Units and Measurements ISC Class 11: Notes and Numericals

What Units and Measurements is about

Weightage: Units and Measurements belongs to unit 1 of the ISC Class XI Physics syllabus. CISCE weights units 1-3 together (Physical World and Measurement; Kinematics; Laws of Motion) at 23 of the 70 marks in Paper I (Theory). Class XI is examined by the school, so your school sets the paper within this weightage.Source: CISCE ISC Physics syllabus, examination year 2028, Class XI unit weightage

Key concepts

Physical quantities, systems of units and the SI base units

A fundamental (base) quantity is chosen to be independent of others; a derived quantity is built from base quantities (speed = length/time). The SI has seven base units, each now defined by fixing a constant of nature: the second by the caesium-133 hyperfine frequency (9 192 631 770 Hz); the metre by the speed of light (299 792 458 m s⁻¹); the kilogram by Planck's constant ($6.62607015\times 10^{-34}$ J s); the ampere by the elementary charge ($1.602176634\times 10^{-19}$ C); the kelvin by the Boltzmann constant ($1.380649\times 10^{-23}$ J K⁻¹); the mole as exactly $6.02214076\times 10^{23}$ entities; and the candela by the luminous efficacy (683 lm W⁻¹) of radiation of frequency $540\times 10^{12}$ Hz. The supplementary units are the radian (plane angle = arc/radius) and the steradian (solid angle = area/radius²). Older systems: CGS, FPS, MKS and MKSA (MKS plus the ampere).

Worked example

Express the SI unit of (a) pressure and (b) power in base units, and state which supplementary unit is used for the solid angle subtended by a cone.

Try it first, then show the solutionSolution

1. (a) Pressure = force/area; 1 N = 1 kg m s⁻², so 1 Pa = 1 N m⁻² = 1 kg m⁻¹ s⁻².
2. (b) Power = work/time; 1 J = 1 kg m² s⁻², so 1 W = 1 J s⁻¹ = 1 kg m² s⁻³.
3. Solid angle is measured in steradian (sr).

Answer: (a) kg m⁻¹ s⁻² (b) kg m² s⁻³; steradian

Prefixes, practical units and the rules for writing units

Prefixes: atto (a) $10^{-18}$, femto (f) $10^{-15}$, pico (p) $10^{-12}$, nano (n) $10^{-9}$, micro (μ) $10^{-6}$, milli (m) $10^{-3}$, centi (c) $10^{-2}$, deci (d) $10^{-1}$, deca (da) $10^1$, hecto (h) $10^2$, kilo (k) $10^3$, mega (M) $10^6$, giga (G) $10^9$, tera (T) $10^{12}$. Practical units: 1 fermi = 1 fm = $10^{-15}$ m (nuclear sizes); 1 angstrom = 1 Å = $10^{-10}$ m (atomic sizes); light year = distance light travels in one year ≈ $9.46\times 10^{15}$ m; astronomical unit = mean Earth-Sun distance ≈ $1.496\times 10^{11}$ m; parsec = distance at which 1 AU subtends 1 second of arc ≈ $3.08\times 10^{16}$ m ≈ 3.26 ly; unified atomic mass unit 1 u = $\frac{1}{12}$ of the mass of a carbon-12 atom ≈ $1.66\times 10^{-27}$ kg (write u, not amu). Rules: unit names are written in lower case even when named after a person (newton, joule) but their symbols take a capital (N, J); symbols take no plural and no full stop (5 kg, not 5 kgs.); leave a space between number and unit; use one prefix only (ns, not mμs).

Worked example

A star is 8.6 light years away. Express this distance in metres and in parsec. (1 ly = $9.46\times 10^{15}$ m, 1 pc = $3.086\times 10^{16}$ m)

Try it first, then show the solutionSolution

1. $d=8.6\times 9.46\times 10^{15}=8.14\times 10^{16}m$
2. $d=\frac{8.14\times 10^{16}}{3.086\times 10^{16}}=2.64pc$

Answer: $8.1\times 10^{16}$ m, about 2.6 pc

Measuring length, mass and time

Length: a metre rule (least count 1 mm), vernier callipers (least count LC = 1 MSD − 1 VSD, usually 0.1 mm) and a screw gauge (LC = pitch ÷ number of circular-scale divisions, usually 0.01 mm). For large distances use the parallax method: viewing a distant object from two points a baseline b apart, the angle θ (in radian) between the two lines of sight gives the distance $D=\frac{b}{\theta }$. For atomic sizes, use indirect methods (electron microscopes, X-ray diffraction). Mass: a common or electronic balance for everyday masses; for atoms, a mass spectrograph, with results in u. Time: pendulum clocks and quartz clocks for everyday use; atomic (caesium) clocks for the most precise standard. A zero error (positive or negative) is a systematic error and must be subtracted from the observed reading.

Worked example

To find the width of a river, a student stands opposite a tree on the far bank and walks 100 m along the bank. The line of sight to the tree turns through 2.0°. Estimate the width of the river.

Try it first, then show the solutionSolution

1. $\theta =2.0\times \frac{\pi }{180}=0.0349rad$
2. $D=\frac{b}{\theta }=\frac{100}{0.0349}=2.86\times 10^{3}m$

Answer: About 2.9 km (the small-angle relation D = b/θ needs θ in radian)

Errors in measurement

Systematic errors push every reading the same way (instrument errors such as zero error, imperfect technique, personal bias); they are reduced by better instruments and corrections. Random errors vary unpredictably from reading to reading; they are reduced by taking many readings and averaging. The least count of an instrument limits its precision. For n readings $a_1,a_2,...,a_n$: true value ≈ mean $\bar{a}$; absolute error $\Delta a_i=a_i-\bar{a}$; mean absolute error $\overline{\Delta a}=\frac{\sum |\Delta a_i|}{n}$; result $a=\bar{a}\pm \overline{\Delta a}$; relative error $=\frac{\overline{\Delta a}}{\bar{a}}$; percentage error $=\frac{\overline{\Delta a}}{\bar{a}}\times 100\%$. Accuracy is how close a result is to the true value; precision is how finely it is resolved (and how closely repeated readings agree).

Worked example

Five readings of the time period of a pendulum are 1.98 s, 2.04 s, 2.01 s, 1.97 s and 2.05 s. Find the mean, the mean absolute error and the percentage error.

Try it first, then show the solutionSolution

1. Mean $=\frac{10.05}{5}=2.01s$
2. |Deviations| = 0.03, 0.03, 0.00, 0.04, 0.04; mean absolute error $=\frac{0.14}{5}=0.028\approx 0.03s$
3. Percentage error $=\frac{0.028}{2.01}\times 100=1.4\%$

Answer: T = (2.01 ± 0.03) s; about 1.4%

Combination of errors

Sum or difference: if Z = A + B or Z = A − B, the maximum absolute error is $\Delta Z=\Delta A+\Delta B$ (absolute errors always add). Product or quotient: if Z = AB or Z = A/B, $\frac{\Delta Z}{Z}=\frac{\Delta A}{A}+\frac{\Delta B}{B}$ (relative errors add). Power: if $Z=A^n$, $\frac{\Delta Z}{Z}=n\frac{\Delta A}{A}$. In general, for $Z=\frac{A^p{B}^q}{C^r}$, $\frac{\Delta Z}{Z}=p\frac{\Delta A}{A}+q\frac{\Delta B}{B}+r\frac{\Delta C}{C}$. The quantity with the highest power contributes most, so it should be measured most carefully. Errors never cancel: a minus sign in the formula still gives a plus in the error.

Worked example

Two resistances $R_1=(100\pm 3)\Omega$ and $R_2=(200\pm 4)\Omega$ are joined in series. Find the equivalent resistance with its error, and the percentage error.

Try it first, then show the solutionSolution

1. $R=R_1+R_2=300\Omega$
2. $\Delta R=3+4=7\Omega$
3. Percentage error $=\frac{7}{300}\times 100=2.3\%$

Answer: (300 ± 7) Ω; about 2.3%

Significant figures and rounding off

Significant figures are the reliable digits plus the first uncertain digit. Counting rules: all non-zero digits count; zeros between non-zero digits count (2006 has 4); leading zeros never count (0.0045 has 2); trailing zeros after a decimal point count (2.300 has 4); trailing zeros in a whole number without a decimal point are ambiguous, so use scientific notation ($4.50\times 10^3$ has 3). A change of units does not change the number of significant figures. Arithmetic: in multiplication and division, keep as many significant figures as the factor with the fewest significant figures; in addition and subtraction, keep as many decimal places as the quantity with the fewest decimal places. Rounding: if the dropped digit is more than 5, raise the last kept digit; if less than 5, leave it; if exactly 5 (followed by nothing), raise an odd preceding digit and leave an even one. Round only the final answer, not intermediate steps.

Worked example

State the number of significant figures in 0.004060 and in $6.020\times 10^{23}$. Then evaluate 12.6 + 3.215 + 0.04 and 2.5 × 3.142 to the correct significant figures.

Try it first, then show the solutionSolution

1. 0.004060: leading zeros do not count; 4, 0, 6, 0 do: 4 significant figures. $6.020\times 10^{23}$: 4 significant figures.
2. Sum = 15.855; the least number of decimal places is one (12.6), so 15.9.
3. Product = 7.855; 2.5 has two significant figures, so 7.9.

Answer: 4 and 4; 15.9; 7.9

Dimensions, dimensional formula and the principle of homogeneity

The dimensions of a quantity are the powers to which the base quantities must be raised to represent it; the dimensional formula writes these, e.g. force [M L T⁻²]. Useful formulae: velocity [L T⁻¹]; acceleration [L T⁻²]; momentum and impulse [M L T⁻¹]; work and energy [M L² T⁻²]; power [M L² T⁻³]; pressure, stress and Young's modulus [M L⁻¹ T⁻²]; angular momentum and Planck's constant [M L² T⁻¹]; G [M⁻¹ L³ T⁻²]; surface tension [M T⁻²]; coefficient of viscosity [M L⁻¹ T⁻¹]. Angle, strain, refractive index and relative density are dimensionless. A dimensional constant has dimensions (G, h, c); a dimensionless constant has none (π, 2). The principle of homogeneity: quantities can be added, subtracted or equated only if they have the same dimensions, so every term of a correct equation has the same dimensions.

Worked example

Find the dimensional formula of the gravitational constant G from $F=\frac{G{m}_1{m}_2}{r^2}$, and its SI unit.

Try it first, then show the solutionSolution

1. $G=\frac{F{r}^2}{m_1{m}_2}$
2. $[G]=\frac{[ML{T}^{-2}][L^2]}{[M^2]}=[M^{-1}{L}^3{T}^{-2}]$
3. Unit: N m² kg⁻²

Answer: [M⁻¹ L³ T⁻²]; N m² kg⁻²

Uses and limitations of dimensional analysis; order of magnitude

Uses: (1) checking an equation: if the terms have different dimensions it is certainly wrong; (2) deriving a relation: assume $Q=k{A}^a{B}^b{C}^c$, equate powers of M, L and T and solve; (3) converting units: $n_2=n_1{\left[\frac{M_1}{M_2}\right]}^a{\left[\frac{L_1}{L_2}\right]}^b{\left[\frac{T_1}{T_2}\right]}^c$ for a quantity of dimensions $[M^a{L}^b{T}^c]$. Limitations: it cannot find dimensionless constants (the ½ in $\frac{1}{2}m{v}^2$, the 2π in a pendulum's period); it cannot derive relations with sums or differences of terms ($s=ut+\frac{1}{2}a{t}^2$) or with trigonometric, exponential or log functions; it fails if the quantity depends on more than three variables in mechanics (only three equations); a dimensionally correct equation need not be correct. Order of magnitude: write the number as $a\times 10^b$; if a ≤ 5 the order is $10^b$, and if a > 5 it is $10^{b+1}$.

Worked example

Assume the period T of a simple pendulum depends on its length l, the mass m of the bob and g. Derive the relation by dimensions.

Try it first, then show the solutionSolution

1. $T=k{l}^a{m}^b{g}^c$: $[T]=[L{]}^a[M{]}^b[L{T}^{-2}{]}^c$
2. M: b = 0. T: −2c = 1, so c = −½. L: a + c = 0, so a = ½.
3. $T=k\sqrt{\frac{l}{g}}$ (experiment gives k = 2π; the period does not depend on the mass)

Answer: $T=k\sqrt{l/g}$, independent of m

Physics in real life: Units and Measurements

Each concept, met in an everyday situation. Read the situation, try the problem, then check the solution. The one-line hook is what to remember.

Topics in this chapter

• Combination of Errors
• Dimensional Analysis and Its Uses

Units and Measurements formula sheet

Mean absolute error

$\overline{\Delta a}=\frac{|\Delta a_1|+|\Delta a_2|+...+|\Delta a_n|}{n}$

Result: $a=\bar{a}\pm \overline{\Delta a}$.

Relative and percentage error

$\delta a=\frac{\overline{\Delta a}}{\bar{a}},\text{percentage error}=\frac{\overline{\Delta a}}{\bar{a}}\times 100\%$

No unit.

Error in a sum or difference

$Z=A\pm B\Rightarrow \Delta Z=\Delta A+\Delta B$

Absolute errors add even for a difference.

Error in a product or quotient

$Z=AB\text{or}\frac{A}{B}\Rightarrow \frac{\Delta Z}{Z}=\frac{\Delta A}{A}+\frac{\Delta B}{B}$

Relative errors add.

Error in a power

$Z=\frac{A^p{B}^q}{C^r}\Rightarrow \frac{\Delta Z}{Z}=p\frac{\Delta A}{A}+q\frac{\Delta B}{B}+r\frac{\Delta C}{C}$

Powers multiply the relative error.

Parallax distance

$D=\frac{b}{\theta }$

θ in radian; b is the baseline.

Least count of vernier callipers

$LC=1MSD-1VSD=\frac{1MSD}{n}$

Usually 0.1 mm (n = 10 VSD = 9 MSD).

Least count of a screw gauge

$LC=\frac{\text{pitch}}{\text{number of circular-scale divisions}}$

Usually 0.5 mm/50 = 0.01 mm.

Conversion of units

$n_2=n_1{\left[\frac{M_1}{M_2}\right]}^a{\left[\frac{L_1}{L_2}\right]}^b{\left[\frac{T_1}{T_2}\right]}^c$

For a quantity $[M^a{L}^b{T}^c]$; nu = constant.

Practical units

$1ly=9.46\times 10^{15}m;1AU=1.496\times 10^{11}m;1pc=3.08\times 10^{16}m$

1 pc ≈ 3.26 ly; 1 u = $1.66\times 10^{-27}$ kg.

Units and Measurements: diagrams to practise

Practise each one on paper: draw it from the checklist, then tick off every label.

How the school exam asks Units and Measurements

The question patterns to expect, and the method that works for each.

Tricks to remember Units and Measurements

Short memory aids. Say each one aloud once, then use it on a question the same day.

• Seven base units

  "My Kitten Sleeps And Keeps Many Cushions": metre, kilogram, second, ampere, kelvin, mole, candela.

  Use it when: Listing the SI base units in order.

• Errors always add

  Sums and differences add absolute errors; products and quotients add relative errors; a power multiplies its error. Never subtract an error.

  Use it when: Every combination-of-errors numerical.

• Add by places, multiply by figures

  Plus or minus: count decimal Places. Times or divide: count significant Figures.

  Use it when: Rounding results of calculations.

• Prefix ladder

  a f p n μ m | k M G T: each step is 10³ (atto to tera), with c, d, da, h filling the gap near 1.

  Use it when: Prefix conversions.

• Dimensions of the big five

  Force MLT⁻², energy ML²T⁻², power ML²T⁻³, pressure ML⁻¹T⁻², angular momentum ML²T⁻¹: each comes from the one before it.

  Use it when: Writing dimensional formulae quickly.

Units and Measurements: exam-level solved questions

Ordered from exam level to HOTS. Cover the solution, write your own, then compare step by step.

Case-study practice (Section D style)

Read the situation, then answer every part. In a school exam set on the board pattern this is a 5-mark question split into 1 + 1 + 1 + 2 marks.

Where the marks are

How a typical answer is split into step marks. Show every step: a right final answer alone rarely earns full marks.

Where students lose marks in Units and Measurements

The slips examiners see most often, and what to write instead.

• ✗Mistake: Subtracting errors for a difference or a quotient

  Students see a minus sign or a division and subtract the errors, but each error is a maximum possible error and can push the result either way.

  Wrong working

  Z = A − B with ΔA = 0.3 and ΔB = 0.2, so ΔZ = 0.1.

  Right working

  ΔZ = ΔA + ΔB = 0.5; for a quotient, add the relative errors.

  ✓Do this: Write 'errors always add' at the top of every error question.

  Usually costs: 1-2 marks.

• ✗Mistake: Forgetting to multiply the relative error by the power

  In $g=4{\pi }^{2}l/T^2$ the error in T counts twice, and in $\sqrt{d}$ it counts half; students simply add the percentages.

  Wrong working

  Δg/g = 0.1% + 0.5% = 0.6%.

  Right working

  Δg/g = 0.1% + 2(0.5%) = 1.1%.

  ✓Do this: Copy the powers from the formula into the error expression before substituting numbers.

  Usually costs: 1 mark.

• ✗Mistake: Rounding in the middle and using the wrong rule

  Students round each intermediate value, or count significant figures in an addition, so the final digit drifts.

  Wrong working

  12.6 + 3.215 + 0.04 = 15.86 (three decimal-place values kept to two), or 2.5 × 3.142 = 7.855.

  Right working

  Sum to one decimal place: 15.9. Product to two significant figures: 7.9. Round once, at the end.

  ✓Do this: Decimal places for + and −, significant figures for × and ÷.

  Usually costs: 1 mark.

• ✗Mistake: Breaking the rules for writing units

  Units such as 'Kg', '5 kgs.', 'Newton' as a symbol, 'amu' or a light year used as a time lose the mark for the unit.

  Wrong working

  m = 5 Kgs.; 1 amu = 1.66 × 10⁻²⁷ kg; a light year is the time light takes to travel a year.

  Right working

  m = 5 kg; 1 u = 1.66 × 10⁻²⁷ kg; a light year is the distance light travels in one year.

  ✓Do this: Symbols: correct case, no plural, no full stop; u, not amu.

  Usually costs: ½-1 mark.

• ✗Mistake: Getting the sign of the zero error wrong

  When the vernier zero lies to the right of the main-scale zero the error is positive and must be subtracted; students add it.

  Wrong working

  Corrected reading = 2.36 + 0.03 = 2.39 cm.

  Right working

  Corrected reading = observed reading − zero error = 2.36 − (+0.03) = 2.33 cm.

  ✓Do this: Always subtract the zero error with its sign.

  Usually costs: 1 mark.

Practice questions on Units and Measurements

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

1. Q1 · 1 mark · MCQExam level

   Which of the following is not an SI base unit?
   (a) kelvin
   (b) candela
   (c) newton
   (d) mole

   Hint

   Base or derived?

   Answer

   (c) newton (it is derived: kg m s⁻²)

2. Q2 · 1 mark · MCQExam level

   The number of significant figures in 0.050400 is:
   (a) 3
   (b) 4
   (c) 5
   (d) 6

   Hint

   Leading zeros never count.

   Answer

   (c) 5 (5, 0, 4, 0, 0)

3. Q3 · 1 mark · Very short answerExam level

   Define one parsec.

   Hint

   One astronomical unit and one second of arc.

   Answer

   The distance at which a length of 1 AU subtends an angle of 1 second of arc; about $3.08\times 10^{16}$ m.

4. Q4 · 1 mark · Very short answerExam level

   Write the dimensional formula of surface tension (force per unit length) and of stress.

   Hint

   Divide force by length, then by area.

   Answer

   Surface tension [M T⁻²]; stress [M L⁻¹ T⁻²].

5. Q5 · 2 marks · Short answerExam level

   Distinguish between systematic and random errors, giving one way to reduce each.

   Hint

   One direction or both directions?

   Answer

   Systematic errors shift every reading in the same direction (e.g. zero error); reduce them by correcting for them or using a better instrument. Random errors vary irregularly; reduce them by taking many readings and averaging.

6. Q6 · 2 marks · Short answerHarder exam level

   Convert a power of 1 W into erg s⁻¹ using dimensions.

   Hint

   [M L² T⁻³].

   Answer

   $n_2=1\times (1000{)}^1\times (100{)}^2\times 1=10^7$, so 1 W = $10^7$ erg s⁻¹.

7. Q7 · 2 marks · Short answerHarder exam level

   The radius of a sphere is measured as (2.10 ± 0.02) cm. Find the percentage error in its volume.

   Hint

   V ∝ r³.

   Answer

   ΔV/V = 3 × 0.02/2.10 = 0.0286, about 2.9%.

8. Q8 · 2 marks · Short answerHarder exam level

   Check the correctness of the relation $T=2\pi \sqrt{\frac{m}{k}}$ for a mass m on a spring of force constant k (force per unit extension).

   Hint

   [k] = [M T⁻²].

   Answer

   [m/k] = [M]/[M T⁻²] = [T²], so $\sqrt{m/k}$ has dimension [T]; the relation is dimensionally correct.

9. Q9 · 2 marks · Short answerHarder exam level

   A student finds the density of a cube as $\rho =\frac{m}{l^3}$. The percentage errors in m and l are 1.5% and 1%. Find the percentage error in ρ. Which measurement should be improved first, and why?

   Hint

   Power three.

   Answer

   Δρ/ρ = 1.5 + 3(1) = 4.5%. Improve the length measurement: its error is multiplied by 3.

10. Q10 · 2 marks · Short answerHarder exam level

    The distance of the Moon from the Earth is $3.84\times 10^8$ m and of the Sun $1.496\times 10^{11}$ m. Write the order of magnitude of each and of their ratio.

    Hint

    a ≤ 5 keeps the power; a > 5 raises it.

    Answer

    Moon: $10^8$ m (3.84 ≤ 5). Sun: $10^{11}$ m. Ratio = 389.6 = $3.9\times 10^2$, order $10^2$.

11. Q11 · 3 marks · Short answerHarder exam level

    A screw gauge has a pitch of 0.5 mm and 50 circular-scale divisions. Measuring a wire, the main-scale reading is 2 mm and the 34th division coincides; the gauge has a negative zero error of 3 divisions. Find the diameter of the wire.

    Hint

    Subtract a negative error.

    Answer

    LC = 0.5/50 = 0.01 mm. Observed = 2 + 34 × 0.01 = 2.34 mm. Zero error = −0.03 mm, so corrected = 2.34 − (−0.03) = 2.37 mm.

12. Q12 · 5 marks · Long answerHarder exam level

    The kinetic energy of a body depends on its mass m and speed v. (a) Derive the form of the relation by dimensions. (b) Why can the method not give the factor ½? (c) If the percentage errors in m and v are 2% and 3%, find the percentage error in the kinetic energy.

    Hint

    [M L² T⁻²] = [M]^a[L T⁻¹]^b.

    Answer

    (a) a = 1; from T: −b = −2, so b = 2; L: b = 2 ✓, so $E=km{v}^2$. (b) ½ is a pure number with no dimensions, so the method cannot detect it. (c) ΔE/E = 2 + 2(3) = 8%.

13. Q13 · 3 marks · Short answerHOTS / competency

    A tyre is inflated to a gauge pressure of $1.0\times 10^5$ Pa. Express this pressure in a system whose units of mass, length and time are α kg, β m and γ s. Hence find its value in dyn cm⁻².

    Hint

    Pressure is [M L⁻¹ T⁻²].

    Answer

    $n_2=10^5{\left[\frac{1}{\alpha }\right]}^1{\left[\frac{1}{\beta }\right]}^{-1}{\left[\frac{1}{\gamma }\right]}^{-2}=\frac{10^5\beta {\gamma }^2}{\alpha }$ new units. In CGS, α = 10⁻³, β = 10⁻², γ = 1: $n_2=\frac{10^5\times 10^{-2}}{10^{-3}}=10^6$ dyn cm⁻².

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1. 1.Name the seven SI base units.Show answer

   Metre, kilogram, second, ampere, kelvin, mole, candela.

2. 2.What are the two supplementary units?Show answer

   Radian (plane angle) and steradian (solid angle).

3. 3.1 light year in metres?Show answer

   About $9.46\times 10^{15}$ m.

4. 4.How do relative errors combine in a product?Show answer

   They add: $\frac{\Delta Z}{Z}=\frac{\Delta A}{A}+\frac{\Delta B}{B}$.

5. 5.How many significant figures in $4.50\times 10^3$?Show answer

   Three.

6. 6.Dimensional formula of G?Show answer

   [M⁻¹ L³ T⁻²].

7. 7.State the principle of homogeneity.Show answer

   Every term of a correct physical equation has the same dimensions.

8. 8.Least count of a screw gauge with pitch 1 mm and 100 divisions?Show answer

   0.01 mm.

Quick revision checklist

The night before the exam: can you do each of these without looking?

• ☐Can you list the seven SI base units and the two supplementary units?
• ☐Can you define the light year, astronomical unit, parsec and 1 u?
• ☐Can you find the mean absolute and percentage error of a set of readings?
• ☐Can you find the percentage error in a quantity with powers and roots?
• ☐Can you count significant figures and round sums and products correctly?
• ☐Can you write the dimensional formula of G, h, η and surface tension?
• ☐Can you derive a relation and convert a unit by dimensional analysis?
• ☐Can you state three limitations of dimensional analysis?

Units and Measurements: frequently asked questions