In Consumer Reports Best Baby Products, I write about basic bathtub safety 
such as to never leave your baby unattended during bath time, even for a second, and to fill the tub with as little water as possible. According to the U.S. Consumer Product Safety Commission, 39 children under age 5 died from baby bath tubs or bath seats from 2003 to 2005 (the latest stats).
A recent study in Pediatrics shows that bathtubs and showers are also significant source of injury for kids, with an average of 43,600 cases per year. The largest number of injuries were from slips, trips, and falls and involved children age 4 and under.
The study says that to decrease the incidence of these injuries, “increase the coefficient of friction of bathtub and shower surfaces.” In other words, when your baby graduates to a regular bathtub, attach rubber strips to the bottom of the tub to prevent slipping. 
For a strip search, Google “bathtub” and “strips.” I found these bathtub safety strips, for example, on Amazon for roughly $13.
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