Official Explanation
The number of germs in a single dish equals the number of germs divided by the number of dishes. The top of the fraction is given in scientific notation. Changing the bottom to scientific notation will allow you to reduce some annoying 0's and work with more comfortable numbers.
Remember the rule: Maintain the balance between the digit term and the exponential term. If one goes up (↑) by a magnitude of 10, the other must go down (↓) by the same magnitude, and vice versa.
Germs: \(5.4×10^6=54×10^5\)
Dishes: \(10,800=108×10^2\)
Germs per dish: \(\frac{54×10^5}{108×10^2}\)
Note that 54108 can be reduced to \(\frac{1}{2}\). Thus, the calculation can be reduced to
\(\frac{1}{2}×\frac{10^5}{10^2}=\frac{1}{2}×10^{5−2}=\frac{1}{2}×10^3\)
\(=\frac{10^3}{2}=\frac{1,000}{2}=500\) germs per dish.
Answer: C
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