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Devirli Ondalık Sayılar Konusu ve Örnekler

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By on Bilgi Dünyası
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Devirli ondalık sayılar nelerdir? Devirli ondalık sayılar ile ilgili kurallar, örneklerle konu anlatımı, çözümler.

DEVİRLİ ONDALIK SAYILAR

\displaystyle \begin{array}{l}x,\overline{y}=\frac{xy-x}{9}\\x,y\overline{zt}=\frac{xyzt-xy}{990}\end{array}

Örnek;

1) \displaystyle 0,17\overline{32}=\frac{1732-17}{9900}=\frac{1715}{9900}=\frac{343}{1980}

2) \displaystyle 3,4\overline{9}=3,5=\frac{7}{2}

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3) \displaystyle 1,\overline{9}=2

Örnek Soru;

\displaystyle \frac{a}{1,\overline{1}}=\frac{5,\overline{7}}{1,\overline{4}}\Rightarrow a=?

Çözümü;

\displaystyle 1,\overline{1}=\frac{10}{9}

\displaystyle 5,\overline{7}=\frac{57-5}{9}=\frac{52}{9}

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\displaystyle 1,\overline{4}=\frac{14-1}{9}=\frac{13}{9}

\displaystyle \frac{a}{\frac{10}{9}}=\frac{\frac{52}{9}}{\frac{13}{9}}\Rightarrow \frac{9a}{10}=\frac{52}{13}\Rightarrow a=\frac{40}{9}

Örnek

\displaystyle \frac{2}{x+0,\overline{6}}=1,8\overline{3}\Rightarrow x=?

Çözüm;

\displaystyle 1,8\overline{3}=a olsun

\displaystyle \begin{array}{l}183,\overline{3}=100a\\18,\overline{3}=10a\\165=90a\\a=\frac{165}{90}=\frac{33}{18}\Rightarrow a=\frac{11}{6}\\\frac{2}{x+\frac{6}{9}}=\frac{11}{6}\Rightarrow \\12=11x+11\frac{6}{9}\\x=\frac{14}{33}\end{array}

Örnek Soru;

a,b,c birer rakam ve \displaystyle 0,ab\overline{c}=\frac{32}{55} ise a + b + c =?

Çözüm;

\displaystyle 0,ab\overline{c}=\frac{abc-a}{990}=\frac{32}{55}=\frac{576}{990}

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a = 5 576+5=581 abc=581
b = 8
c = 1
a + b + c = 14


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