Answer
The percent for nose reshaping is $10.22\%$.
Work Step by Step
To calculate the percent for a type of cosmetic plastic surgery (let's say type A) in 2009, we need 2 data:
1) The total number of cosmetic plastic surgeries in 2009 ($X$).
2) The number of type A surgeries in 2009 ($X_A$).
Then the percent for type A surgeries is $$P=\frac{X_A}{X}\times100\%$$
In this exercise, the total number of cosmetics plastic surgeries in 2009: $X=1.35million=1,350,000$
The number of nose reshaping surgeries is $X_A=138,000$.
Therefore, the percent for nose reshaping is
$$P=\frac{138,000}{1,350,000}\times100\%.$$
$$P\approx10.22\%$$