Around¶

Represent a value with uncertainty.

$ wo 'Around[5, 0.3]'
Around[5., 0.3]

Exact numbers are converted to machine reals.

$ wo 'Around[3/4, 1/8]'
Around[0.75, 0.125]

Around[x, {δminus, δplus}] represents a value with asymmetric uncertainties.

$ wo 'Around[5, {0.1, 0.2}]'
Around[5., {0.1, 0.2}]

Around[dist] represents an approximate number from a distribution.

$ wo 'Around[NormalDistribution[3, 2]]'
Around[3., 2.]

Around[interval] centers on the interval midpoint with an uncertainty of half the interval width.

$ wo 'Around[Interval[{2, 4}]]'
Around[3., 1.]

Arithmetic propagates the uncertainty, treating each Around as independent.

$ wo 'Around[5, 1] + Around[3, 1]'
Around[8., 1.4142135623730951]

$ wo 'Around[5, 1]^2'
Around[25., 10.]

Asymmetric uncertainties are propagated per side; a negative coefficient swaps the two sides.

$ wo 'Times[-1, Around[5, {0.1, 0.2}]]'
Around[-5., {0.2, 0.1}]

Elementary functions propagate the uncertainty through their derivative.

$ wo 'Sqrt[Around[4, 1]]'
Around[2., 0.25]

A vanishing uncertainty collapses to the bare value.

$ wo 'Around[5, 0]'
5

around["Value"] and around["Uncertainty"] extract the stored components.

$ wo 'Around[5, 0.3]["Uncertainty"]'
0.3