\documentclass[10pt,letterpaper,twoside,openright]{article}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\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,
	inner=20mm,
	outer=20mm,
	top=20mm,
	bottom=20mm,
	bindingoffset=10mm,
	marginparsep=10mm,
	marginparwidth=25mm,
	includemp, % to include marginparsep and marginparwidth
]{geometry}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Miscellaneous Commands %%%%%%%%%%%%%%%%%%%%%
\graphicspath{{images/}}
\renewcommand{\baselinestretch}{1.2}
\setlength{\FrameSep}{3mm}
\setlength{\OuterFrameSep}{0mm}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Style our margin notes %%%%%%%%%%%%%%%%%%%%%
%% https://tex.stackexchange.com/a/58266/245702
\NewCommandCopy{\oldmarginpar}{\marginpar}
\RenewDocumentCommand{\marginpar}{om}{%
  \IfNoValueTF{#1}
    {\oldmarginpar{\mymparsetup #2}}
    {\oldmarginpar[\mymparsetup #1]{\mymparsetup #2}}}
\newcommand{\mymparsetup}{\raggedright\sffamily\footnotesize}

\author{Kenneth John Odle}
\title{Significant Figures}
\usepackage{lipsum}
\begin{document}

\maketitle

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.

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}. 

\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}

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}, 

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.

\begin{tcolorbox}
\lipsum[7]
\end{tcolorbox}
\lipsum[2-5]

\begin{tcolorbox}[sharp corners, colback=red9, colframe=red4, title=Another paragraph with title]
\lipsum[2]
\end{tcolorbox}

\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}