Question

So sanh A va B biet rang:

\(A=\frac{10^{15}+1}{10^{16}+1}\)                \(B=\frac{10^{16}+1}{10^{17}+1}\)

 

TOÁN 6 NHA

Answer 1

Trước hết ta so sánh 10A và 10B

Ta có:

           \(10A=\frac{10^{16}+10}{10^{16}+1}=1+\frac{9}{10^{16}+1}\)                \(10B=\frac{10^{17}+10}{10^{17}+1}=1+\frac{9}{10^{17}+1}\)

Vì:  \(\frac{9}{10^{16}+1}>\frac{9}{10^{17}+1}\) nên 10A > 10B, do đó A>B

 

Answer 2

Ta thấy:B<1 vì 10¹⁵+1<10¹⁶+1 
Theo quy tắc :\(\frac{a}{b}\)<\(\frac{a+m}{b+m}\)nên ta có: B =\(\frac{10^{16}+1}{10^{17}+1}\)<\(\frac{10^{16}+1+9}{10^{17}+1+9}\)<\(\frac{10^{16}+10}{10^{17}+10}\)<\(\frac{10\left(10^{15}+1\right)}{10\left(10^{16}+1\right)}\)=A
Suy ra B<A

Answer 3

trước hết ta so sánh 10A và 10B                                     

10A =10^16+10/10^16+1                                                   10B=10^17+10/10^17+1

10A=1+9/10^16+1                                                               10B=1+9/10^17 +1

                           mà 1=1;9/10^16+1>9/10^17+1 nên 10A>10B nên A>B

Answer 4

cách mik làm cũng ra mà

Answer 5

tui cũng zậy

 

Answer 6

bạn ơi, làm sao mà lớn hơn được, A=B mà

Answer 7

Ta có :

10A = \(\frac{10\left(10^{15}+1\right)}{10^{16}+1}\) = \(\frac{10^{16}+10}{10^{16}+1}\) = \(\frac{10^{16}+1+10}{10^{16}+1}\) = \(\frac{10^{16}+1}{10^{16}+1}\) + \(\frac{9}{10^{16}+1}\) = 1 + \(\frac{9}{10^{16}+1}\)

10B = \(\frac{10\left(10^{16}+1\right)}{10^{17}+1}\) = \(\frac{10^{17}+10}{10^{17}+1}\) = \(\frac{10^{17}+1+9}{10^{17}+1}\) = \(\frac{10^{17}+1}{10^{17}+1}\) + \(\frac{9}{10^{17}+1}\) = 1 + \(\frac{9}{10^{17}+1}\)

Vì \(\frac{9}{10^{16}+1}\) > \(\frac{9}{10^{17}+1}\) \(\Rightarrow\) 1 + \(\frac{9}{10^{16}+1}\) > 1 + \(\frac{9}{10^{17}+1}\)

\(\Rightarrow\) 10A > 10B

\(\Rightarrow\) A > B

Vậy A > B