Question

Представте в виде обыкновенной дроби бесконечнуб десятичную дробь a)0.(27) b) 0.5(6) sos

Answer 1

X=0.(27)
100x=27.(27)
100x-x=27
99x=27
$x=\frac{27}{99}=\frac{3}{11}$
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$b_1=0.27;q=0.01$
$S=\frac{b_1}{1-q}=\frac{0.27}{1-0.01}=\frac{27}{99}=\frac{3}{11}$
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x=0.5(6)
10x=5.6(6)
$10x-x=5.1$
$9x=5.1$
$90x=51$
$x=\frac{51}{90}=\frac{17}{30}$
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$b_1=0.06;q=0.1$
$S=0.5+\frac{b_1}{1-q}=0.5+\frac{0.06}{1-0.1}=\\\\\frac{45}{90}+\frac{6}{90}=\frac{51}{90}=\frac{17}{30}$

Answer 2

0,27=27/100

0,5=5/10=1/5

0,6=6/10=3/5