Scientific Notation in LaTeX

\documentclass{article}
\usepackage{amsmath,amssymb}
\usepackage{siunitx} % For units
\begin{document}

% Common physics constants
$c = \SI{3.0e8}{\meter\per\second}$ % Speed of light
$h = \SI{6.626e-34}{\joule\second}$ % Planck constant
$\hbar = \frac{h}{2\pi}$ % Reduced Planck constant
$k_B = \SI{1.381e-23}{\joule\per\kelvin}$ % Boltzmann constant
$e = \SI{1.602e-19}{\coulomb}$ % Elementary charge

% Common variables
$\vec{F}$ % Force vector
$\vec{v}$ % Velocity vector
$\vec{E}$ % Electric field
$\vec{B}$ % Magnetic field
$\mathbf{r}$ % Position vector

\end{document}

% Dirac notation
$\langle \psi | \phi \rangle$ % Inner product
$| \psi \rangle$ % Ket
$\langle \phi |$ % Bra
$\langle \psi | \hat{H} | \phi \rangle$ % Expectation value

% Schrödinger equation
$i\hbar \frac{\partial}{\partial t} |\psi\rangle = \hat{H}|\psi\rangle$

% Wave function
$\Psi(x,t) = A e^{i(kx - \omega t)}$

% Commutation relations
$[\hat{x}, \hat{p}] = i\hbar$
$[\hat{L}_i, \hat{L}_j] = i\hbar\epsilon_{ijk}\hat{L}_k$

% Uncertainty principle
$\Delta x \Delta p \geq \frac{\hbar}{2}$

% Maxwell's equations
\begin{align}
\nabla \cdot \vec{E} &= \frac{\rho}{\epsilon_0} \\
\nabla \cdot \vec{B} &= 0 \\
\nabla \times \vec{E} &= -\frac{\partial \vec{B}}{\partial t} \\
\nabla \times \vec{B} &= \mu_0 \vec{J} + \mu_0\epsilon_0\frac{\partial \vec{E}}{\partial t}
\end{align}

% Lorentz force
$\vec{F} = q(\vec{E} + \vec{v} \times \vec{B})$

% Electromagnetic wave
$\vec{E}(\vec{r},t) = \vec{E}_0 \cos(\vec{k} \cdot \vec{r} - \omega t + \phi)$

% Poynting vector
$\vec{S} = \frac{1}{\mu_0} \vec{E} \times \vec{B}$

% First law of thermodynamics
$dU = \delta Q - \delta W$

% Entropy
$S = k_B \ln \Omega$

% Maxwell-Boltzmann distribution
$f(v) = 4\pi n \left(\frac{m}{2\pi k_B T}\right)^{3/2} v^2 e^{-\frac{mv^2}{2k_B T}}$

% Partition function
$Z = \sum_i e^{-\beta E_i}$

% Boltzmann factor
$P_i \propto e^{-\beta E_i}$ where $\beta = \frac{1}{k_B T}$

% Heat capacity
$C_V = \left(\frac{\partial U}{\partial T}\right)_V$

\documentclass{article}
\usepackage{chemfig} % For chemical structures
\usepackage{mhchem}  % For chemical equations
\begin{document}

% Simple molecules
\ce{H2O} % Water
\ce{CO2} % Carbon dioxide
\ce{NH3} % Ammonia
\ce{C6H12O6} % Glucose

% Chemical reactions
\ce{2H2 + O2 -> 2H2O}
\ce{CaCO3 <=> CaO + CO2}
\ce{A + B <<>> C + D}

% Ions and charges
\ce{Na+} \ce{Cl-} \ce{SO4^2-} \ce{NH4+}

% Isotopes
\ce{^{14}C} \ce{^{235}U} \ce{^{1}H}

% Reaction conditions
\ce{A + B ->[\Delta][catalyst] C + D}

\end{document}

\usepackage{chemfig}

% Simple structures
\chemfig{H-C(-[2]H)(-[6]H)-H} % Methane
\chemfig{*6(=-=-=-)} % Benzene
\chemfig{H-N(-H)-H} % Ammonia

% More complex molecules
\chemfig{[:30]*6((-=O)-N(-CH_3)-*5(-N=-N(-CH_3)-=)-=-=-=-)}

% Reaction schemes
\schemestart
\chemfig{A}
\arrow{->}
\chemfig{B}
\arrow{<=>}
\chemfig{C}
\schemestop

% NMR notation
$^1$H NMR: $\delta$ \SI{7.26}{\ppm}
$^{13}$C NMR: $\delta$ \SI{77.16}{\ppm}

% IR frequencies
$\tilde{\nu} = \SI{3000}{\per\centi\meter}$ % Wavenumber

% UV-Vis
$\lambda_{\max} = \SI{280}{\nano\meter}$
$\epsilon = \SI{1500}{\liter\per\mole\per\centi\meter}$ % Molar absorptivity

% Mass spectrometry
$m/z = 91$ % Mass-to-charge ratio
$[\text{M}]^+ = 120$ % Molecular ion

\usepackage{siunitx}

% Basic units
\SI{10}{\meter}
\SI{5.2}{\kilogram}
\SI{3.7}{\second}
\SI{298}{\kelvin}
\SI{2.5}{\ampere}

% Derived units
\SI{9.8}{\meter\per\second\squared} % Acceleration
\SI{101325}{\pascal} % Pressure
\SI{4.18}{\joule\per\gram\per\kelvin} % Specific heat
\SI{1.5}{\tesla} % Magnetic field

% Powers of 10
\SI{6.022e23}{\per\mole} % Avogadro's number
\SI{1.38e-23}{\joule\per\kelvin} % Boltzmann constant

% Ranges
\SIrange{10}{20}{\celsius}
\SIrange{1e-3}{1e-6}{\meter}

% Complex units
\SI{2.5e-4}{\meter\squared\per\second}
\SI{1.6e-19}{\joule\per\particle}

% Correct formatting
The reaction proceeded at \SI{298}{\kelvin}.
Pressure was maintained at \SI{1.5}{\bar}.
The sample had a mass of \SI{2.5 \pm 0.1}{\gram}.

% Avoid these common mistakes
% Wrong: 298 K, 1.5 bar, 2.5±0.1 g
% Right: Use siunitx as shown above

% Scientific notation
\num{6.022e23} particles per mole
\SI{1.602e-19}{\coulomb} per electron

% Percentages and ratios
\SI{15}{\percent} yield
\num{1:2:1} stoichiometric ratio

\usepackage{physics}

% Derivatives
\dv{f}{x} % df/dx
\dv[2]{f}{x} % d²f/dx²
\pdv{f}{x} % ∂f/∂x
\pdv{f}{x}{y} % ∂²f/∂x∂y

% Integrals
\int \dd{x} % Better spacing
\int f(x) \dd{x}
\int \dd[3]{r} % 3D integral

% Operators
\grad % Gradient
\div % Divergence
\curl % Curl
\laplacian % Laplacian

% Brackets
\abs{x} % |x|
\norm{v} % ||v||
\eval{f(x)}_a^b % Evaluated at limits

% Commutators and anticommutators
\comm{A}{B} % [A,B]
\anticomm{A}{B} % {A,B}

% Matrix elements
\matrixel{n}{A}{m} % ⟨n|A|m⟩
\ev{A}{\psi} % ⟨ψ|A|ψ⟩

% mhchem for chemical equations
\usepackage[version=4]{mhchem}
\ce{H2SO4} % Sulfuric acid
\ce{^{235}U} % Uranium-235
\ce{A + B -> C + D} % Reaction

% chemfig for structures
\usepackage{chemfig}
\chemfig{H-C(-[2]H)(-[6]H)-H}

% chemmacros for chemical symbols
\usepackage{chemmacros}
\pH % pH symbol
\pOH % pOH symbol
\Enthalpy{298} % Enthalpy at 298K
\Entropy{298} % Entropy at 298K

% chemformula alternative
\usepackage{chemformula}
\ch{H2O} % Water
\ch{"\ox{+1,Na}" + "\ox{-1,Cl}" -> NaCl} % Oxidation states

% Vector operators
\vec{\nabla} \cdot \vec{F} % Divergence
\vec{\nabla} \times \vec{F} % Curl
\nabla^2 \phi % Laplacian

% Green's theorem
\oint_C \vec{F} \cdot d\vec{r} = \iint_D (\nabla \times \vec{F}) \cdot \hat{n} \, dA

% Gauss's theorem
\iiint_V (\nabla \cdot \vec{F}) \, dV = \oiint_S \vec{F} \cdot \hat{n} \, dA

% Stokes' theorem
\oint_C \vec{F} \cdot d\vec{r} = \iint_S (\nabla \times \vec{F}) \cdot \hat{n} \, dA

% Einstein notation
$g_{\mu\nu} x^\mu x^\nu$ % Metric tensor
$T^{\mu\nu}$ % Stress-energy tensor
$R_{\mu\nu} - \frac{1}{2}Rg_{\mu\nu} = 8\pi G T_{\mu\nu}$ % Einstein field equation

% Christoffel symbols
$\Gamma^\lambda_{\mu\nu} = \frac{1}{2}g^{\lambda\rho}(\partial_\mu g_{\rho\nu} + \partial_\nu g_{\rho\mu} - \partial_\rho g_{\mu\nu})$

% Covariant derivative
$\nabla_\mu V^\nu = \partial_\mu V^\nu + \Gamma^\nu_{\mu\lambda} V^\lambda$

% Measurements with uncertainty
$m = \SI{2.45 \pm 0.05}{\gram}$
$T = \SI{298.2 \pm 0.3}{\kelvin}$

% Relative error
$\frac{\Delta x}{x} = \SI{2.3}{\percent}$

% Error propagation
$\Delta f = \sqrt{\left(\frac{\partial f}{\partial x}\Delta x\right)^2 + \left(\frac{\partial f}{\partial y}\Delta y\right)^2}$

% Statistical measures
$\bar{x} = \frac{1}{n}\sum_{i=1}^n x_i$ % Mean
$s = \sqrt{\frac{\sum_{i=1}^n (x_i - \bar{x})^2}{n-1}}$ % Standard deviation
$\sigma_{\bar{x}} = \frac{s}{\sqrt{n}}$ % Standard error of mean

% Significant figures
\num{1.23e-4} % Scientific notation
\num{1.234567} % Regular number

% Tables with uncertainties
\begin{tabular}{cS[table-format=3.2(2)]}
\toprule
Trial & {Mass (\si{\gram})} \\
\midrule
1 & 2.45(5) \\
2 & 2.52(3) \\
3 & 2.48(4) \\
\bottomrule
\end{tabular}

% Concentration notation
$[\text{HCl}] = \SI{0.1}{\Molar}$
$c(\text{NaOH}) = \SI{0.05}{\mol\per\liter}$

% Physics
$\hbar$ % Reduced Planck constant
$\alpha$ % Fine structure constant
$\mu_0$ % Permeability of free space
$\epsilon_0$ % Permittivity of free space
$\sigma$ % Stefan-Boltzmann constant

% Chemistry
$\Delta H$ % Enthalpy change
$\Delta S$ % Entropy change
$\Delta G$ % Gibbs free energy change
$K_{\text{eq}}$ % Equilibrium constant
$K_{\text{sp}}$ % Solubility product

% Mathematics/Statistics
$\sigma$ % Standard deviation
$\mu$ % Population mean
$\chi^2$ % Chi-squared
$R^2$ % Coefficient of determination
$p$ % p-value