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  be the grew in the percentage of the diameter. 
Now we can establish a ratio and solve for :


%
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:


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

Seventh power of 10

Step-by-step explanation:

X > 1 so exponent will be positive and decimal point moves left. At each point divide X by 10, add 1 to exponent of 10. Exponent starts at zero.

Each time you move the decimal point one to left, you have divided the number by 10, so you have to compensate by multiplying the 10^n factor by 10, say 10 × 10^3 = 10×10×10×10 = 10^4.

12345678 = 12345678 × 10^0

= 1234567.8 × 10^1

= 123456.78 × 10^2

= 12345.678 × 10^3

= 1234.5678 × 10^4

= 123.45678 × 10^5

= 12.345678 × 10^6

= 1.2345678 × 10^7

Each time you move decimal to right, you have multiplied the number by 10, so you have to compensate by dividing the 10^n by 10, subtracting one from exponent.

0.000123 × 10^0 = 0.00123 × 10^-1

= 0.0123 × 10^-2 = 0.123 × 10^-3 = 1.23 × 10^-4

10^-2 / 10 = (1/(10×10)) / 10 = 1/(10×10×10) = 10^-3