Quantities of dimension one, or numerical quantities, are numbers which may be integers (or exceptionally half-integers) when obtained by counting (e.g. number of molecules, quantum numbers, ...), rational numbers such as ratios, factors and fractions when obtained as ratios of two quantities of the same kind or real numbers when obtained by taking logarithms (e.g. absorbance, power levels, ...).
Sources:
Green Book, 2nd ed., p. 77 (https://goldbook.iupac.org/files/pdf/green_book_2ed.pdf)
PAC, 1996, 68, 957. 'Glossary of terms in quantities and units in Clinical Chemistry (IUPAC-IFCC Recommendations 1996)' on page 969 (https://doi.org/10.1351/pac199668040957)