Bài 2.42 trang 34 SBT Toán 7 Kết nối tri thức: So sánh (a = 1,0left( {10} right);b = 1,left( {01} right))...

So sánh \(a = 1,0\left( {10} \right);b = 1,\left( {01} \right)\)

Đặt \(x = 0,0\left( {10} \right) \Rightarrow 1000x = 10,0\left( {10} \right) \Rightarrow \)Tìm x

        \(y = 0,\left( {01} \right) \Rightarrow 100y = 1,\left( {01} \right) \Rightarrow \)Tìm y

Tính a, b

So sánh a, b

Đặt \(x = 0,0\left( {10} \right) \Rightarrow 1000x = 10,\left( {10} \right) \Rightarrow 1000x = 10 + 10x \Rightarrow 990x = 10 \Rightarrow x = \dfrac{1}{{99}}\)

\( \Rightarrow a = 1 + 0,0\left( {10} \right) = 1 + \dfrac{1}{{99}} = \dfrac{{100}}{{99}}\)

Đặt \(y = 0,\left( {01} \right) \Rightarrow 100y = 1,\left( {01} \right) \Rightarrow 100y = 1 + y \Rightarrow 99y = 1 \Rightarrow y = \dfrac{1}{{99}}\)

\( \Rightarrow b = 1 + 0,\left( {01} \right) = 1 + \dfrac{1}{{99}} = \dfrac{{100}}{{99}}\)

Vậy \(a = b\).