Chant: ‘divide by 3.6’ for km/h → m/s.
- 🧠 Base seven: ‘My Kid Saw A Kangaroo Making Cookies’ (m, kg, s, A, K, mol, cd).
- 🧠 N and J: ‘Newton pushes kg·m/s²; Joule carries kg·m²/s²’.
- 🏠 Daily: electricity units (kWh) = 3.6 MJ each.
- 🏠 Daily: Mars Orbiter crashed on a unit mixup — units are money.
Quick revision
- A physical quantity = number × unit; the number is meaningless without the unit
- Seven SI base units: metre (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol), candela (cd)
- Everything else (speed, force, energy…) is a DERIVED unit built from these seven
- Prefixes are powers of ten: kilo = 10³, milli = 10⁻³, micro = 10⁻⁶, nano = 10⁻⁹
- Check any equation: units on the left must match units on the right (homogeneity)
- Quantity = number × unit
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