Question

Cho A=\(\dfrac{10^7+1}{10^8+ 1}\)

B=\(\dfrac{10^8+1}{10^9+1}\)

Answer 1

đề kêu là gì zậy ?

Answer 2

Ta có:

\(10A=10.\dfrac{10^7+1}{10^8+1}=\dfrac{10.10^7+1}{10^8+1}=\dfrac{10^8+1}{10^8+1}=1\)

\(10B=\dfrac{10.10^8+1}{10^9+1}=\dfrac{10^9+1}{10^9+1}=1\)

\(\Rightarrow10A=10B\)

\(\Rightarrow A=B\)

Answer 3

Ta có: \(B=\dfrac{10^8+1}{10^9+1}< 1\)

\(B=\dfrac{10^8+1}{10^9+1}< \dfrac{10^8+1+9}{10^9+1+9}=\dfrac{10^8+10}{10^9+10}=\dfrac{10.\left(10^7+1\right)}{10.\left(10^8+1\right)}=A\)

=> B < A

Vậy B < A

Answer 4

B = \(\dfrac{10^8+1}{10^9+1}\) < \(\dfrac{10^8+1+9}{10^9+1+9}\) (1)
Ta có:
\(\dfrac{10^8+1+9}{10^9+1+9}\) = \(\dfrac{10^8+10}{10^9+10}=\dfrac{10.\left(10^7+1\right)}{10.\left(10^8+1\right)}\) = \(\dfrac{10^7+1}{10^8+1}\)= A (2)
Từ (1) và (2), suy ra:
B < A hay:
A > B.