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The Wikipedia lists the mass as (1.98855±0.00025)E30 kilograms. The plus-minus, of course, refers to the probable error in the Sun's mass, as currently known. That means this mass is currently known with a probable error of about 0.01%.

It is also necessary to realize that the mass of the sun is slowly but continuously decreasing. due mostly to the conversion of mass to energy in fusion (4.29E9 kilograms/second) but also the solar wind (~1E9 kilograms/second). Admittedly this mass loss is so small compared to the probable error in the total mass that it is usually ignored, but still it makes knowledge of "exact mass of the Sun" impossible.

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