Scientists wanted to estimate the number of bacterial cells in a 45 cm345\text{ cm}^345 cm3 suspension of Lactobacillus acidophilus. They carried out the following two serial dilutions:
The scientists transferred 0.2 cm30.2\text{ cm}^30.2 cm3 of Solution 3 onto an agar plate. After incubation, 333333 separate bacterial colonies grew on the plate.
Calculate the number of bacterial cells in the original 45 cm345\text{ cm}^345 cm3 suspension.
Express your answer in standard form to three significant figures. Show your working.