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Formula
Convert decimals to fractions
Answer
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$4. \dot{ 0 } 5 \dot{ 6 }$
$\dfrac { 4052 } { 999 }$
Convert the repeating decimal number to a fraction
$\color{#FF6800}{ 4. \dot{ 0 } 5 \dot{ 6 } }$
$ $ Set the repeating decimal number to x $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ 4. \dot{ 0 } 5 \dot{ 6 } }$
$\color{#FF6800}{ x } = \color{#FF6800}{ 4. \dot{ 0 } 5 \dot{ 6 } }$
$ $ Multiply both sides by an appropriate power of 10 to make two expressions with the same part of the prime number $ $
$\begin{cases} \color{#FF6800}{ 1000 } \color{#FF6800}{ x } = \color{#FF6800}{ 4056. \dot{ 0 } 5 \dot{ 6 } } \\ \color{#FF6800}{ 1 } \color{#FF6800}{ x } = \color{#FF6800}{ 4. \dot{ 0 } 5 \dot{ 6 } } \end{cases}$
$\begin{cases} \color{#FF6800}{ 1000 } \color{#FF6800}{ x } = \color{#FF6800}{ 4056. \dot{ 0 } 5 \dot{ 6 } } \\ \color{#FF6800}{ 1 } \color{#FF6800}{ x } = \color{#FF6800}{ 4. \dot{ 0 } 5 \dot{ 6 } } \end{cases}$
$ $ Since the prime number part of the right side of the two expressions is the same, only the integer part remains $ $
$\color{#FF6800}{ 999 } \color{#FF6800}{ x } = \color{#FF6800}{ 4052 }$
$\color{#FF6800}{ 999 } \color{#FF6800}{ x } = \color{#FF6800}{ 4052 }$
$ $ Divide both sides by the same number $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 4052 } { 999 } }$
Solution search results
search-thumbnail-$80\bar{6} $ 
$4.$ $10$ 3R $250$ 65
10th-13th grade
Geometry
search-thumbnail-$3.$ $\dfrac {2} {3}x=3y-\dfrac {1} {6}$ 
$4.$ $3\left(2x-y\right)=4\left(x+y\right)-6$
7th-9th grade
Other
search-thumbnail-$a^{6}$ 
$4$ . Solve $\bar{z} =iz^{2}$ $\left(z$ being a $comPlex$ number) $\right)$
10th-13th grade
Other
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