# How does the function Around[] work?

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 From the Wolfram Blog (Computing Exact Uncertainties—Physical Constants in the Current and in the New SI): The arithmetic model of Around[] follows the GUM (Guide to the Expression of Uncertainty in Measurement)—not to be confused with Leibniz’s Plus-Minus-calculus. I do not get what this has to do with the Plus-Minus-Calculus, perhaps the author meant interval arithmetic? Anyway, Around[1.2, 0.1]^2 leads to $1.44\pm0.24$ although $[1.2-0.1,1.2+0.1]^2=[1.45-0.24,1.45+0.24]$, so why do I get the value 1.44 instead of 1.45?Also, does anyone know how CODATA calculates with uncertainties? I tried to reproduce the CODATA 2018 values in SI units of the base Planck units, and indeed, it all fits except for the Planck time. Sqrt[6.62607015/(2 * Pi) * 10^(-34) * Around[6.67430, 0.00015] * 10^(-11)/299792458^5] gives $(5.39125\pm 0.00006)\times 10^{-44}$ while the CODATA 2018 value is $5.391\,247(60)\times10^{-44}\,\mathrm s$.
 At https://reference.wolfram.com/language/ref/Around.html under 'Properties & Relations' there is just the same operation you are asking about: Around[10, 1]^2 According to this: (x+y)^2=x^2+2xy+y^2,computing (1.2+0.1)^2=1.2^2+21.20.1+0.1^2Let 0.1=delta, then ( 1.2 + 0.1 )^2= 1.2^2 + 2 * 1.2 * delta + delta^2Around makes a first order series approximation, i.e. the highest delta power is 1, and you can check that 2 * 1.2 * 0.1=0.24, no 0.1^2 added to it.I Hope this helps.