Macaulay and Modified Duration

現在マコレーデュレーションと修正デュレーションの単位違いを考えている。マコレーはキャッシュフローの残存年数の加重平均です。平均回収期間ともていぎされる。(Wikipedia). Units are thus time (years).
修正デュレーションは利子による値段の敏感さ。modified duration describes the percent change in the price of a bond per one percent increase in yield. The units are percentage. However, I am not sure how the forma equating Macaulay and Modified durations reconciles thee units. D*=D/(1+y/k) where D* is the Modified Duration.
I am also unclear about the units of Convexity, as the interest is written in decimal form when computing the price effect. Delta p = .5*C*(delta y)^2.
Units for convexity and duration seem to be the percentage value change per one unit move in yield (100%), not per 100bps, as is written in some texts. In fact, the units are actually fractional (decimal) change in price, and must be multiplied by 100 to obtain the percent change.