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$Convert the following repeating decimal to a fraction in simplest form. . bar(42) Answer:$

Convert the following repeating decimal to a fraction in simplest form. $\newline$ $. \overline{42}$ $\newline$ Answer:

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Roots of integers

Full solution

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

\newline

. \overline{42}

\newline

Answer:

Assign $x$ value: Let $x$ equal the repeating decimal $0.42$ (with $42$ repeating). $\newline$ $x = 0.424242...$
Multiply by $100$ : Multiply $x$ by $100$ since two digits are repeating. This will shift the decimal point two places to the right, making the digits after the decimal point the same as the original number. $\newline$ $100x = 42.424242\ldots$
Subtract original number: Subtract the original number $x$ from the result of Step $2$ to get rid of the repeating decimal part. $\newline$ $100x - x = 42.424242... - 0.424242...$ $\newline$ $99x = 42$
Divide by $99$ : Divide both sides of the equation by $99$ to solve for $x$ . $x = \frac{42}{99}$
Simplify the fraction: Simplify the fraction by finding the greatest common divisor (GCD) of $42$ and $99$ and divide both numerator and denominator by the GCD. $\newline$ The GCD of $42$ and $99$ is $3$ . $\newline$ $x = (\frac{42}{3}) / (\frac{99}{3})$ $\newline$ $x = \frac{14}{33}$

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