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$Convert the following repeating decimal to a fraction in simplest form. bar(94) Answer:$

Convert the following repeating decimal to a fraction in simplest form. $\newline$ $\overline{94}$ $\newline$ Answer:

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Roots of rational numbers

Full solution

Q. Convert the following repeating decimal to a fraction in simplest form.

\newline

\overline{94}

\newline

Answer:

Assign Variable $x$ : Let $x$ equal the repeating decimal $0.949494\ldots$ $\newline$ $x = 0.949494\ldots$
Multiply by Power of $10$ : To convert the repeating decimal to a fraction, multiply $x$ by a power of $10$ that matches the length of the repeating pattern. Since the repeating pattern is two digits ( $94$ ), we multiply by $100$ . $\newline$ $100x = 94.949494\ldots$
Subtract Equations: Subtract the original equation $x = 0.949494...$ from the new equation $100x = 94.949494...$ to get rid of the repeating decimal. $\newline$ $100x - x = 94.949494... - 0.949494...$ $\newline$ $99x = 94$
Divide by $99$ : Divide both sides of the equation by $99$ to solve for $x$ . $x = \frac{94}{99}$
Simplify Fraction: Simplify the fraction by looking for the greatest common divisor (GCD) of $94$ and $99$ . The GCD of $94$ and $99$ is $1$ , so the fraction is already in simplest form. $\newline$ $x = \frac{94}{99}$

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