JEE Mains Physics · Units and Measurements

Units, Significant Figures and Order of Magnitude

A result keeps the fewest decimal places of its terms when they are added and the fewest significant figures of its factors when they are multiplied; very large distances are given in astronomical units, light years and parsecs.

All Units and Measurements notes JEE Mains Physics strategy

Why this matters

Ten PYQs, all multiple choice, and two from 2026. Five apply the significant-figure rules to a sum, a product or a mean, or count the significant figures in a number; five are about astronomical distances, angles in seconds of arc and the order of magnitude of a number. Each one is a single rule, so the marks go to knowing the rule exactly.

Concept 1 of 2: Significant figures in sums, products and means

A measured number shows how precisely it was read. A sum cannot be more precise than its roughest term, so it keeps the fewest DECIMAL PLACES. A product or a quotient cannot be more precise than its least precise factor, so it keeps the fewest SIGNIFICANT FIGURES. The two rules look alike and the options are built to catch a mix-up.

Definition

Counting: every non-zero digit counts; zeros between non-zero digits count; leading zeros never count (0.0042 has 2); trailing zeros count only when there is a decimal point (4.200 has 4, 4200 is ambiguous; write 4.2 × 10³ for 2).
Adding or subtracting: round the answer to the fewest decimal places among the terms.
Multiplying or dividing: round the answer to the fewest significant figures among the factors.
A mean of readings is reported to the decimal place of the least precise reading.
Rounding: above 5, round up; below 5, round down; exactly 5 followed by nothing, round to the even digit (2.745 → 2.74, 2.735 → 2.74).
Exact numbers (a count, the 2 in 2πr) have unlimited significant figures and never limit the answer.

Rounding rules

\text{sum or difference: fewest decimal places} \qquad \text{product or quotient: fewest significant figures}

Worked example

Report, to the correct significant figures, (a) the sum of 12.11 g, 3.2 g and 0.456 g, and (b) the product 4.52 cm × 2.1 cm.

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

JEE Mains · 2026 · 21 Jan 2026 Shift 2 · Q11Moderate

Example 1 · Units and Measurements · Units, Significant Figures and Order of Magnitude

Keeping the significant figures in view, the sum of the physical quantities

52.01\text{ }m,153.2\text{ }m

and 0.123 m is :

A sum is rounded by decimal places, not by significant figures

When numbers are added, the answer keeps the fewest decimal places, even if that leaves it with more significant figures than some term. 101.1 + 0.25 = 101.35, reported as 101.4 with four significant figures, although 0.25 has only two.

Leading zeros never count

In 0.0010010 the first three zeros only place the decimal point. The significant figures are 1, 0, 0, 1, 0 — five of them. The trailing zero counts because the number has a decimal point.

Drill 4 more on significant figures in sums, products and means

Concept 2 of 2: Astronomical units of length, seconds of arc and order of magnitude

Distances in astronomy are too large for metres, so three bigger units are used. In increasing size: the astronomical unit (Earth to Sun), the light year (the distance light covers in a year) and the parsec. A distant object's size is found from the small angle it subtends: size = angle in radians × distance.

Definition

$1\ \text{AU} < 1\ \text{ly} < 1\ \text{pc}$ .
One second of arc: $1'' = \dfrac{1}{3600}$ degree $= 4.85 \times 10^{-6}$ rad.
Small angle: $d = \theta D$ , with $\theta$ in radians.
A parsec is the distance at which 1 AU subtends 1″.
Order of magnitude of $a \times 10^{b}$ (with $1 \le a < 10$ ): $b$ if $a \le 5$ , and $b + 1$ if $a > 5$ .

Unit or quantity	Value	How it is defined
Astronomical unit (AU)	$1.496 \times 10^{11}$ m	Mean distance from the Earth to the Sun
Light year (ly)	$9.46 \times 10^{15}$ m	Distance light travels in one year
Parsec (pc)	$3.08 \times 10^{16}$ m	Distance at which 1 AU subtends one second of arc The parsec is the largest of the three, about 3.26 light years.
Light second	$3.0 \times 10^{8}$ m	Distance light travels in one second
One second of arc (1″)	$4.85 \times 10^{-6}$ rad	One 3600th of a degree
One degree	$1.745 \times 10^{-2}$ rad	$\pi/180$ radian

In increasing size: astronomical unit, light year, parsec.

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

JEE Mains · 2023 · 11 April 2023 · Q17Moderate

Example 2 · Units and Measurements · Units, Significant Figures and Order of Magnitude

Given below are two statements: Statements I: Astronomical unit (Au). Parsec (Pc) and Light year (ly) are units for measuring astronomical distances. Statements II:

Au <

Parsec

(Pc) <

ly In the light of the above statements. choose the most appropriate answer from the options given below:

The parsec is bigger than the light year

A parsec is about 3.26 light years. The order is AU < light year < parsec. A statement that puts the parsec between the AU and the light year is false.

Convert the angle to radians first

In d = θD the angle must be in radians. Seconds of arc are multiplied by 4.85 × 10⁻⁶; leaving the angle in seconds or degrees gives a size wrong by a factor of thousands.

Drill 4 more on astronomical units of length, seconds of arc and order of magnitude

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (1)

Significant figures in sums, products and means
Rounding rules
$\text{sum or difference: fewest decimal places} \qquad \text{product or quotient: fewest significant figures}$

Reference tables (1)

Astronomical units of length, seconds of arc and order of magnitude6 rows

Unit or quantity	Value	How it is defined
Astronomical unit (AU)	$1.496 \times 10^{11}$ m	Mean distance from the Earth to the Sun
Light year (ly)	$9.46 \times 10^{15}$ m	Distance light travels in one year
Parsec (pc)	$3.08 \times 10^{16}$ m	Distance at which 1 AU subtends one second of arc The parsec is the largest of the three, about 3.26 light years.
Light second	$3.0 \times 10^{8}$ m	Distance light travels in one second
One second of arc (1″)	$4.85 \times 10^{-6}$ rad	One 3600th of a degree
One degree	$1.745 \times 10^{-2}$ rad	$\pi/180$ radian

In increasing size: astronomical unit, light year, parsec.

Watch out for (4)

A sum is rounded by decimal places, not by significant figures
→ Significant figures in sums, products and means
Leading zeros never count
→ Significant figures in sums, products and means
The parsec is bigger than the light year
→ Astronomical units of length, seconds of arc and order of magnitude
Convert the angle to radians first
→ Astronomical units of length, seconds of arc and order of magnitude

Test yourself on Units and Measurements

20 past JEE Mains questions from this chapter, timed at 48 minutes and marked the way the exam marks it. You see your score and every answer the moment you finish. Free to start.

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