Question

So sánh

\(M=\left(\dfrac{9}{11}-0,81\right)^{2014}\) \(N=\dfrac{1}{10^{4028}}\)

Answer 1

Ta có:

\(M=\left(\dfrac{9}{11}-0,81\right)^{2014}\)

\(=\left(\dfrac{9}{1100}\right)^{2014}\)

\(=\left(\dfrac{9}{11}.\dfrac{1}{100}\right)^{2014}\)

\(=\dfrac{9^{2014}}{11^{2014}}.\dfrac{1}{100^{2.2014}}\)

\(=\dfrac{9^{2014}}{11^{2014}}.\dfrac{1}{10^{2048}}\)

Vì: \(\dfrac{1}{10^{2048}}=\dfrac{1}{10^{2048}}\)

Nên: \(\dfrac{9^{2014}}{11^{2014}}.\dfrac{1}{10^{2048}}>\dfrac{1}{10^{2048}}\)

Hay: M>N

Vậy M>N

Answer 2

\(\dfrac{9}{11}-0,81=\dfrac{9}{11}-\dfrac{81}{100}=\dfrac{81}{99}-\dfrac{81}{100}< \dfrac{81+1}{99+1}-\dfrac{81}{100}\)

\(=\dfrac{82}{100}-\dfrac{81}{100}=\dfrac{1}{100}\)

\(\Rightarrow\left(\dfrac{9}{11}-0,81\right)^{2014}< \left(\dfrac{1}{100}\right)^{2014}=\dfrac{1}{10^{4028}}\)

\(M< N\)

Vậy \(M< N\)