Which of the following may appear on floors and indicate where fuel burned in that location?

Charring is the correct choice because it refers to the blackened, burned appearance of materials that have been exposed to intense heat and flames. When fuel burns in a particular location, the surface material will combust, leading to charring. This is a significant indicator in fire investigations as it provides clear evidence of the fire's origin and intensity. The presence of charred materials typically indicates direct exposure to flames, which supports the assessment of where the fuel was located and how the fire developed.

The other options—cracking, sooting, and discoloration—while they can also occur in fire situations, do not specifically point to where fuel has burned to the same extent as charring does. For instance, cracking may indicate structural damage but does not directly correlate to burned fuel locations. Sooting relates to the deposition of soot from incomplete combustion, which might not be limited to places where fuel was burned, and discoloration can result from heat damage but is less definitive in determining the origin of the fire compared to charring. Thus, charring serves as a more direct and unequivocal sign of where fuel was burned during a fire incident.