Introduction to Units and Measurement

Physics begins where guessing ends: every law you will ever quote — F = ma, PV = nRT, E = hν — is a quantitative statement, and quantitative statements demand measurement. This opening topic of Units and Measurements builds the vocabulary for the whole chapter: what a physical quantity is, how the number-and-unit pair n × u works, why seven quantities are chosen as fundamental while the rest are derived, and how the same physics spans lengths from a nucleus to the observable universe. The vocabulary you meet here feeds directly into International System of Units (SI Units).

What is Introduction to Units and Measurement? — Complete Theory

1. Measurement: the number–unit pair

Any physical quantity is specified completely only when a number (how much) is paired with a unit (of what). We write Q = n × u, read as "the quantity equals n times the unit u". If you switch to a smaller unit, the number must grow so that the product stays fixed: 1 m = 100 cm. In symbols, n₁u₁ = n₂u₂, so n₂ = n₁(u₁/u₂). This innocent-looking relation is the seed of the full unit-conversion machinery you will meet on the dimensional analysis page, and it is why a "naked number" — a number without a unit — is physically meaningless and always wrong in an exam answer.

What makes a quantity "physical"? It must be measurable in principle: length, mass, time, temperature, current, pressure. Quantities like sadness or beauty admit no operational measurement, so they belong to philosophy, not physics. A good unit, in turn, must be (i) well defined — everyone agrees on its magnitude, (ii) invariable — it does not change with time or place, (iii) easily reproducible — any lab in the world can realise it, and (iv) internationally accepted. Historical units failed these tests: the cubit varied from forearm to forearm, and even the original metre (one ten-millionth of the Paris–North-Pole quadrant) depended on a survey with errors.

2. Fundamental (base) and derived quantities

Physics needs a surprisingly small toolkit. NCERT's strategy: pick a minimal set of quantities that are independent of each other — none can be expressed in terms of the others — define their units carefully, and build everything else by formula. The chosen seven are the fundamental (base) quantities: length, mass, time, electric current, thermodynamic temperature, amount of substance and luminous intensity. Their units are called base units and are tabulated in full on the SI units page.

Every other quantity is derived: its definition algebraically combines base quantities. Velocity is length/time, force is mass × length/time², charge is current × time. Two quantities deserve a special mention because they are geometric ratios with no base-dimension powers: the plane angle (radian) and solid angle (steradian). NCERT calls them supplementary units — they carry special names yet are dimensionless. You will see their exact definitions in the SI topic page.

3. Systems of units

Three historical systems coexisted before SI: CGS (centimetre, gram, second — used in older physics literature), FPS (foot, pound, second — British engineering) and MKS (metre, kilogram, second). SI, adopted in 1960 and revised in 2019, is MKS extended to all seven base quantities plus a clean prefix system. For JEE Main and NEET you must be fluent in switching between SI and CGS because NTA deliberately mixes them: energy arrives in erg, viscosity in poise, magnetic field in gauss. The conversion pipeline n₂ = n₁(M₁/M₂)ᵃ(L₁/L₂)ᵇ(T₁/T₂)ᶜ is worked out step by step on the Dimensional Analysis page; the memorised results (1 J = 10⁷ erg, 1 N = 10⁵ dyne) sit in the conversion bank on the chapter hub.

4. The range of physics: lengths, masses, times

One of the most exam-productive tables in NCERT is the range table. Physics spans lengths from ~10⁻¹⁵ m (a nucleus, measured in fermis) to ~10²⁶ m (the observable universe) — about 41 orders of magnitude. Masses run from the electron at 9.1 × 10⁻³¹ kg to the universe at ~10⁵⁵ kg. Times run from nuclear processes around 10⁻²² s (lifetime of unstable particles such as the muon in some tables ~10⁻²⁴ s) to the age of the universe, ~10¹⁸ s (a few billion years in seconds). Because no single unit is human-friendly across 41 decades, special units exist: fermi for nuclei, angstrom for atoms, astronomical unit for the solar system, light year and parsec for stars and galaxies.

5. Nature of physical laws (why measurement matters)

NCERT closes the introduction with a big-picture idea: conservation laws — of energy, linear momentum, angular momentum, charge — are the deep regularities that survive every change of units, frame and theory. Symmetry of nature implies conservation; conservation constrains what equations of physics may say. This is exactly why equations must be dimensionally homogeneous: a law that mixed kilograms with metres could not be a law at all. The formal test of homogeneity is developed on the Dimensions of Physical Quantities page.

Visualising Introduction to Units and Measurement

The ladder above is the visual anchor of this topic. Reproduce it mentally in the exam: place the object, locate the nearest anchor, count decades. For mass and time, build parallel ladders — electron 10⁻³₀ kg → Earth 10²⁴ →⁵ kg → Sun 10³⁰ kg → universe 10⁵⁵ kg; nuclear time 10⁻²² s → human heartbeat 10⁰ s → human lifetime 10⁹ s → age of universe 10¹⁸ s. Three anchors per ladder is enough to answer any ranking question.

Solved Examples on Introduction to Units and Measurement (Step-by-Step)

Solved Example 1 — Same quantity, three unit systems

Q. The rest mass of an electron is 9.11 × 10⁻³¹ kg. Express it (a) in gram, (b) in atomic mass units (1 u = 1.66 × 10⁻²⁷ kg).

Step 1 (kg → g). 1 kg = 10³ g, so multiply by 10³: m = 9.11 × 10⁻³¹ × 10³ g = 9.11 × 10⁻²⁸ g.

Step 2 (kg → u). Divide by the u-value: m = (9.11 × 10⁻³¹ kg) ÷ (1.66 × 10⁻²⁷ kg/u). Numbers: 9.11 ÷ 1.66 = 5.49 (since 1.66 × 5.49 ≈ 9.11). Powers: 10⁻³¹ ÷ 10⁻²⁷ = 10⁻⁴. So m = 5.49 × 10⁻⁴ u.

Step 3 (sanity check). An electron must be far lighter than a proton (≈1 u); 5.49 × 10⁻⁴ u is indeed about 1/1823 u — consistent with the known m_p/m_e ≈ 1836. ✔

Solved Example 2 — Ranking by orders of magnitude

Q. Arrange in increasing order: (i) thickness of paper ≈ 10⁻⁴ m, (ii) diameter of the Sun ≈ 1.4 × 10⁹ m, (iii) wavelength of green light ≈ 5 × 10⁻⁷ m, (iv) distance of the Sun from Earth ≈ 1.5 × 10¹¹ m.

Step 1. Extract exponents: 10⁻⁴, 10⁹·¹⁵, 10⁻⁶·³, 10¹¹·¹⁸.

Step 2. Sort exponents: −6.3 < −4 < +9.15 < +11.18.

Step 3. Map back: green light < paper < Sun's diameter < Sun–Earth distance.

Practice Questions on Introduction to Units and Measurement (With Solutions)

Practice Q1 (Numerical-value type)

Q. How many micrometres are there in exactly 1 kilometre?

Solution. 1 km = 10³ m; 1 μm = 10⁻⁶ m. Count = 10³ ÷ 10⁻⁶ = 10⁹.

Practice Q2 (Single-correct MCQ)

Q. Which of the following is a derived quantity? (a) length (b) electric current (c) force (d) thermodynamic temperature

Solution. Length, current and temperature are three of the seven base quantities. Force = mass × acceleration is built from them, so it is derived.

Practice Q3 (Assertion–Reason)

Q. Assertion (A): The statement "the length of this rod is 4.2" is physically incomplete. Reason (R): A physical quantity is fully specified only as n × u, a number with a unit.

Solution. Both A and R are true, and R is exactly the reason A fails: without the unit the number 4.2 could be metres, feet or light years — the quantity is unspecified.

Key Formulas & Takeaways

FAQs on Introduction to Units and Measurement

What is a physical quantity in physics?

A physical property that can be measured and expressed as a number with a unit, written as n × u — for example, length = 4.2 m. The number alone is meaningless without the unit.

Which quantities are called fundamental (base) quantities?

Seven quantities — length, mass, time, electric current, thermodynamic temperature, amount of substance and luminous intensity — are independent of each other and are chosen as fundamental (base) quantities; all others are derived from them.

What is the range of lengths physics deals with?

From the size of a nucleus (~10⁻¹⁵ m) to the size of the observable universe (~10²⁶ m) — a span of about 41 orders of magnitude, which is why special units like the fermi, light year and parsec exist.

Why do we need measurement in physics?

Physics is an exact experimental science: laws are verified quantitatively, so every observation must be expressed as a measured number with a unit; without measurement, laws like F = ma could not be tested.