unitless
Unitlessexact by definition
A pure number with no unit at all — a Reynolds number, a logarithm, a diffraction order, a factor of safety. It is not a count of anything and not a fraction of anything, so there is nothing to convert it to and nothing to print after it. Its conversion factor is one because the only unit it has is none.
Watch out: Three different things get called dimensionless and only one of them is unitless. A percentage is dimensionless but a percent IS a unit. A count is dimensionless but a dozen is a unit. And a slope or a strain has no dimension of its own yet is still spoken with one — metres per metre, rise over run — because its unit is inherited from the quantities that made it. Only the pure numbers here have nothing to say after the digits.
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Quantities of this kind arise wherever the units cancel completely. A Reynolds number is built from a density, a speed, a length and a viscosity, and every dimension in it divides out — which is precisely what makes it useful, because the same value describes a model ship in a tank and the full-size hull at sea. That transferability is the whole point of a dimensionless group, and it survives only because the number carries no unit to disagree about.