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Formula
Convert decimals to fractions
Answer
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$0.2 \dot{ 1 }$
$\dfrac { 19 } { 90 }$
Convert the repeating decimal number to a fraction
$\color{#FF6800}{ 0.2 \dot{ 1 } }$
$ $ Set the repeating decimal number to x $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ 0.2 \dot{ 1 } }$
$\color{#FF6800}{ x } = \color{#FF6800}{ 0.2 \dot{ 1 } }$
$ $ Multiply both sides by an appropriate power of 10 to make two expressions with the same part of the prime number $ $
$\begin{cases} \color{#FF6800}{ 100 } \color{#FF6800}{ x } = \color{#FF6800}{ 21. \dot{ 1 } } \\ \color{#FF6800}{ 10 } \color{#FF6800}{ x } = \color{#FF6800}{ 2. \dot{ 1 } } \end{cases}$
$\begin{cases} \color{#FF6800}{ 100 } \color{#FF6800}{ x } = \color{#FF6800}{ 21. \dot{ 1 } } \\ \color{#FF6800}{ 10 } \color{#FF6800}{ x } = \color{#FF6800}{ 2. \dot{ 1 } } \end{cases}$
$ $ Since the prime number part of the right side of the two expressions is the same, only the integer part remains $ $
$\color{#FF6800}{ 90 } \color{#FF6800}{ x } = \color{#FF6800}{ 19 }$
$\color{#FF6800}{ 90 } \color{#FF6800}{ x } = \color{#FF6800}{ 19 }$
$ $ Divide both sides by the same number $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 19 } { 90 } }$
Solution search results
search-thumbnail-$2$ (a) Prove that $sin^{-1}0.8-sin^{-1}0.6=sin^{-1}0.28$ 
$Hint$ Let $A=sin^{-1}0.8$ and $B=sin^{-1}0.6.1$
10th-13th grade
Other
search-thumbnail-Which of the following is an example of a terminating decimal? 
B.) $A.\right)$ $0.\bar{1} $ 
$0.25$ 
C.) $0.\dfrac {1\bar{7} } {21}$ $0.$ 
D.)
1st-6th grade
Calculus
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