Предмет: Математика, автор: Pustobaeva99

Предстаыьте периодическую дробь в виде обыкновенной 0(1);0,(27);3,(5);0,1(23);0,12(7)

Ответы

Автор ответа: arsenlevadniy
0
x=0,(1), \ 10x=1,(1), \ 9x=1, \ x=frac{1}{9};

0,(27)=frac{27-0}{99}=frac{27}{99}=frac{3}{11};

3,(5)=frac{35-3}{9}=frac{32}{9};

0,1(23)=frac{123-1}{990}=frac{122}{990}=frac{61}{495};

x=0,12(7), \ 100x=12,(7), \ 1000x=127,(7), \ 900x=127-12, \ x=frac{115}{900}=frac{23}{180}.

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