There are two equivalent definitions of differential graded algebras with different point of view. The first one is that it is a sequence $A=(A^n)_{n\in \mathbb{Z}}$ of vector spaces together with a differential $d:A\to A$ of degree $1$ and a multiplication $\mu:A\otimes A\to A$ satisfying certain conditions. The second one is that it is an algebra $A$ together with a decomposition $A=\bigoplus_{n\in \mathbb{Z}}A^n$ and a linear map $d:A\to A$ satisfying certain conditions.
My question is which one is more natural. Thanks very much!