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Convert decimals to fractions
Answer
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$0. \dot{ 8 } \dot{ 7 }$
$\dfrac { 29 } { 33 }$
Convert the repeating decimal number to a fraction
$\color{#FF6800}{ 0. \dot{ 8 } \dot{ 7 } }$
$ $ Set the repeating decimal number to x $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ 0. \dot{ 8 } \dot{ 7 } }$
$\color{#FF6800}{ x } = \color{#FF6800}{ 0. \dot{ 8 } \dot{ 7 } }$
$ $ Multiply both sides by an appropriate power of 10 to make two expressions with the same part of the prime number $ $
$\begin{cases} \color{#FF6800}{ 100 } \color{#FF6800}{ x } = \color{#FF6800}{ 87. \dot{ 8 } \dot{ 7 } } \\ \color{#FF6800}{ 1 } \color{#FF6800}{ x } = \color{#FF6800}{ 0. \dot{ 8 } \dot{ 7 } } \end{cases}$
$\begin{cases} \color{#FF6800}{ 100 } \color{#FF6800}{ x } = \color{#FF6800}{ 87. \dot{ 8 } \dot{ 7 } } \\ \color{#FF6800}{ 1 } \color{#FF6800}{ x } = \color{#FF6800}{ 0. \dot{ 8 } \dot{ 7 } } \end{cases}$
$ $ Since the prime number part of the right side of the two expressions is the same, only the integer part remains $ $
$\color{#FF6800}{ 99 } \color{#FF6800}{ x } = \color{#FF6800}{ 87 }$
$\color{#FF6800}{ 99 } \color{#FF6800}{ x } = \color{#FF6800}{ 87 }$
$ $ Divide both sides by the same number $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 29 } { 33 } }$
Solution search results
search-thumbnail-Que $26-$ What are the values of a, $b$ and $C$ for the equation $y=0.5x+\sqrt{7} $ 
when written in the standard $form$ $ax+by+c=07$ 
$0.5,1,\sqrt{7} $ 
$0.5,1,-\sqrt{7} $ 
$0.5,-1,\sqrt{7} $ 
$-0.5,1,$ $\sqrt{7} $
10th-13th grade
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