Units and Measurements Class 11: Worked Examples

In Class 11 Units and Measurements, a correct calculator answer can still be a poor physics answer. A length needs a unit; a calculated result needs sensible precision; an equation needs matching dimensions. This chapter teaches you to check all three before moving to longer numericals.

The CBSE 2026-27 Physics syllabus lists Units and Measurements as Chapter 1. Its scope includes SI units, fundamental and derived units, significant figures, uncertainty in results, dimensions and dimensional analysis. Use the worked examples below to practise those ideas, rather than memorising an unexplained formula list.

Start with the quantity, then its unit

A measurement compares a physical quantity with an agreed standard. In 2.4 m, the number is 2.4 and the unit is metre. Writing only 2.4 leaves the measurement incomplete.

The seven SI base quantity-unit pairs are:

• Length: metre (m)
• Mass: kilogram (kg)
• Time: second (s)
• Electric current: ampere (A)
• Thermodynamic temperature: kelvin (K)
• Amount of substance: mole (mol)
• Luminous intensity: candela (cd)

Derived units come from combinations of base units. Speed is distance divided by time, so its SI unit is m/s. Acceleration has unit m/s²; force has unit kg m/s², also called the newton (N). The kilogram, not the gram, is the SI base unit of mass.

Convert the whole unit, including its power

Worked example: convert 36 km/h into m/s.

36 × 1000 ÷ 3600 = 10, so 36 km/h = 10 m/s. Both the kilometre and the hour need converting.

For area, square the conversion factor: 1 cm² = (10⁻² m)² = 10⁻⁴ m². For volume, cube it. Thus 1 cm³ = 10⁻⁶ m³. Changing only the prefix while ignoring the power gives a different physical quantity.

Count significant figures without counting every zero

Significant figures describe the precision conveyed by a measured value. Non-zero digits count. Zeros between non-zero digits count. Leading zeros merely locate the decimal point; trailing zeros after a decimal can record precision.

• 0.00420 has three significant figures: 4, 2 and the final 0.
• 5.006 has four significant figures.
• 2.50 × 10³ has three significant figures, regardless of the exponent.

A bare whole number such as 2500 can leave its intended precision unclear. Scientific notation distinguishes 2.5 × 10³ from 2.500 × 10³. Converting units must not invent extra measurement precision.

Choose the calculation rule before rounding

Multiplication or division: keep as many significant figures as the measured input with the fewest significant figures. A rectangle measures 3.24 cm by 2.1 cm. Its calculated area is 6.804 cm², reported as 6.8 cm² because 2.1 has two significant figures.

Addition or subtraction: use decimal places instead. Adding 12.36 cm and 1.2 cm gives 13.56 cm, reported as 13.6 cm. The second measurement is stated only to one decimal place.

Keep extra digits during intermediate steps and round the final result. For an exact halfway case, NCERT uses the round-to-even convention: 2.465 becomes 2.46 to three significant figures, while 2.475 becomes 2.48. These examples assume there are no further non-zero digits after the 5.

Read a stated uncertainty carefully

If a question supplies a length as (25.0 ± 0.2) cm, keep the uncertainty with the same unit. Its relative uncertainty is 0.2/25.0 = 0.008; expressed as a percentage, that is 0.8%.

This calculation uses the uncertainty given in the question. Do not replace it with a guessed instrument error, or treat the central value as exact. A percentage alone also does not tell you a confidence level: that needs the stated uncertainty model. Significant-figure rounding is not a substitute for a full uncertainty calculation.

Build dimensions from a defining equation

Units and dimensions answer different questions. Metres and centimetres are different units of length, but both have dimension L. In mechanics, M, L and T represent mass, length and time.

Start from force = mass × acceleration. Since acceleration has dimension LT⁻², force has dimensional formula [MLT⁻²]. Pressure is force/area, so its formula is [ML⁻¹T⁻²]. Deriving the powers makes the result easier to check.

Test v = u + at: each term has dimension LT⁻¹. By contrast, v = u + at² fails because at² has dimension L. A dimensional mismatch proves an equation wrong. Matching dimensions does not prove it right: dimensions cannot decide whether a numerical coefficient should be 1 or 1/2.

Use a short mixed practice check

Without looking back, convert 2 cm² to m², count the significant figures in 0.0300, and derive the dimensions of energy from force × distance. The answers are 2 × 10⁻⁴ m², three, and [ML²T⁻²]. If one goes wrong, record the exact reason in an exam mistake log, then retry a changed example.

Sources: chapter scope checked against the CBSE 2026-27 Physics syllabus, pages 2-3. Concepts and rounding conventions follow NCERT Physics Chapter 1; the relative-uncertainty ratio is also explained by NIST. Worked examples here are original.

Frequently asked questions

Is Units and Measurements Chapter 1 in CBSE Class 11?

Yes. The CBSE 2026-27 Physics syllabus lists it as Chapter 1 under Physical World and Measurement.

Is dimensional analysis enough to verify a formula?

No. It detects dimensional mismatches but cannot determine dimensionless numerical coefficients.

Do addition and multiplication use the same rounding rule?

No. Addition uses decimal-place precision; multiplication uses the fewest significant figures among measured inputs.

Do leading zeros count as significant figures?

No. In 0.0300, the leading zeros do not count, but the two trailing zeros do, giving three significant figures.