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Formula
Convert decimals to fractions
Answer
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$0.0 \dot{ 3 }$
$\dfrac { 1 } { 30 }$
Convert the repeating decimal number to a fraction
$\color{#FF6800}{ 0.0 \dot{ 3 } }$
$ $ Set the repeating decimal number to x $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ 0.0 \dot{ 3 } }$
$\color{#FF6800}{ x } = \color{#FF6800}{ 0.0 \dot{ 3 } }$
$ $ Multiply both sides by an appropriate power of 10 to make two expressions with the same part of the prime number $ $
$\begin{cases} \color{#FF6800}{ 100 } \color{#FF6800}{ x } = \color{#FF6800}{ 3. \dot{ 3 } } \\ \color{#FF6800}{ 10 } \color{#FF6800}{ x } = \color{#FF6800}{ 0. \dot{ 3 } } \end{cases}$
$\begin{cases} \color{#FF6800}{ 100 } \color{#FF6800}{ x } = \color{#FF6800}{ 3. \dot{ 3 } } \\ \color{#FF6800}{ 10 } \color{#FF6800}{ x } = \color{#FF6800}{ 0. \dot{ 3 } } \end{cases}$
$ $ Since the prime number part of the right side of the two expressions is the same, only the integer part remains $ $
$\color{#FF6800}{ 90 } \color{#FF6800}{ x } = \color{#FF6800}{ 3 }$
$\color{#FF6800}{ 90 } \color{#FF6800}{ x } = \color{#FF6800}{ 3 }$
$ $ Divide both sides by the same number $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 1 } { 30 } }$
Solution search results
search-thumbnail-$P\left(B\right)=1$ 

$B$ $P\left(8^{|}0.03^{|}0.17\left(0.22$ $0$ $1$ $2$ $|$ $|^{3}$ $0.31^{|^{4}}.15$ $0$ $|^{5}$ $0.12$
10th-13th grade
Probability and Statistics
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