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Formula

Convert decimals to fractions

Answer

$0. \dot{ 3 }$

$\dfrac { 1 } { 3 }$

Convert the repeating decimal number to a fraction

$\color{#FF6800}{ 0. \dot{ 3 } }$

$ $ Set the repeating decimal number to x $ $

$\color{#FF6800}{ x } = \color{#FF6800}{ 0. \dot{ 3 } }$

$ $ Multiply both sides by an appropriate power of 10 to make two expressions with the same part of the prime number $ $

$\begin{cases} \color{#FF6800}{ 10 } \color{#FF6800}{ x } = \color{#FF6800}{ 3. \dot{ 3 } } \\ \color{#FF6800}{ 1 } \color{#FF6800}{ x } = \color{#FF6800}{ 0. \dot{ 3 } } \end{cases}$

$ $ Since the prime number part of the right side of the two expressions is the same, only the integer part remains $ $

$\color{#FF6800}{ 9 } \color{#FF6800}{ x } = \color{#FF6800}{ 3 }$

$ $ Divide both sides by the same number $ $

$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 1 } { 3 } }$

Solution search results

$2.$ Consider the proper subsets of $\left(1,2,3,4\right)$ How many of these proper subsets are superset of the set $\left(3\right)$ ? $\left($ (a) $\right)$ $5$ $\left($ (b) $0\right)$ $6$ $\left($ (c) $7$ $\left($ (d) $\right)$ $8$

10th-13th grade

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