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Formula
Convert decimals to fractions
Answer
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$0. \dot{ 1 } 2 \dot{ 9 }$
$\dfrac { 43 } { 333 }$
Convert the repeating decimal number to a fraction
$\color{#FF6800}{ 0. \dot{ 1 } 2 \dot{ 9 } }$
$ $ Set the repeating decimal number to x $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ 0. \dot{ 1 } 2 \dot{ 9 } }$
$\color{#FF6800}{ x } = \color{#FF6800}{ 0. \dot{ 1 } 2 \dot{ 9 } }$
$ $ Multiply both sides by an appropriate power of 10 to make two expressions with the same part of the prime number $ $
$\begin{cases} \color{#FF6800}{ 1000 } \color{#FF6800}{ x } = \color{#FF6800}{ 129. \dot{ 1 } 2 \dot{ 9 } } \\ \color{#FF6800}{ 1 } \color{#FF6800}{ x } = \color{#FF6800}{ 0. \dot{ 1 } 2 \dot{ 9 } } \end{cases}$
$\begin{cases} \color{#FF6800}{ 1000 } \color{#FF6800}{ x } = \color{#FF6800}{ 129. \dot{ 1 } 2 \dot{ 9 } } \\ \color{#FF6800}{ 1 } \color{#FF6800}{ x } = \color{#FF6800}{ 0. \dot{ 1 } 2 \dot{ 9 } } \end{cases}$
$ $ Since the prime number part of the right side of the two expressions is the same, only the integer part remains $ $
$\color{#FF6800}{ 999 } \color{#FF6800}{ x } = \color{#FF6800}{ 129 }$
$\color{#FF6800}{ 999 } \color{#FF6800}{ x } = \color{#FF6800}{ 129 }$
$ $ Divide both sides by the same number $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 43 } { 333 } }$
Solution search results
search-thumbnail-
Fraction Decimal form 
$\dfrac {1} {9}$ $0.1111$ $..$ 
$→$ $0.3333...$ 
$\dfrac {7} {9}$
7th-9th grade
Other
search-thumbnail-$\right)$ $β2$ $∩$ $-$ $\dfrac {1} {7}$ $-$ $77$ $\sqrt{} $ 
$7$ $-$ $β8$ $3$ $\dfrac {1} {1}$ $-$ $\tarc{7} $ $N$ $9^{1}2\longdiv{}$ $2$
10th-13th grade
Trigonometry
search-thumbnail-$5$ Express in the form of $\bar{9} $ $0.\bar{38} +1.\bar{27} $
10th-13th grade
Other
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