Giải thích các bước giải:
a.Ta có:
$M=\dfrac{33.10^3}{23.5.10^3+7000}$
$\to M=\dfrac{33.10^3}{115.10^3+7.10^3}$
$\to M=\dfrac{33.10^3}{(115+7).10^3}$
$\to M=\dfrac{33.10^3}{122.10^3}$
$\to M=\dfrac{33}{122}<\dfrac{33}{66}=\dfrac12$
Ta có:
$N=\dfrac{3773}{5214}>\dfrac{2607}{5214}=\dfrac12$
$\to M<\dfrac12<N$
$\to M<N$
b.Ta có:
$B=\dfrac47+5+\dfrac3{7^2}+\dfrac5{7^3}+\dfrac6{7^4}$
$\to B=\dfrac6{7^4}+\dfrac5{7^3}+\dfrac3{7^2}+\dfrac47+5$
$Q=\dfrac{5}{7^3}+\dfrac{6}{7^2}+\dfrac{5}{7^4}+\dfrac47+5$
$\to Q=\dfrac{5}{7^4}+\dfrac{5}{7^3}+\dfrac{6}{7^2}+\dfrac47+5$
$\to B-Q=\dfrac{1}{7^4}-\dfrac{3}{7^2}$
$\to B-Q<\dfrac{1}{7^2}-\dfrac{3}{7^2}$
$\to B-Q<\dfrac{3}{7^2}-\dfrac{3}{7^2}$
$\to B-Q<0$
$\to B<Q$
