So sánh \(a = 0,\left( {12} \right)\) và \(b = 0,1\left( {21} \right)\)
\(a = 0,\left( {12} \right) \Rightarrow 100a = 12,\left( {12} \right)\)
Tính 0,(21) dưới dạng phân số
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\(a = 0,\left( {12} \right) \Rightarrow 100a = 12,\left( {12} \right) \Rightarrow 100a = 12 + a \Rightarrow 99a = 12 \Rightarrow a = \dfrac{{12}}{{99}}\)
\(b = 0,1\left( {21} \right) = 0,1 + 0,0\left( {21} \right) = \dfrac{1}{{10}} + \dfrac{1}{{10}}.0,\left( {21} \right)\)
Đặt \(x = 0,\left( {21} \right) \Rightarrow 100x = 21,\left( {21} \right) \Rightarrow 100x = 21 + x \Rightarrow 99x = 21 \Rightarrow x = \dfrac{{21}}{{99}}\)
\( \Rightarrow b = \dfrac{1}{{10}} + \dfrac{1}{{10}}.\dfrac{{21}}{{99}} = \dfrac{1}{{10}}.\left( {1 + \dfrac{{21}}{{99}}} \right) = \dfrac{1}{{10}}.\dfrac{{120}}{{99}} = \dfrac{{12}}{{99}}\)
Vậy \(a = b\)