"a whole number" (as opposed to a fraction), 1570s, from noun use of Latin integer (adj.) "intact, whole, complete," figuratively, "untainted, upright," literally "untouched," from in- "not" (see in- (1)) + root of tangere "to touch" (from PIE root *tag- "to touch, handle"). The word was used earlier in English as an adjective in the Latin sense, "whole, entire" (c. 1500).
Proto-Indo-European root meaning "to break."
It forms all or part of: anfractuous; Brabant; bracken; brake (n.1) "stopping device for a wheel;" brake (n.2) "kind of fern;" brash; breach; break; breccia; breeches; brioche; chamfer; defray; diffraction; fractal; fraction; fractious; fracture; fragile; fragility; fragment; frail; frangible; infraction; infringe; irrefragable; irrefrangible; naufragous; ossifrage; refract; refraction; refrain (n.); refrangible; sassafras; saxifrage; suffragan; suffrage.
It is the hypothetical source of/evidence for its existence is provided by: Sanskrit (giri)-bhraj "breaking-forth (out of the mountains);" Latin frangere "to break (something) in pieces, shatter, fracture;" Lithuanian braškėti "crash, crack;" Old Irish braigim "break wind;" Gothic brikan, Old English brecan "to break."
before vowels mer-, word-forming element meaning "part, partial, fraction," from Greek meros "a part, a fraction," from PIE root *(s)mer- (2) "to get a share of something."
c. 1600, "pertaining to a tenth or ten," from Medieval Latin decimalis "of tithes or tenths," from Latin decimus "tenth," from decem "ten" (from PIE root *dekm- "ten"). Applied to Arabic notation before modern use in reference to decimal fractions (fraction whose denominator is a power of 10) emerged 1610s. As a noun from 1640s, "a decimal fraction." Decimal point is by 1711; the use of the point seems to be due to Scottish mathematician John Napier, "Marvellous Merchiston," c. 1619.