phân số là gì vậy bạn

\(A=\dfrac{-9\cdot10+\left(-19\right)}{10^{2011}}=\dfrac{-28}{10^{2011}}\)

\(B=\dfrac{-9\cdot10-19}{10^{2011}}=\dfrac{-109}{10^{2011}}\)

=>A>B

nhanh với 

A=\(\frac{-199}{10^{2011}}\)

B=\(\frac{-109}{10^{2011}}\)

Dễ dàng so sánh được A<B

A=-9/10²⁰¹¹+(-19/10²⁰¹⁰)

B=-9/10²⁰¹⁰+(-19/10²⁰¹¹)

Vì -9/10²⁰¹¹>(-19/10²⁰¹¹) và -9/10²⁰¹¹-(-19/10²⁰¹¹)=10/10²⁰¹¹

-19/10²⁰¹⁰<(-9/10²⁰¹⁰) và -9/10²⁰¹⁰-(-19/10²⁰¹⁰)=10/10²⁰¹⁰

mà 10/10²⁰¹¹<10/10²⁰¹⁰ nên suy ra B>A

ta có -9\10^2011=-9\10^2011

mà -19\10^2011>-19\10^2011

nên A>B

****

Xét  -A= \(\frac{9}{10^{2010}}+\frac{19}{10^{2011}}=\frac{9}{10^{2010}}+\frac{10+9}{10^{2011}}=\frac{9}{10^{2010}}+\frac{10}{10^{2011}}+\frac{9}{10^{2011}}=\frac{9}{10^{2010}}+\frac{9}{10^{2011}}+\frac{1}{10^{2010}}\)

Xét -B = \(\frac{9}{10^{2011}}+\frac{19}{10^{2010}}=\frac{9}{10^{2011}}+\frac{10+9}{10^{2010}}=\frac{9}{10^{2011}}+\frac{10}{10^{2010}}+\frac{9}{10^{2010}}=\frac{9}{10^{2010}}+\frac{9}{10^{2011}}+\frac{1}{10^{2009}}\)

Nhận xét : 10²⁰¹⁰ > 10²⁰⁰⁹\(\Rightarrow\frac{1}{10^{2010}}< \frac{1}{10^{2009}}\Leftrightarrow\frac{9}{10^{2010}}+\frac{9}{10^{2011}}+\frac{1}{10^{2010}}< \frac{9}{10^{2010}}+\frac{9}{10^{2011}}+\frac{1}{10^{2009}}\)

=> -A < -B => A > B