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Convert decimals to fractions
Answer
$\dfrac { 5 } { 9 }$
Convert the repeating decimal number to a fraction
$\color{#FF6800}{ 0. \dot{ 5 } }$
$ $ Set the repeating decimal number to x $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ 0. \dot{ 5 } }$
$\color{#FF6800}{ x } = \color{#FF6800}{ 0. \dot{ 5 } }$
$ $ Multiply both sides by an appropriate power of 10 to make two expressions with the same part of the prime number $ $
$\begin{cases} \color{#FF6800}{ 10 } \color{#FF6800}{ x } = \color{#FF6800}{ 5. \dot{ 5 } } \\ \color{#FF6800}{ 1 } \color{#FF6800}{ x } = \color{#FF6800}{ 0. \dot{ 5 } } \end{cases}$
$\begin{cases} \color{#FF6800}{ 10 } \color{#FF6800}{ x } = \color{#FF6800}{ 5. \dot{ 5 } } \\ \color{#FF6800}{ 1 } \color{#FF6800}{ x } = \color{#FF6800}{ 0. \dot{ 5 } } \end{cases}$
$ $ Since the prime number part of the right side of the two expressions is the same, only the integer part remains $ $
$\color{#FF6800}{ 9 } \color{#FF6800}{ x } = \color{#FF6800}{ 5 }$
$\color{#FF6800}{ 9 } \color{#FF6800}{ x } = \color{#FF6800}{ 5 }$
$ $ Divide both sides by the same number $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 5 } } { \color{#FF6800}{ 9 } } }$
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