TITLE: "Natural" example of cosets
QUESTION [57 upvotes]: Do you know natural/concrete/appealing examples of right/left cosets in group theory ?
This notion is a powerful tool but also a very abstract one for beginners so this is why I'm looking for friendly examples.

REPLY [2 votes]: The slide rule is an old analog computing device that can be considered as being based on the quotient group $(\mathbb{R_+^*}, \times)/\{10^k, \ k \in \mathbb{Z} \}$ which could be called as well the "floating point universe". An example:
$$\cdots \ \equiv \ 7530 \ \equiv \ 753 \ \equiv \ 75.3 \ \equiv  \ 7.53 \ \equiv \ 0.753 \ \equiv  0.0753 \equiv \cdots $$