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Formula
Convert decimals to fractions
Answer
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$3.3 \dot{ 4 }$
$\dfrac { 301 } { 90 }$
Convert the repeating decimal number to a fraction
$\color{#FF6800}{ 3.3 \dot{ 4 } }$
$ $ Set the repeating decimal number to x $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ 3.3 \dot{ 4 } }$
$\color{#FF6800}{ x } = \color{#FF6800}{ 3.3 \dot{ 4 } }$
$ $ Multiply both sides by an appropriate power of 10 to make two expressions with the same part of the prime number $ $
$\begin{cases} \color{#FF6800}{ 100 } \color{#FF6800}{ x } = \color{#FF6800}{ 334. \dot{ 4 } } \\ \color{#FF6800}{ 10 } \color{#FF6800}{ x } = \color{#FF6800}{ 33. \dot{ 4 } } \end{cases}$
$\begin{cases} \color{#FF6800}{ 100 } \color{#FF6800}{ x } = \color{#FF6800}{ 334. \dot{ 4 } } \\ \color{#FF6800}{ 10 } \color{#FF6800}{ x } = \color{#FF6800}{ 33. \dot{ 4 } } \end{cases}$
$ $ Since the prime number part of the right side of the two expressions is the same, only the integer part remains $ $
$\color{#FF6800}{ 90 } \color{#FF6800}{ x } = \color{#FF6800}{ 301 }$
$\color{#FF6800}{ 90 } \color{#FF6800}{ x } = \color{#FF6800}{ 301 }$
$ $ Divide both sides by the same number $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 301 } { 90 } }$
Solution search results
search-thumbnail-$3.16$ $3\dfrac {7} {20}$ 
$3.35$ $3$ $\dfrac {1} {5}$ 
$:3+\dfrac {35} {29}$ $=y+035$ $=3^{35}$ $\infty $ 
$375$ $3\dfrac {4} {5}$ 
$325$ $3$ $\bar{4} $ 
$3.2$ $3\dfrac {3} {4}$ 
$3.8$ $3\dfrac {4} {25}$
10th-13th grade
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