The exact width is determined by taking the definition of the time required for an active line in PAL or NTSC, and dividing it by the pixel clock of 13.5MHz of Digital SDTV. PAL is exactly 52μs, so it will equate to exactly 702 pixels.
Notably, screen shapes and aspect ratios were defined in an era of purely analogue broadcasting for TV. This means that any picture with nominal analogue blanking, whether it be 702, around 704, or less, will be — by definition — a 4:3 picture. Therefore when cross-converting into a square-pixel environment (like MPEG-4 and its variants), this width must always scale to 768 (PAL) or 640 (NTSC). This has the outcome of causing a full picture of 720x576 or 720x480 to be wider than 4:3. In fact, a purely digitally sourced SDTV image, with no analogue blanking, will be close to 788x576 or 655x480 once stretched to square pixels.
Standard definition widescreen pictures were also defined in an analogue environment and must also be treated as such. This means that a purely digitally sourced widescreen SDTV image, with no analogue blanking, will be close to 1050x576 or 873x480.
For details, see the technical specifications of overscan amounts.