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Units, Dimensions & Errors revision notes

Every idea in the Units, Dimensions & Errors chapter for JEE Main, with the usual mistakes and the fast methods. Topic 1 is open to everyone; sign in free to read all 38 and download the PDF.

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SI units and measurement

SI base quantities
Radian and steradian are dimensionless.
Base quantitySI unitSymbol
lengthmetrem
masskilogramkg
timeseconds
electric currentampereA
temperaturekelvinK
amount of substancemolemol
luminous intensitycandelacd
Derived SI units
8× asked, last 2026
1 N=1 kg m s−2,1 J=1 N m,1 Pa=1 N m−21\,\text{N}=1\,\text{kg m s}^{-2},\qquad 1\,\text{J}=1\,\text{N m},\qquad 1\,\text{Pa}=1\,\text{N m}^{-2}
Build each from its defining formula: power N m s⁻¹, viscosity Pa s, energy density J m⁻³ = N m⁻², E/HE/H in V/A = Ω.
  • Heat units: heat capacity J K⁻¹, specific heat J kg⁻¹ K⁻¹, latent heat J kg⁻¹, thermal conductivity W m⁻¹ K⁻¹ (= J m⁻¹ K⁻¹ s⁻¹). Each extra 'per' adds one inverse unit.
  • Not N m⁻² for torque. Torque is force × distance, N m; N m⁻² is stress or pressure and J kg⁻¹ is latent heat. Match units through the defining formula, not by look.
Changing the system of units
2× asked, last 2026
n2=n1[M1M2]a[L1L2]b[T1T2]cn_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}
Dimensions [MaLbTc][M^aL^bT^c]; nunu is fixed. Systems given by vv and aa: use L=v2/aL=v^2/a, T=v/aT=v/a.
Large and small lengths
1× asked, last 2023
1 AU≈1.5×1011 m,1 ly≈9.46×1015 m,1 pc≈3.08×1016 m1\,\text{AU}\approx1.5\times10^{11}\,\text{m},\qquad 1\,\text{ly}\approx9.46\times10^{15}\,\text{m},\qquad 1\,\text{pc}\approx3.08\times10^{16}\,\text{m}
1 pc ≈ 3.26 ly, so AU < ly < pc; all are distances. Also 1 Å = 10⁻¹⁰ m, 1 fermi = 10⁻¹⁵ m.
10−1510^{-15}10−1010^{-10}10−510^{-5}1110510^{5}101010^{10}1 fermi1 Å1 m1 AU1 ly1 pcmetres
Each step is 10510^5: a parsec is only about 3 light years
Order of magnitude
1× asked, last 2024
N=a×10b (1≤a<10):order=b  (a≤5),b+1  (a>5)N=a\times10^{b}\ (1\le a<10):\qquad \text{order}=b\ \ (a\le5),\qquad b+1\ \ (a>5)
The order is always a power of ten, never the prefactor aa.

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Practise Units, Dimensions & Errors

33 more concepts in 6 topics

Dimensions: mechanics and heat, Dimensions: electricity and magnetism, Dimensional analysis, Significant figures, Errors and their propagation and Vernier callipers and screw gauge. Read the first part free. Sign in free with Google to read the rest and download the PDF.

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Dimensions: mechanics and heat

  • Dimensional formula5×
  • Force, energy and power15×
  • Momentum and angular momentum16×
  • Pressure, stress and energy density24×
  • Heat and gas constants9×
  • Heat flow and radiation constants6×
  • Gravitation and rate constants11×

Dimensions: electricity and magnetism

  • Charge, field and potential12×
  • Resistance, capacitance, inductance7×
  • Permittivity and permeability11×
  • Magnetic quantities8×
  • Shortcut combinations9×

Dimensional analysis

  • Principle of homogeneity11×
  • Van der Waals constants6×
  • Arguments of sin, log and exp8×
  • Finding a relation by dimensions7×
  • Changing the base quantities8×
  • Planck units5×
  • Also remember1

Significant figures

  • Counting significant figures2×
  • Arithmetic with significant figures5×

Errors and their propagation

  • Errors, accuracy and least count7×
  • Mean absolute and relative error2×
  • Sum and difference1×
  • Product, quotient and power24×
  • Volume and density7×
  • Resistance, resistivity and heat7×
  • Parallel resistors2×
  • Exponential factor1×
  • Simple pendulum and spring7×
  • Young's modulus experiments5×
  • Small changes with sign3×

Vernier callipers and screw gauge

  • Vernier callipers
  • Screw gauge2×
  • Also remember1

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