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Formula
Convert decimals to fractions
Answer
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$0.3 \dot{ 7 }$
$\dfrac { 17 } { 45 }$
Convert the repeating decimal number to a fraction
$\color{#FF6800}{ 0.3 \dot{ 7 } }$
$ $ Set the repeating decimal number to x $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ 0.3 \dot{ 7 } }$
$\color{#FF6800}{ x } = \color{#FF6800}{ 0.3 \dot{ 7 } }$
$ $ Multiply both sides by an appropriate power of 10 to make two expressions with the same part of the prime number $ $
$\begin{cases} \color{#FF6800}{ 100 } \color{#FF6800}{ x } = \color{#FF6800}{ 37. \dot{ 7 } } \\ \color{#FF6800}{ 10 } \color{#FF6800}{ x } = \color{#FF6800}{ 3. \dot{ 7 } } \end{cases}$
$\begin{cases} \color{#FF6800}{ 100 } \color{#FF6800}{ x } = \color{#FF6800}{ 37. \dot{ 7 } } \\ \color{#FF6800}{ 10 } \color{#FF6800}{ x } = \color{#FF6800}{ 3. \dot{ 7 } } \end{cases}$
$ $ Since the prime number part of the right side of the two expressions is the same, only the integer part remains $ $
$\color{#FF6800}{ 90 } \color{#FF6800}{ x } = \color{#FF6800}{ 34 }$
$\color{#FF6800}{ 90 } \color{#FF6800}{ x } = \color{#FF6800}{ 34 }$
$ $ Divide both sides by the same number $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 17 } { 45 } }$
Solution search results
search-thumbnail-$x=\dfrac {1} {0.11} \begin{cases} 0.3 \\ 0.7 \end{cases} $ $0.1$ $6.8$ $0.6$ $10.2$
10th-13th grade
Other
search-thumbnail-$0.1\right)$ Add $:$ and? 
$0.2\right)$ Find: $\dfrac {2} {3}$ of $\dfrac {1} {7}$ 
$0.3\right)$ Multiply: $\dfrac {6} {5}$ and $5\dfrac {5} {3}$ 
$0.4\right)$ Find: $\dfrac {3} {8}\div \dfrac {1} {16}$
7th-9th grade
Other
search-thumbnail-$9\times 10^{9}\times z\times 10^{-4}\times 0.1\times 10^{-7}$ 
$0.3$ 
$9$
1st-6th grade
Physics
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