PNG files may contain chunks of optional informations. One of these optional information blocks is the physical resolution of the image (chunk-signature pHYs).[1] [2] It contains separate values for horizontal and vertical resolution as pixels per unit, and a unit specifier, that can be 0 for unit unspecified, or 1 for meter ← that's quite confusing, because resolutions are traditionally expressed in DPIs.
The Inch is defined as 25.4 mm in the metric system.
So, if I calculate this correctly, 96 DPIs means 3779.527559... dots per metre. For the pHYs chunk, this has to be rounded. I'd say 3780 is the right value, but I found also 3779 suggested on the web. Images of both kind also coexist on my machine.
The difference may not be important in most cases,
3779 * 0.054 = 95.9866
3780 * 0.054 = 96.012
but I try to avoid tricky layout problems when mixing images of both kind in processes that are DPI-aware like creating PDF files using LaTeX.
[2] PNG Specification: Chunk Specifications, section 4.2.4.2. pHYs Physical pixel dimensions