A fractional entitlement is the portion of a security, smaller than one whole unit, that arises when the terms of a corporate action are applied to a holding and the result is not a whole number. If a company announces a stock dividend of one new share for every eight held, an investor with 100 shares is entitled to 12.5 shares; the 0.5 is the fractional entitlement.
Most markets do not allow fractions of a share to be held or settled at a central securities depository, so the event terms state how they are handled: rounded up, rounded down, or sold with the proceeds paid as a cash-in-lieu payment. The method chosen, and the level in the custody chain at which it is applied, is described under fractional share treatment and is part of the entitlement calculation.