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Formula
Convert decimals to fractions
Answer
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$1. \dot{ 0 } \dot{ 3 }$
$\dfrac { 34 } { 33 }$
Convert the repeating decimal number to a fraction
$\color{#FF6800}{ 1. \dot{ 0 } \dot{ 3 } }$
$ $ Set the repeating decimal number to x $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ 1. \dot{ 0 } \dot{ 3 } }$
$\color{#FF6800}{ x } = \color{#FF6800}{ 1. \dot{ 0 } \dot{ 3 } }$
$ $ Multiply both sides by an appropriate power of 10 to make two expressions with the same part of the prime number $ $
$\begin{cases} \color{#FF6800}{ 100 } \color{#FF6800}{ x } = \color{#FF6800}{ 103. \dot{ 0 } \dot{ 3 } } \\ \color{#FF6800}{ 1 } \color{#FF6800}{ x } = \color{#FF6800}{ 1. \dot{ 0 } \dot{ 3 } } \end{cases}$
$\begin{cases} \color{#FF6800}{ 100 } \color{#FF6800}{ x } = \color{#FF6800}{ 103. \dot{ 0 } \dot{ 3 } } \\ \color{#FF6800}{ 1 } \color{#FF6800}{ x } = \color{#FF6800}{ 1. \dot{ 0 } \dot{ 3 } } \end{cases}$
$ $ Since the prime number part of the right side of the two expressions is the same, only the integer part remains $ $
$\color{#FF6800}{ 99 } \color{#FF6800}{ x } = \color{#FF6800}{ 102 }$
$\color{#FF6800}{ 99 } \color{#FF6800}{ x } = \color{#FF6800}{ 102 }$
$ $ Divide both sides by the same number $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 34 } { 33 } }$
Solution search results
search-thumbnail-
$p$ form of $1.\bar{3} $ 1.3is 
$q$
7th-9th grade
Other
search-thumbnail-$L$ $\sqrt{3} $ 1. 
Prove thot $\sqrt{2} $
10th-13th grade
Other
search-thumbnail-0 $\left($ अगर किसी संख्या का $16\dfrac {2} {3}/.$ 
शरी मे जीड़ दिया जाए तो ५१56 
बनता $1$ वास्तविक सेण्या ज्ञात $1$
10th-13th grade
Other
search-thumbnail-$-$ 
$2-\sqrt{3} $ $-\dfrac {1} {2-\sqrt{3} }\right)^{3}$
10th-13th grade
Other
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