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Outline of significant figures complete

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significant_figures.tex
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\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{graphicx}
\usepackage{siunitx}
\usepackage{lmodern}
\usepackage{fourier}
\usepackage{tabularray}
\usepackage{enumitem}
\usepackage{floatflt} % Floating images with good spacing
\usepackage{tcolorbox} % Colored boxes
\usepackage{framed} % To put frames around our images
\usepackage[
showframe,
% showframe,
inner=20mm,
outer=20mm,
top=20mm,
bottom=20mm,
marginparsep=3mm,
bindingoffset=10mm,
marginparsep=10mm,
marginparwidth=25mm,
includemp, % to include marginparsep and marginparwidth
]{geometry}
\usepackage{lipsum}
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\setlength{\FrameSep}{3mm}
\setlength{\OuterFrameSep}{0mm}
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%% Style our margin notes %%%%%%%%%%%%%%%%%%%%%
%% https://tex.stackexchange.com/a/58266/245702
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\newcommand{\mymparsetup}{\sffamily\footnotesize}
\newcommand{\mymparsetup}{\raggedright\sffamily\footnotesize}
\author{Kenneth John Odle}
\title{Significant Figures}
\usepackage{lipsum}
\begin{document}
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Sed mattis magna in mollis fringilla. Suspendisse vitae ante id ipsum posuere pulvinar. Mauris eleifend leo justo, in dictum lacus malesuada eget. Suspendisse sed congue enim. Sed quis ultrices augue, a ornare lacus. Curabitur est nisl, ornare id varius nec, egestas non erat. Maecenas lacinia tortor in auctor rhoncus. Sed condimentum nisi a consectetur interdum.\marginpar[First note is on the left side]{First note is on the right side} Donec id dapibus turpis. Ut faucibus lorem consequat ligula congue, non efficitur arcu lacinia. Aliquam sed elit sapien. Duis in fermentum ipsum, ac mattis metus. Donec varius mauris lorem, quis sollicitudin massa feugiat vel. Aliquam id sapien a sapien sollicitudin bibendum.
\maketitle
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Like many people, scientists often spend their days measuring things. They use a wide variety of measuring tools, from rulers to digital balances. Any measurement tool is limited in its accuracy. A conventional bathroom scale can give us a weight in pounds, but it does not have the accuracy required to weigh an apple accurately. Likewise, a kitchen balance can give us the weight of an apple in tenths of an ounce, but could not accurately weigh \SI{100}{\milli\gram} of sugar.
\newpage
No measuring device is 100\% accurate, and so there is always a small amount of uncertaintly in our measurements. Thus, every\marginpar[Measurements]{Measurements} measurement contains a number of digits that we know for certain to be accurate, and a final digit that is an estimate. These digits—the digits we are certain about, plus the one that is an estimate only—are called \textit{significant figures}.
Aliquam malesuada, nunc quis vulputate scelerisque, nibh purus lobortis ligula, quis dictum ipsum justo et dolor. Suspendisse lacinia placerat malesuada. Nullam a bibendum ipsum. In pretium mi id nisl porttitor sodales. Curabitur laoreet purus ut dolor viverra tempor id non nibh. Praesent at urna ullamcorper, luctus massa ac, laoreet ipsum. Morbi vel ante ultrices, aliquam justo eget, hendrerit odio. Morbi tempus ante id ligula imperdiet, vel blandit nisi dapibus. Vivamus faucibus augue est, in tincidunt lorem pulvinar id. Etiam accumsan facilisis porta. Donec interdum feugiat mauris in tincidunt. Nunc mattis rutrum neque, sed consequat sapien viverra ut. Maecenas interdum felis nec purus efficitur, sed aliquam nisi tristique. Integer venenatis suscipit felis. Etiam rhoncus congue elementum.
\begin{floatingfigure}{0.45\textwidth}
\begin{framed}
\centering
\includegraphics[width=0.8\textwidth]{balance_01}
\caption{A balance displaying mass in grams.}
\label{fig:balance1}
\end{framed}
\end{floatingfigure}
Nam commodo, tellus id euismod dapibus, lectus erat laoreet nisl, at sagittis turpis nibh id tortor. Etiam vestibulum arcu at dignissim eleifend. Etiam et lectus vel nunc luctus malesuada. Class aptent taciti sociosqu ad litora torquent per conubia nostra, per inceptos himenaeos. Aenean tincidunt nulla interdum nulla condimentum ultrices. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Donec non augue tellus.\marginpar[Second note is on the left side]{Second note is on the right side}
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For example, the balance displayed in Figure \ref{fig:balance1} is showing a weight of \SI{3.23}{\gram}. The first two digits are accurate, and the third digit (3) is the balance's estimate of that value. In other words, the value here could be \SI{3.22}{\gram}, \SI{3.23}{\gram}, or \SI{3.24}{\gram},
Ut congue id nisl eu posuere. Maecenas pretium imperdiet velit in hendrerit. Phasellus vulputate neque at nisl iaculis, sit amet faucibus ipsum mattis. Suspendisse potenti. Praesent non dolor velit. Pellentesque aliquet justo ac turpis cursus cursus. Integer nec congue lacus. Duis scelerisque vestibulum sapien, et blandit orci dapibus id. Praesent vel felis pharetra leo fermentum mollis nec at ante. Etiam non justo diam. Maecenas id dictum leo. Ut mi dolor, volutpat nec nunc ac, lacinia cursus lorem. Aenean mollis lorem vel feugiat maximus. Maecenas sit amet aliquet sapien.
In this case, we would say that this balance can accurately estimate the mass to the nearest one-hundredth of a gram. We are certain that the \SI{3.2} portion is correct, and we accept that the third digit has an acceptable level of uncertainty in it.
Uncertainty\marginpar[Symbol for uncertainty]{Symbol for uncertainty} in measurements is denoted by $\sigma_x$ (``sigma sub x''). In digital instruments, the uncertainty is simply the smallest increment the device shows. In the case of our balance above, $\sigma_x$ = \SI{0.01}{\gram}.
For analog instruments that have a scale on them, such as a ruler or thermometer, the uncertainty is the smallest increment the device shows divided by two.
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\section{Rules for Determining Significant Figures}
The following guidelines indicate whether or not a digit is significant.
\begin{enumerate}[nolistsep]
\item Any non-zero number is significant.
\item Any zero between two non-zero numbers is significant.
\item Leading zeros (i.e, zeros at the beginning of a number, either before or after the decimal point) are not significant.
\item Trailing zeros (i.e., zeros at the end of a number) are significant only if a decimal point is present.
\end{enumerate}
The\marginpar[Scientific Notation]{Scientific Notation} last two rules are often confusing. Rewriting numbers with a significant number of leading or trailing in scientific notation can help to reduce ambiguity because leading zeros get converted to an exponent and trailing zeros depend on the presence of a decimal point.
\section{Rules for Using Significant Figures in Calculations}
\begin{tcolorbox}[sharp corners, colback=yellow9, colframe=yellow7, title=\textbf{\sffamily Caution:}]
The rules for using significant figures in calculations are fairly straightforward. Where most people make a mistake is in using the wrong set of rules for their calculations, such as using the rules for addition and subtraction when they are actually multiplying or dividing.
\end{tcolorbox}
\subsection{Addition and Subtraction}
\subsection{Multiplication and Division}
\end{document}