\documentclass[10pt,a4paper]{article} % Packages \usepackage{fancyhdr} % For header and footer \usepackage{multicol} % Allows multicols in tables \usepackage{tabularx} % Intelligent column widths \usepackage{tabulary} % Used in header and footer \usepackage{hhline} % Border under tables \usepackage{graphicx} % For images \usepackage{xcolor} % For hex colours %\usepackage[utf8x]{inputenc} % For unicode character support \usepackage[T1]{fontenc} % Without this we get weird character replacements \usepackage{colortbl} % For coloured tables \usepackage{setspace} % For line height \usepackage{lastpage} % Needed for total page number \usepackage{seqsplit} % Splits long words. %\usepackage{opensans} % Can't make this work so far. Shame. Would be lovely. \usepackage[normalem]{ulem} % For underlining links % Most of the following are not required for the majority % of cheat sheets but are needed for some symbol support. \usepackage{amsmath} % Symbols \usepackage{MnSymbol} % Symbols \usepackage{wasysym} % Symbols %\usepackage[english,german,french,spanish,italian]{babel} % Languages % Document Info \author{Mudassir Khan (mvdassir\_)} \pdfinfo{ /Title (units-dimension-and-measurements.pdf) /Creator (Cheatography) /Author (Mudassir Khan (mvdassir\_)) /Subject (Units, Dimension \& Measurements Cheat Sheet) } % Lengths and widths \addtolength{\textwidth}{6cm} \addtolength{\textheight}{-1cm} \addtolength{\hoffset}{-3cm} \addtolength{\voffset}{-2cm} \setlength{\tabcolsep}{0.2cm} % Space between columns \setlength{\headsep}{-12pt} % Reduce space between header and content \setlength{\headheight}{85pt} % If less, LaTeX automatically increases it \renewcommand{\footrulewidth}{0pt} % Remove footer line \renewcommand{\headrulewidth}{0pt} % Remove header line \renewcommand{\seqinsert}{\ifmmode\allowbreak\else\-\fi} % Hyphens in seqsplit % This two commands together give roughly % the right line height in the tables \renewcommand{\arraystretch}{1.3} \onehalfspacing % Commands \newcommand{\SetRowColor}[1]{\noalign{\gdef\RowColorName{#1}}\rowcolor{\RowColorName}} % Shortcut for row colour \newcommand{\mymulticolumn}[3]{\multicolumn{#1}{>{\columncolor{\RowColorName}}#2}{#3}} % For coloured multi-cols \newcolumntype{x}[1]{>{\raggedright}p{#1}} % New column types for ragged-right paragraph columns \newcommand{\tn}{\tabularnewline} % Required as custom column type in use % Font and Colours \definecolor{HeadBackground}{HTML}{333333} \definecolor{FootBackground}{HTML}{666666} \definecolor{TextColor}{HTML}{333333} \definecolor{DarkBackground}{HTML}{00D1B1} \definecolor{LightBackground}{HTML}{EFFCFA} \renewcommand{\familydefault}{\sfdefault} \color{TextColor} % Header and Footer \pagestyle{fancy} \fancyhead{} % Set header to blank \fancyfoot{} % Set footer to blank \fancyhead[L]{ \noindent \begin{multicols}{3} \begin{tabulary}{5.8cm}{C} \SetRowColor{DarkBackground} \vspace{-7pt} {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}} } \end{tabulary} \columnbreak \begin{tabulary}{11cm}{L} \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Units, Dimension \& Measurements Cheat Sheet}}}} \\ \normalsize{by \textcolor{DarkBackground}{Mudassir Khan (mvdassir\_)} via \textcolor{DarkBackground}{\uline{cheatography.com/160173/cs/33720/}}} \end{tabulary} \end{multicols}} \fancyfoot[L]{ \footnotesize \noindent \begin{multicols}{3} \begin{tabulary}{5.8cm}{LL} \SetRowColor{FootBackground} \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}} \\ \vspace{-2pt}Mudassir Khan (mvdassir\_) \\ \uline{cheatography.com/mvdassir} \\ \end{tabulary} \vfill \columnbreak \begin{tabulary}{5.8cm}{L} \SetRowColor{FootBackground} \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}} \\ \vspace{-2pt}Published 19th August, 2022.\\ Updated 20th August, 2022.\\ Page {\thepage} of \pageref{LastPage}. \end{tabulary} \vfill \columnbreak \begin{tabulary}{5.8cm}{L} \SetRowColor{FootBackground} \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Sponsor}} \\ \SetRowColor{white} \vspace{-5pt} %\includegraphics[width=48px,height=48px]{dave.jpeg} Measure your website readability!\\ www.readability-score.com \end{tabulary} \end{multicols}} \begin{document} \raggedright \raggedcolumns % Set font size to small. Switch to any value % from this page to resize cheat sheet text: % www.emerson.emory.edu/services/latex/latex_169.html \footnotesize % Small font. \begin{multicols*}{2} \begin{tabularx}{8.4cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Fundamental or Base Quantities}} \tn \SetRowColor{white} \mymulticolumn{1}{x{8.4cm}}{The quantities which do not depend upon other quantities for their complete definition are known as {\emph{fundamental}} or {\emph{base quantities}}. \newline % Row Count 3 (+ 3) e.g.: length, mass, time, etc.% Row Count 4 (+ 1) } \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{8.4cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Derived Quantities}} \tn \SetRowColor{white} \mymulticolumn{1}{x{8.4cm}}{The quantities which can be expressed in terms of the fundamental quantities are known as {\emph{derived quantities}} \newline % Row Count 3 (+ 3) e.g.: Speed (= distance/time), Volume, acceleration, force, pressure, etc.% Row Count 5 (+ 2) } \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{8.4cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Units of Physical Quantities}} \tn \SetRowColor{white} \mymulticolumn{1}{x{8.4cm}}{The chosen reference standard of measurement in multiples of which, a physical quantity is expressed is called the {\emph{unit}} of the quantity. \newline % Row Count 3 (+ 3) e.g.: Physcial Quantity = Numerical Value x Unit% Row Count 4 (+ 1) } \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{8.4cm}{x{1.14 cm} x{4.332 cm} x{2.128 cm} } \SetRowColor{DarkBackground} \mymulticolumn{3}{x{8.4cm}}{\bf\textcolor{white}{Set of Quantities having same Dimensions}} \tn % Row 0 \SetRowColor{LightBackground} {\bf{Sr. No.}} & {\bf{Quantities}}\{\{ac\}\} & {\bf{Dimensions}}\{\{ac\}\} \tn % Row Count 2 (+ 2) % Row 1 \SetRowColor{white} 1 & strain, refractive index, relative density, angle, solid angle, phase, distance gradient, relative permeability, relative permittivity, angle of contact, Reynolds number, coefficient of friction, mechanical equivalent of heat, electric susceptibility, etc. & {[}M\textasciicircum{}0\textasciicircum{}L\textasciicircum{}0\textasciicircum{}T\textasciicircum{}0\textasciicircum{}{]} \tn % Row Count 14 (+ 12) % Row 2 \SetRowColor{LightBackground} 2 & Mass or inertial mass & {[}M\textasciicircum{}1\textasciicircum{}L\textasciicircum{}0\textasciicircum{}T\textasciicircum{}0\textasciicircum{}{]} \tn % Row Count 16 (+ 2) % Row 3 \SetRowColor{white} 3 & Momentum and impulse & {[}M\textasciicircum{}1\textasciicircum{}L\textasciicircum{}1\textasciicircum{}T\textasciicircum{}-1\textasciicircum{}{]} \tn % Row Count 18 (+ 2) % Row 4 \SetRowColor{LightBackground} 4 & Thrust, Force, weight, tension, energy gradient & {[}M\textasciicircum{}1\textasciicircum{}L\textasciicircum{}1\textasciicircum{}T\textasciicircum{}-2\textasciicircum{}{]} \tn % Row Count 21 (+ 3) % Row 5 \SetRowColor{white} 5 & Pressure, stress, Young's modulus, bulk modulus, shear modulus, modulus of rigidity, energy density & {[}M\textasciicircum{}1\textasciicircum{}L\textasciicircum{}-1\textasciicircum{}T\textasciicircum{}-2\textasciicircum{}{]} \tn % Row Count 26 (+ 5) % Row 6 \SetRowColor{LightBackground} 6 & Angular momentum and Planck's constant & {[}M\textasciicircum{}1\textasciicircum{}L\textasciicircum{}2\textasciicircum{}T\textasciicircum{}-1\textasciicircum{}{]} \tn % Row Count 28 (+ 2) % Row 7 \SetRowColor{white} 7 & Acceleration, g and gravitational field intensity & {[}M\textasciicircum{}0\textasciicircum{}L\textasciicircum{}1\textasciicircum{}T\textasciicircum{}-2\textasciicircum{}{]} \tn % Row Count 31 (+ 3) \end{tabularx} \par\addvspace{1.3em} \vfill \columnbreak \begin{tabularx}{8.4cm}{x{1.14 cm} x{4.332 cm} x{2.128 cm} } \SetRowColor{DarkBackground} \mymulticolumn{3}{x{8.4cm}}{\bf\textcolor{white}{Set of Quantities having same Dimensions (cont)}} \tn % Row 8 \SetRowColor{LightBackground} 8 & Surface tension, free surface energy (energy per unit area), force gradient, spring constant & {[}M\textasciicircum{}1\textasciicircum{}L\textasciicircum{}0\textasciicircum{}T\textasciicircum{}-2\textasciicircum{}{]} \tn % Row Count 5 (+ 5) % Row 9 \SetRowColor{white} 9 & Latent heat and gravitational potential & {[}M\textasciicircum{}0\textasciicircum{}L\textasciicircum{}2\textasciicircum{}T\textasciicircum{}-2\textasciicircum{}{]} \tn % Row Count 7 (+ 2) % Row 10 \SetRowColor{LightBackground} 10 & Thermal capacity, Boltzmann constant, entropy & {[}M\textasciicircum{}1\textasciicircum{}L\textasciicircum{}2\textasciicircum{}T\textasciicircum{}-2\textasciicircum{}K\textasciicircum{}-1\textasciicircum{}{]} \tn % Row Count 10 (+ 3) % Row 11 \SetRowColor{white} 11 & Work, Torque, internal energy, potential energy, kinetic energy, moment of force, (q/C\textasciicircum{}2\textasciicircum{}), (LI\textasciicircum{}2\textasciicircum{}), (qV), (V\textasciicircum{}2\textasciicircum{}C), (I\textasciicircum{}2\textasciicircum{}Rt), (VIt), (V\textasciicircum{}2\textasciicircum{}t/R), (PV), (RT), (mL), (mc ΔT) & {[}M\textasciicircum{}1\textasciicircum{}L\textasciicircum{}2\textasciicircum{}T\textasciicircum{}-2\textasciicircum{}{]} \tn % Row Count 18 (+ 8) % Row 12 \SetRowColor{LightBackground} 12 & Frequency, angular frequency, angular velocity, velocity gradient, radioactivity, (R/L), (1/RC), (1/ (LC)\textasciicircum{}1/2\textasciicircum{}) & {[}M\textasciicircum{}0\textasciicircum{}L\textasciicircum{}0\textasciicircum{}T\textasciicircum{}-1\textasciicircum{}{]} \tn % Row Count 24 (+ 6) % Row 13 \SetRowColor{white} 13 & (l/g)\textasciicircum{}1/2\textasciicircum{}, (m/k)\textasciicircum{}1/2\textasciicircum{}, (L/R), (RC), (LC)\textasciicircum{}1/2\textasciicircum{}, time & {[}M\textasciicircum{}0\textasciicircum{}L\textasciicircum{}0\textasciicircum{}T\textasciicircum{}1\textasciicircum{}{]} \tn % Row Count 27 (+ 3) % Row 14 \SetRowColor{LightBackground} 14 & (VI), (I\textasciicircum{}2\textasciicircum{}R), (V\textasciicircum{}2\textasciicircum{}/R), Power & {[}M\textasciicircum{}1\textasciicircum{}L\textasciicircum{}2\textasciicircum{}T\textasciicircum{}-3\textasciicircum{}{]} \tn % Row Count 29 (+ 2) \hhline{>{\arrayrulecolor{DarkBackground}}---} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{8.4cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Rules for Counting Significant Figures}} \tn \SetRowColor{white} \mymulticolumn{1}{x{8.4cm}}{{\bf{For numbers greater than 1}} \newline % Row Count 1 (+ 1) •All non-zero digits are significant \newline % Row Count 2 (+ 1) •All zeroes between two non-zero digits are significant. The location of the decimal does not matter. \newline % Row Count 5 (+ 3) •If the number is without a decimal point, then the trailing zeroes are not significant. \newline % Row Count 7 (+ 2) •Trailing zeroes in the decimal part are significant. \newline % Row Count 9 (+ 2) {\bf{For numbers less than 1}} \newline % Row Count 10 (+ 1) •Any zero to the right of a non-zero digit is significant. \newline % Row Count 12 (+ 2) •All zeroes between the decimal point and the first non-zero digit are not significant,% Row Count 14 (+ 2) } \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{8.4cm}{x{2.56 cm} x{5.44 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Supplementary Units}} \tn % Row 0 \SetRowColor{LightBackground} Radian (rad) & for measurement of plane angle \tn % Row Count 2 (+ 2) % Row 1 \SetRowColor{white} Steradian (sr) & for measurement of solid angle \tn % Row Count 4 (+ 2) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{8.4cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Prefixes used for different Powers of 10}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{1}{x{8.4cm}}{\{\{ac\}\}Power of 10} \tn % Row Count 1 (+ 1) % Row 1 \SetRowColor{white} \mymulticolumn{1}{x{8.4cm}}{\{\{ac\}\}10\textasciicircum{}18\textasciicircum{}} \tn % Row Count 2 (+ 1) % Row 2 \SetRowColor{LightBackground} \mymulticolumn{1}{x{8.4cm}}{\{\{ac\}\}10\textasciicircum{}15\textasciicircum{}} \tn % Row Count 3 (+ 1) % Row 3 \SetRowColor{white} \mymulticolumn{1}{x{8.4cm}}{\{\{ac\}\}10\textasciicircum{}12\textasciicircum{}} \tn % Row Count 4 (+ 1) % Row 4 \SetRowColor{LightBackground} \mymulticolumn{1}{x{8.4cm}}{\{\{ac\}\}10\textasciicircum{}9\textasciicircum{}} \tn % Row Count 5 (+ 1) % Row 5 \SetRowColor{white} \mymulticolumn{1}{x{8.4cm}}{\{\{ac\}\}10\textasciicircum{}6\textasciicircum{}} \tn % Row Count 6 (+ 1) % Row 6 \SetRowColor{LightBackground} \mymulticolumn{1}{x{8.4cm}}{\{\{ac\}\}10\textasciicircum{}3\textasciicircum{}} \tn % Row Count 7 (+ 1) % Row 7 \SetRowColor{white} \mymulticolumn{1}{x{8.4cm}}{\{\{ac\}\}10\textasciicircum{}2\textasciicircum{}} \tn % Row Count 8 (+ 1) % Row 8 \SetRowColor{LightBackground} \mymulticolumn{1}{x{8.4cm}}{\{\{ac\}\}10\textasciicircum{}1\textasciicircum{}} \tn % Row Count 9 (+ 1) \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{8.4cm}{x{2.66 cm} x{1.52 cm} x{3.42 cm} } \SetRowColor{DarkBackground} \mymulticolumn{3}{x{8.4cm}}{\bf\textcolor{white}{Some Fundamental Constants}} \tn % Row 0 \SetRowColor{LightBackground} {\bf{Constant}} & {\bf{Symbol}} & {\bf{Value}} \tn % Row Count 2 (+ 2) % Row 1 \SetRowColor{white} Gravitational Constant & G & 6.6*10\textasciicircum{}-11\textasciicircum{} Nm\textasciicircum{}2\textasciicircum{}kg\textasciicircum{}-2\textasciicircum{} \tn % Row Count 4 (+ 2) % Row 2 \SetRowColor{LightBackground} Speed of Light in Vacuum & c & 3*10\textasciicircum{}8\textasciicircum{} ms\textasciicircum{}-1\textasciicircum{} \tn % Row Count 6 (+ 2) % Row 3 \SetRowColor{white} Permeability of vacuum & μ & 4π*10\textasciicircum{}-7\textasciicircum{} Hm\textasciicircum{}-1\textasciicircum{} \tn % Row Count 8 (+ 2) % Row 4 \SetRowColor{LightBackground} Permittivity of vacuum & ε & 8.85*10\textasciicircum{}-12\textasciicircum{} Fm\textasciicircum{} -1\textasciicircum{} \tn % Row Count 10 (+ 2) % Row 5 \SetRowColor{white} Planck's Constant & h & 6.63*10\textasciicircum{}-34\textasciicircum{} Js \tn % Row Count 12 (+ 2) % Row 6 \SetRowColor{LightBackground} Atomic Mass Unit & amu & 1.66*10\textasciicircum{}-27\textasciicircum{} kg \tn % Row Count 14 (+ 2) % Row 7 \SetRowColor{white} Energy equivalent of 1 amu & MeV & 931.5 MeV \tn % Row Count 16 (+ 2) % Row 8 \SetRowColor{LightBackground} Electron rest mass & mₑ & 9.1*10\textasciicircum{}-31\textasciicircum{}= 0.511 MeV \tn % Row Count 18 (+ 2) % Row 9 \SetRowColor{white} Avogadro constant & Nₐ & 6.02*10\textasciicircum{}23\textasciicircum{} mol\textasciicircum{}-1\textasciicircum{} \tn % Row Count 20 (+ 2) % Row 10 \SetRowColor{LightBackground} Faraday Constant & F & 9.648*10\textasciicircum{}4\textasciicircum{} C mol\textasciicircum{}-1\textasciicircum{} \tn % Row Count 22 (+ 2) % Row 11 \SetRowColor{white} \seqsplit{Stefan-Boltzmann} Constant & σ & 5.67*10\textasciicircum{}-8\textasciicircum{} W m\textasciicircum{}-2\textasciicircum{}K\textasciicircum{}-4\textasciicircum{} \tn % Row Count 24 (+ 2) % Row 12 \SetRowColor{LightBackground} Wien Constant & b & 2.89{\emph{10}}-3\textasciicircum{} mK \tn % Row Count 25 (+ 1) % Row 13 \SetRowColor{white} Rydberg Constant & R∞ & 1.097*10\textasciicircum{}7\textasciicircum{} m\textasciicircum{}-1\textasciicircum{} \tn % Row Count 27 (+ 2) % Row 14 \SetRowColor{LightBackground} Triple point for water & K / \textasciicircum{}o\textasciicircum{}C / \textasciicircum{}o\textasciicircum{}F & 273.16K (0.01\textasciicircum{}o\textasciicircum{}C) \tn % Row Count 29 (+ 2) % Row 15 \SetRowColor{white} Molar volume of ideal gas & m\textasciicircum{}3\textasciicircum{} mol\textasciicircum{}-1\textasciicircum{} & 22.4 L = 22.4*10\textasciicircum{}-3\textasciicircum{} m\textasciicircum{}3\textasciicircum{} mol\textasciicircum{}-1\textasciicircum{} \tn % Row Count 31 (+ 2) \hhline{>{\arrayrulecolor{DarkBackground}}---} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{8.4cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Order of Magnitude}} \tn \SetRowColor{white} \mymulticolumn{1}{x{8.4cm}}{Power of 10 required to represent a quantity. \newline % Row Count 1 (+ 1) 49 = 4.9*10\textasciicircum{}1\textasciicircum{} ≈ 10\textasciicircum{}1\textasciicircum{} → order of magnitude = 1 \newline % Row Count 3 (+ 2) 0.051 = 5.1*10\textasciicircum{}-2\textasciicircum{} ≈ 10\textasciicircum{}-2\textasciicircum{} → order of magnitude = -2% Row Count 5 (+ 2) } \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{8.4cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{System of Units}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{1}{x{8.4cm}}{} \tn % Row Count 0 (+ 0) % Row 1 \SetRowColor{white} \mymulticolumn{1}{x{8.4cm}}{(i)} \tn % Row Count 1 (+ 1) % Row 2 \SetRowColor{LightBackground} \mymulticolumn{1}{x{8.4cm}}{(ii)} \tn % Row Count 2 (+ 1) % Row 3 \SetRowColor{white} \mymulticolumn{1}{x{8.4cm}}{(iii)} \tn % Row Count 3 (+ 1) % Row 4 \SetRowColor{LightBackground} \mymulticolumn{1}{x{8.4cm}}{(iv)} \tn % Row Count 4 (+ 1) \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{8.4cm}{x{1.44 cm} x{2.52 cm} x{1.944 cm} x{1.296 cm} } \SetRowColor{DarkBackground} \mymulticolumn{4}{x{8.4cm}}{\bf\textcolor{white}{Fundamental Quantities in S.I. System}} \tn % Row 0 \SetRowColor{LightBackground} \{\{ac\}\}Sr. No. & \{\{ac\}\}Physical Quantity & \{\{ac\}\}Name of Unit & \{\{ac\}\}Symbol \tn % Row Count 2 (+ 2) % Row 1 \SetRowColor{white} \{\{ac\}\}1 & Mass & \{\{ac\}\}kilogram & \{\{ac\}\}kg \tn % Row Count 4 (+ 2) % Row 2 \SetRowColor{LightBackground} \{\{ac\}\}2 & Length & \{\{ac\}\}meter & \{\{ac\}\}m \tn % Row Count 6 (+ 2) % Row 3 \SetRowColor{white} \{\{ac\}\}3 & Time & \{\{ac\}\}second & \{\{ac\}\}s \tn % Row Count 8 (+ 2) % Row 4 \SetRowColor{LightBackground} \{\{ac\}\}4 & Temperature & \{\{ac\}\}kelvin & \{\{ac\}\}K \tn % Row Count 10 (+ 2) % Row 5 \SetRowColor{white} \{\{ac\}\}5 & Luminous Intensity & \{\{ac\}\}candela & \{\{ac\}\}Cd \tn % Row Count 12 (+ 2) % Row 6 \SetRowColor{LightBackground} \{\{ac\}\}6 & Electric Current & \{\{ac\}\}ampere & \{\{ac\}\}A \tn % Row Count 14 (+ 2) % Row 7 \SetRowColor{white} \{\{ac\}\}7 & Amount of Substance & \{\{ac\}\}mole & \{\{ac\}\}mol \tn % Row Count 16 (+ 2) \hhline{>{\arrayrulecolor{DarkBackground}}----} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{8.4cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Dimensional Formula}} \tn \SetRowColor{white} \mymulticolumn{1}{x{8.4cm}}{The relation which expresses physical quantities in terms of appropriate powers of fundamental quantities.% Row Count 3 (+ 3) } \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{8.4cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Use of Dimensional Analysis}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{1}{x{8.4cm}}{To check the dimensional correctness of a given physical relation.} \tn % Row Count 2 (+ 2) % Row 1 \SetRowColor{white} \mymulticolumn{1}{x{8.4cm}}{To derive relationship between different physical quantities.} \tn % Row Count 4 (+ 2) % Row 2 \SetRowColor{LightBackground} \mymulticolumn{1}{x{8.4cm}}{To convert units of a physical quantity from one system to another.} \tn % Row Count 6 (+ 2) \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{8.4cm}{x{2.016 cm} x{1.008 cm} x{2.736 cm} x{1.44 cm} } \SetRowColor{DarkBackground} \mymulticolumn{4}{x{8.4cm}}{\bf\textcolor{white}{Units of Important Physical Quantities}} \tn % Row 0 \SetRowColor{LightBackground} {\bf{Physical Quantity}} & {\bf{Unit}} & {\bf{Physical Quantity}} & {\bf{Unit}} \tn % Row Count 2 (+ 2) % Row 1 \SetRowColor{white} Angular \seqsplit{acceleration} & rad s\textasciicircum{}-2\textasciicircum{} & Frequency & hertz \tn % Row Count 4 (+ 2) % Row 2 \SetRowColor{LightBackground} Moment of Inertia & kg m\textasciicircum{}2\textasciicircum{} & Resistance & kh m\textasciicircum{}2\textasciicircum{} A\textasciicircum{}-2\textasciicircum{} s\textasciicircum{}-3\textasciicircum{} \tn % Row Count 7 (+ 3) % Row 3 \SetRowColor{white} \seqsplit{Self-Inductance} & henry & Surface Tension & N/m \tn % Row Count 9 (+ 2) % Row 4 \SetRowColor{LightBackground} Magnetic Flux & weber & Universal Gas Constant & J K\textasciicircum{}-1\textasciicircum{} mol\textasciicircum{}-1\textasciicircum{} \tn % Row Count 11 (+ 2) % Row 5 \SetRowColor{white} Pole Strength & A m & Dipole Moment & C m \tn % Row Count 13 (+ 2) % Row 6 \SetRowColor{LightBackground} Viscosity* & poise & Stefan Constant & W m\textasciicircum{}-2\textasciicircum{} K\textasciicircum{}-4* \tn % Row Count 15 (+ 2) % Row 7 \SetRowColor{white} Reactance & ohm & Permittivity of free space εₒ ​ & C\textasciicircum{}2\textasciicircum{}/N m\textasciicircum{}2\textasciicircum{} \tn % Row Count 18 (+ 3) % Row 8 \SetRowColor{LightBackground} Specific Heat & J/kg \textasciicircum{}o\textasciicircum{}C & Permeability of free space µₒ & weber/ A m \tn % Row Count 21 (+ 3) % Row 9 \SetRowColor{white} Strength of magnetic field & N A\textasciicircum{}-1\textasciicircum{} m\textasciicircum{}-1\textasciicircum{} & Planck's Constant & J s \tn % Row Count 24 (+ 3) % Row 10 \SetRowColor{LightBackground} \seqsplit{Astronomical} distance & \seqsplit{Parsec} & Entropy & J/K \tn % Row Count 26 (+ 2) \hhline{>{\arrayrulecolor{DarkBackground}}----} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{8.4cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Error in Summation and Difference}} \tn \SetRowColor{white} \mymulticolumn{1}{x{8.4cm}}{x = a + b then, △x = ± (△a + △b)% Row Count 1 (+ 1) } \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{8.4cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Error in Product and Division}} \tn \SetRowColor{LightBackground} \mymulticolumn{1}{p{8.4cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/mvdassir_1660901972_chart.png}}} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \SetRowColor{LightBackground} \mymulticolumn{1}{x{8.4cm}}{If X = Y\textasciicircum{}a\textasciicircum{}Z\textasciicircum{}b\textasciicircum{} then the maximum possible fractional error in X is given by the above equation} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} % That's all folks \end{multicols*} \end{document}