James had a peach that was 98mm in diameter. One day he watered it with a magical solution, and it grew to 188,869 mm in diameter. Approximately how many times as large did the diameter of the peach become after James watered it?

We know that 98mm is the 100% of the diameter of the plant before James watered with the magical solution; after he watered, the diameter of the plant grew to 188.869mm. Let [tex]x[/tex] be the grew in the percentage of the diameter. 
Now we can establish a ratio and solve for [tex]x[/tex]:
[tex] \frac{98}{100} = \frac{188.869}{x} [/tex]
[tex]x= \frac{(188.869)(100)}{98} [/tex]
[tex]x=192.7[/tex] %
Now that we know the diameter of the plant grew 192.7%, we just need to divide that quantity by 100% to find how many times the diameter grew:
[tex] \frac{192.7}{100} =1.927[/tex]

We can conclude that the diameter of the peach become approximately 1.9 times larger after James watered it.