\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{Sushi (aishanya\_.\_)} \pdfinfo{ /Title (units-and-measurements.pdf) /Creator (Cheatography) /Author (Sushi (aishanya\_.\_)) /Subject (Units and 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}{103B08} \definecolor{LightBackground}{HTML}{F7F8F7} \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 and Measurements Cheat Sheet}}}} \\ \normalsize{by \textcolor{DarkBackground}{Sushi (aishanya\_.\_)} via \textcolor{DarkBackground}{\uline{cheatography.com/172469/cs/45959/}}} \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}Sushi (aishanya\_.\_) \\ \uline{cheatography.com/aishanya} \\ \end{tabulary} \vfill \columnbreak \begin{tabulary}{5.8cm}{L} \SetRowColor{FootBackground} \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}} \\ \vspace{-2pt}Published 7th April, 2025.\\ Updated 7th April, 2025.\\ 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{tabularx}{17.67cm}{x{6.0445 cm} x{11.2255 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{17.67cm}}{\bf\textcolor{white}{Introduction}} \tn % Row 0 \SetRowColor{LightBackground} Need for measurements: & Physics is a science of measurement. It is to provide a proper description of any natural phenomenon. \tn % Row Count 4 (+ 4) % Row 1 \SetRowColor{white} Physical quantities: & A quantity which is subjected to measurement may be treated as a physical quantity. \tn % Row Count 8 (+ 4) % Row 2 \SetRowColor{LightBackground} Units of measurement: & \textgreater{}The unit \textgreater{}and numerical value \tn % Row Count 10 (+ 2) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{17.67cm}{p{1.647 cm} x{4.6116 cm} x{6.0939 cm} x{4.1175 cm} } \SetRowColor{DarkBackground} \mymulticolumn{4}{x{17.67cm}}{\bf\textcolor{white}{System of Units}} \tn % Row 0 \SetRowColor{LightBackground} S.No. & Name & Unit & Symbol \tn % Row Count 2 (+ 2) % Row 1 \SetRowColor{white} 1. & length & metre & m \tn % Row Count 3 (+ 1) % Row 2 \SetRowColor{LightBackground} 2. & mass & kilogram & kg \tn % Row Count 4 (+ 1) % Row 3 \SetRowColor{white} 3. & time & second & s \tn % Row Count 5 (+ 1) % Row 4 \SetRowColor{LightBackground} 4. & electric current & ampere & A \tn % Row Count 7 (+ 2) % Row 5 \SetRowColor{white} 5. & \seqsplit{temperature} & kelvin & K \tn % Row Count 8 (+ 1) % Row 6 \SetRowColor{LightBackground} 6. & amount of substance & mole & mol \tn % Row Count 10 (+ 2) % Row 7 \SetRowColor{white} 7. & luminous intensity & candela & cd \tn % Row Count 12 (+ 2) % Row 8 \SetRowColor{LightBackground} 8. & plane angle & radian & rad \tn % Row Count 13 (+ 1) % Row 9 \SetRowColor{white} 9. & solid angle & steradian & sr \tn % Row Count 14 (+ 1) % Row 10 \SetRowColor{LightBackground} . & 4 \seqsplit{fundamental} systems: & i) CGS (cm,gram,sec) & iii) FPS (ft,lb,sec) \tn % Row Count 16 (+ 2) % Row 11 \SetRowColor{white} . & . & ii) SI (the above table of units) & iv) MKS (m,kg,sec) \tn % Row Count 19 (+ 3) \hhline{>{\arrayrulecolor{DarkBackground}}----} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{17.67cm}{x{11.9163 cm} x{5.3537 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{17.67cm}}{\bf\textcolor{white}{Conversions}} \tn % Row 0 \SetRowColor{LightBackground} 1 kilo m & 10\textasciicircum{}3\textasciicircum{}m \tn % Row Count 1 (+ 1) % Row 1 \SetRowColor{white} 1 centi m & 10\textasciicircum{}-2\textasciicircum{}m \tn % Row Count 2 (+ 1) % Row 2 \SetRowColor{LightBackground} 1 milli m & 10\textasciicircum{}-3\textasciicircum{}m \tn % Row Count 3 (+ 1) % Row 3 \SetRowColor{white} 1 micron & 10\textasciicircum{}-6\textasciicircum{}m \tn % Row Count 4 (+ 1) % Row 4 \SetRowColor{LightBackground} 1 nano m & 10\textasciicircum{}-9\textasciicircum{}m \tn % Row Count 5 (+ 1) % Row 5 \SetRowColor{white} 1 angstrom & 10\textasciicircum{}-10\textasciicircum{}m \tn % Row Count 6 (+ 1) % Row 6 \SetRowColor{LightBackground} 1 X-unit & 10\textasciicircum{}-13\textasciicircum{}m \tn % Row Count 7 (+ 1) % Row 7 \SetRowColor{white} 1 fermi & 10\textasciicircum{}-15\textasciicircum{}m \tn % Row Count 8 (+ 1) % Row 8 \SetRowColor{LightBackground} \textasciitilde{} & \textasciitilde{} \tn % Row Count 9 (+ 1) % Row 9 \SetRowColor{white} 1 astronomical unit (AU) & 1.5 x 10\textasciicircum{}11\textasciicircum{}m \tn % Row Count 11 (+ 2) % Row 10 \SetRowColor{LightBackground} 1 light year (ly) & 10\textasciicircum{}16\textasciicircum{}m \tn % Row Count 12 (+ 1) % Row 11 \SetRowColor{white} 1 parallactic sound/parsec (pc) & 3.26 x 10\textasciicircum{}16\textasciicircum{}m \tn % Row Count 14 (+ 2) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{17.67cm}{x{4.4902 cm} x{12.7798 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{17.67cm}}{\bf\textcolor{white}{Derived units}} \tn % Row 0 \SetRowColor{LightBackground} Volume & length x breadth x height (m\textasciicircum{}3\textasciicircum{}) \tn % Row Count 2 (+ 2) % Row 1 \SetRowColor{white} Density & mass/volume (kg m\textasciicircum{}-3\textasciicircum{}) \tn % Row Count 3 (+ 1) % Row 2 \SetRowColor{LightBackground} Velocity & displacement/time (m\textasciicircum{}-1\textasciicircum{}) \tn % Row Count 4 (+ 1) % Row 3 \SetRowColor{white} \seqsplit{Acceleration} & change in velocity/time (ms\textasciicircum{}-2\textasciicircum{}) \tn % Row Count 6 (+ 2) % Row 4 \SetRowColor{LightBackground} Force & mass x acceleration (kg m s\textasciicircum{}-2\textasciicircum{}) \tn % Row Count 8 (+ 2) % Row 5 \SetRowColor{white} Pressure & force/area (N m\textasciicircum{}-2\textasciicircum{}) \tn % Row Count 9 (+ 1) % Row 6 \SetRowColor{LightBackground} Work & force x displacement (kg m\textasciicircum{}2\textasciicircum{}s\textasciicircum{}-2\textasciicircum{}) \tn % Row Count 11 (+ 2) % Row 7 \SetRowColor{white} Power & work/time (J s\textasciicircum{}-1\textasciicircum{}) \tn % Row Count 12 (+ 1) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{17.67cm}{x{5.6991 cm} x{11.5709 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{17.67cm}}{\bf\textcolor{white}{Measurement of length}} \tn % Row 0 \SetRowColor{LightBackground} {\bf{Direct methods}} & Least count= Pitch/ no. of divisions \tn % Row Count 2 (+ 2) % Row 1 \SetRowColor{white} Vernier calliper & 0.01cm \tn % Row Count 4 (+ 2) % Row 2 \SetRowColor{LightBackground} Screw Gauge & 0.001cm \tn % Row Count 5 (+ 1) % Row 3 \SetRowColor{white} Spherometer & 0.001cm \tn % Row Count 6 (+ 1) % Row 4 \SetRowColor{LightBackground} {\bf{Indirect methods}} & full form \tn % Row Count 8 (+ 2) % Row 5 \SetRowColor{white} Echo & (reflection) \tn % Row Count 9 (+ 1) % Row 6 \SetRowColor{LightBackground} RADAR & Radio Detection And Ranging \tn % Row Count 11 (+ 2) % Row 7 \SetRowColor{white} LASER & Light Amplification by Stimulated Emission of Radiation \tn % Row Count 14 (+ 3) % Row 8 \SetRowColor{LightBackground} SONAR & Sound Navigation And Randing \tn % Row Count 16 (+ 2) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{17.67cm}{x{8.635 cm} x{8.635 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{17.67cm}}{\bf\textcolor{white}{Errors in measurement}} \tn % Row 0 \SetRowColor{LightBackground} {\bf{Systematic errors}} & What is it? \tn % Row Count 2 (+ 2) % Row 1 \SetRowColor{white} Instrumental errors & errors due to defected alignment \tn % Row Count 4 (+ 2) % Row 2 \SetRowColor{LightBackground} Error due to imperfection & imperfection of apparatus \tn % Row Count 6 (+ 2) % Row 3 \SetRowColor{white} Gross errors & improper adjustment of setup \tn % Row Count 8 (+ 2) % Row 4 \SetRowColor{LightBackground} {\bf{Random Errors}} & \textgreater{} \tn % Row Count 9 (+ 1) % Row 5 \SetRowColor{white} \textasciicircum{}\_\textasciicircum{}Small changes in conditions of experiment & \textasciicircum{}\_\textasciicircum{}Incorrect judgement of the observer \tn % Row Count 12 (+ 3) % Row 6 \SetRowColor{LightBackground} {\bf{Methods to express an error}} & how? \tn % Row Count 14 (+ 2) % Row 7 \SetRowColor{white} Absolute Error & The difference between the true and measured value \tn % Row Count 17 (+ 3) % Row 8 \SetRowColor{LightBackground} Mean Error & Arithmetic mean of errors of different measurements \tn % Row Count 20 (+ 3) % Row 9 \SetRowColor{white} Relative/Fractional Error & Ratio of mean error to the true value \tn % Row Count 22 (+ 2) % Row 10 \SetRowColor{LightBackground} Percentage Error & Fractional error multiplied by 100 \tn % Row Count 24 (+ 2) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{17.67cm}{x{8.635 cm} x{8.635 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{17.67cm}}{\bf\textcolor{white}{Significant figures}} \tn % Row 0 \SetRowColor{LightBackground} Rules: & i) decimal point does not effect \tn % Row Count 2 (+ 2) % Row 1 \SetRowColor{white} ii) all 0's between two non-zeros are significant & iii) all 0's to the right of non-zero digit and before the decimal point are not significant \tn % Row Count 7 (+ 5) % Row 2 \SetRowColor{LightBackground} iv) all 0's after the decimal point are significant & v) all 0's after the decimal point but before non-zeros are not significant \tn % Row Count 11 (+ 4) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \end{document}