Rounding and representing as string quantities with uncertainty in MATLAB.

approx.m

function y = approx(x, n)
% APPROX  Round the number to 1+n significant digits.
%   y = APPROX(x) shorthand for round(x, 4, 'significant').
%   y = APPROX(x, n) shorthand for round(x, 1 + n, 'significant').

%   Copyright 2016 Pyry Jahkola

if nargin < 2
    n = 3;
end

m = floor(log10(abs(x)));
unit = 10 .^ (max(m) - n);
y = bsxfun(@times, round(bsxfun(@rdivide, x, unit)), unit);

concise.m

function str = concise(x, d)
% CONCISE  Concise representation of a quantity value x ± d.
%   str = CONCISE(x, d) returns the concise form string representation of
%   x ± d where the precision in x is kept up to the two most significant
%   digits of d and those two digits are shown in parentheses.
%
%   The result is shown with power-of-ten representation which is omitted
%   if the exponent is zero.
%
% Examples
%
%   CONCISE(3.14159, 0.0485) %=> '3.142(49)'
%   CONCISE(6.02214129e23, 2.7e16) %=> '6.02214129(27) × 10^23'
%   CONCISE(6.67408e-11, 3.1e-15) %=> '6.67408(31) × 10^-11'

%   Copyright 2016 Pyry Jahkola

xmag = floor(log10(abs(x)));
dmag = floor(log10(abs(d)));
mag = max(xmag, dmag);
prec = mag - dmag + 1;
x = round(x, 1 - dmag);
if dmag >= 0
    D = round(d / 10 ^ (dmag - 1));
else
    D = round(d * 10 ^ (1 - dmag));
end

if mag > 0
    X = x / 10 ^ mag;
    fmt = sprintf('%%.%df(%%02d) × 10^%%d', prec);
    str = sprintf(fmt, X, D, mag);
elseif mag < 0
    X = x * 10 ^ -mag;
    fmt = sprintf('%%.%df(%%02d) × 10^%%d', prec);
    str = sprintf(fmt, X, D, mag);
else
    X = x / 10 ^ mag;
    fmt = sprintf('%%.%df(%%02d)', prec);
    str = sprintf(fmt, X, D);
end

magnitude.m

function m = magnitude(x)
% MAGNITUDE  Get the power-of-ten order of a number.
%   m = MAGNITUDE(x) returns the largest integer m where 10^m <= abs(x).
%   m = MAGNITUDE(0) returns -Inf.

%   Copyright 2016 Pyry Jahkola

m = floor(log10(abs(x)));

plusminus.m

function str = plusminus(x, d)
% PLUSMINUS  Full representation of quantity value x ± d
%   str = PLUSMINUS(x, d) returns the value x ± d as a string of
%   form of either '(x ± d) × 10^e' or 'x ± d', keeping precision
%   up to two most significant digits of d, and omitting the
%   power-of-ten representation for values within range [0.1, 1000).
%
% Examples
%
%   PLUSMINUS(3.14159, 0.0485)       %=> '3.142 ± 0.049'
%   PLUSMINUS(6.02214129e23, 2.7e16) %=> '(6.02214129 ± 0.00000027) × 10^23'
%   PLUSMINUS(6.67408e-11, 3.1e-15)  %=> '(6.67408 ± 0.00031) × 10^-11'

%   Copyright 2016 Pyry Jahkola

xmag = floor(log10(abs(x)));
dmag = floor(log10(abs(d)));
mag = max(xmag, dmag);
prec = mag - dmag + 1;
x = round(x, 1 - dmag);
d = round(d, 1 - dmag);

if mag > 3
    X = x / 10 ^ mag;
    D = d / 10 ^ mag;
    fmt = sprintf('(%%.%df ± %%.%df) × 10^%%d', prec, prec);
    str = sprintf(fmt, X, D, mag);
elseif mag < -2
    X = x * 10 ^ -mag;
    D = d * 10 ^ -mag;
    fmt = sprintf('(%%.%df ± %%.%df) × 10^%%d', prec, prec);
    str = sprintf(fmt, X, D, mag);
elseif xmag > dmag && mag < 0
    fmt = sprintf('%%#.%dg ± %%.%dg', prec + 1, prec + 1);
    str = sprintf(fmt, x, d);
else
    fmt = sprintf('%%.%df ± %%.%df', max(0, 1 - dmag), max(0, 1 - dmag));
    str = sprintf(fmt, x, d);
end