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Formula
Convert decimals to fractions
Answer
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$0. \dot{ 2 } 0 \dot{ 6 }$
$\dfrac { 206 } { 999 }$
Convert the repeating decimal number to a fraction
$\color{#FF6800}{ 0. \dot{ 2 } 0 \dot{ 6 } }$
$ $ Set the repeating decimal number to x $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ 0. \dot{ 2 } 0 \dot{ 6 } }$
$\color{#FF6800}{ x } = \color{#FF6800}{ 0. \dot{ 2 } 0 \dot{ 6 } }$
$ $ Multiply both sides by an appropriate power of 10 to make two expressions with the same part of the prime number $ $
$\begin{cases} \color{#FF6800}{ 1000 } \color{#FF6800}{ x } = \color{#FF6800}{ 206. \dot{ 2 } 0 \dot{ 6 } } \\ \color{#FF6800}{ 1 } \color{#FF6800}{ x } = \color{#FF6800}{ 0. \dot{ 2 } 0 \dot{ 6 } } \end{cases}$
$\begin{cases} \color{#FF6800}{ 1000 } \color{#FF6800}{ x } = \color{#FF6800}{ 206. \dot{ 2 } 0 \dot{ 6 } } \\ \color{#FF6800}{ 1 } \color{#FF6800}{ x } = \color{#FF6800}{ 0. \dot{ 2 } 0 \dot{ 6 } } \end{cases}$
$ $ Since the prime number part of the right side of the two expressions is the same, only the integer part remains $ $
$\color{#FF6800}{ 999 } \color{#FF6800}{ x } = \color{#FF6800}{ 206 }$
$\color{#FF6800}{ 999 } \color{#FF6800}{ x } = \color{#FF6800}{ 206 }$
$ $ Divide both sides by the same number $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 206 } { 999 } }$
Solution search results
search-thumbnail-Which number is rational? 
$O$ $\dfrac {\sqrt{4} } {6}$ 
$0.75n$ 
$0$ $\sqrt{8} $ 
$\sqrt{2} n$
7th-9th grade
Other
search-thumbnail-$1|k_{2}0 \,_{+}H_{2} 0->k0$
7th-9th grade
Other
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