Worksheets with Big Numbers

Question

I am trying to make mental math worksheets with exercises such as

25% of 80 trillion is ___

It seems that pgf and/or pgfmath is not capable of doing this as the numbers are too large. The code compiles with smaller numbers.

How should I do this?

When I figure out what's going on, I'll switch to random numbers that generate exercises and solutions worksheets, but I believe the MWE below demonstrates the problem.

\documentclass{article}

\usepackage{pgf}
\usepackage{pgfmath}

\pagestyle{empty}


\begin{document}

\pgfmathsetmacro{\Product}{int(20000*50000)}

\Product

\end{document}

Answer 1

You can use xfp or xint. For the above purpose they have the advantage that they can yield expandable expressions. pgf also works with the fpu library (and also with the fixedpointarithmetic library together with the fp package, but the latter is arguably superseded by xfp). Here is one example.

\documentclass{article}

\usepackage{xfp}

\pagestyle{empty}


\begin{document}

\fpeval{20000*50000}

\end{document}

Answer 2

DISCLAIMER: This only works with LuaTeX and only with integers.

If you want to work with arbitrary-precision integers, a pure Lua module which handles very well with otherwise difficult cases is lua-nums. You need to download bn.lua and put it in the same folder as your main file.

I've avoided parsing, but you could look at LPEG for more advanced examples. For the moment, basic operations (+, -, *, /, ^, //, %) and binary operators (&, |, >>, <<, ~, |) should work, although passing special characters to Lua is kinda a pain. There's a trade-off between cumbersome typing and speed of operations as lua-nums runs smoothly.

\documentclass{article}
%\usepackage{geometry}
%\geometry{paperwidth=100mm,paperheight=85mm,margin=2em}
\usepackage{luacode}
\begin{luacode*}
userdata = userdata or {}
--bn.lua should be in the same folder as \jobname.tex
userdata.bn = require"bn"
userdata.evaluatebn = function(s)
    return load("return ".. s:gsub("%d+", "userdata.bn(%1)"))()
end
\end{luacode*}
\newcommand{\evaluatebn}[1]{\directlua{tex.sprint(tostring(userdata.evaluatebn("#1")))}}
\begin{document}
\section{Rationale}
In Spanish and English (long scale), a trillion stands for $10^{18}$: \evaluatebn{10^18}.

%Integer division, so // and / are interchangeable
25\% of 80 trillion (long scale) is \evaluatebn{80*10^18//4}

25\% of 80 trillion (short scale) is \evaluatebn{80*10^12//4}

\section{Some other examples}
\begin{itemize}
\item $2^{70} = \evaluatebn{1 << 70}$
% \string& instead of Lua's &
\item $47542121789123 = 4\times\evaluatebn{(47542121789123 >> 2)} + \evaluatebn{(47542121789123 \string& 3)}$
\item $15! = \evaluatebn{1*2*3*4*5*6*7*8*9*10*11*12*13*14*15}$
% \csstring\% instead of Lua's %
\item $47542121789\% 4787973 = \evaluatebn{(47542121789 \csstring\% 4787973)}$
\end{itemize}
\end{document}