The rational number, which equals the number 2.357 with recurring decimal is

(c) : 2 . / line357=2+0.357+0.000357+ * s infinity =2+(357 / 10^3)+(357 / 10^6)+ * s * infinity=2+frac(357 / 10^3)1-(1 / 10^3) =2+(357 / 999)=(2355 / 999) Let x=2 . / line357 => 1000 x=2357 . / line357 On subtracting, we get 999 x=2355 \ => x=(2355 / 999)

The rational number, which equals the number 2.357 with... | Sequence & Series (Mathematics)

(c) $: 2 . \overline{357}=2+0.357+0.000357+\cdots \infty$ $\\=2+\frac{357}{10^3}+\frac{357}{10^6}+\cdots \cdot \infty=2+\frac{\frac{357}{10^3}}{1-\frac{1}{10^3}}\\=2+\frac{357}{999}=\frac{2355}{999}\\$ Let $x=2 . \overline{357} \Rightarrow 1000 x=2357 . \overline{357}\\$ On subtracting, we get $999 x=2355 \\ \Rightarrow x=\frac{2355}{999}$

Explanation

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