Final answer:
The nurse should document the finding as blanching, which is the temporary whitening of the skin when pressure is applied.
Step-by-step explanation:
The term that the nurse should document for the finding where the area of erythema on the child's skin becomes white when pressed down is blanching. Blanching is the temporary whitening of the skin that occurs when pressure is applied and blood flow to the area is momentarily disrupted.
In this case, the blanching indicates that the erythema is caused by dilation of blood vessels in the area, such as in inflammation or a type I hypersensitivity reaction, where increased blood flow to the area causes redness. When pressure is applied, the blood flow is temporarily interrupted and the area becomes white.
Other terms mentioned in the options are not relevant to this finding. Hyperemia refers to increased blood flow to an area, purpura refers to purple discoloration caused by bleeding into the skin, and petechiae are small red or purple spots caused by blood leaking from damaged vessels.