Question

so sánh \(\frac{10^{11}-1}{10^{12}-1}\) và\(\frac{10^{10}+1}{10^{11}+1}\)

Answer 1

Ta dựa vào công thức:

\(\frac{a}{b}<1\Leftrightarrow\frac{a+n}{b+n}>\frac{a}{b}\)

\(\left(1\right)=\frac{10^{11}-1}{10^{12}-1}<\frac{10^{11}-1+11}{10^{12}-1+11}=\frac{10^{11}+10}{10^{12}+10}=\frac{10.\left(10^{10}+1\right)}{10.\left(10^{11}+1\right)}=\frac{10^{10}+1}{10^{11}+1}=\left(2\right)\)

Answer 2

Đặt (1) là cái đầu

(2) là cái thứ 2 

Answer 3

Vì \(\frac{10^{11}-1}{10^{12}-1}=\frac{-1}{10-1}=\frac{-1}{9};\frac{10^{10}+1}{10^{11}+1}=\frac{1}{10+1}=\frac{1}{11}\)

mà \(\frac{-1}{9}=\frac{-1.11}{9.11}=\frac{-11}{99};\frac{1}{11}=\frac{1.9}{11.9}=\frac{9}{99}\)

nên \(\frac{-11}{99}<\frac{9}{99}\)

vậy \(\frac{10^{11}-1}{10^{12}-1}<\frac{10^{10}+1}{10^{11}+1}\)