Full solution

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

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. \overline{79}

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Answer:

Define $x$ as decimal: Let $x$ equal the repeating decimal $0.797979...$ $x = 0.797979...$ To convert this repeating decimal to a fraction, we will create an equation that isolates the repeating part.
Multiply by $100$ : Multiply $x$ by $100$ since there are two digits in the repeating sequence. This will shift the decimal two places to the right. $\newline$ $100x = 79.797979\ldots$ $\newline$ Now we have a new equation with the same repeating decimal part.
Subtract equations: Subtract the original equation $x = 0.797979...$ from the new equation $100x = 79.797979...$ to eliminate the repeating part. $\newline$ $100x - x = 79.797979... - 0.797979...$ $\newline$ $99x = 79$
Divide by $99$ : Divide both sides of the equation by $99$ to solve for $x$ . $x = \frac{79}{99}$
Simplify fraction: Simplify the fraction by looking for the greatest common divisor (GCD) of $79$ and $99$ . Since $79$ is a prime number and does not divide $99$ , the GCD is $1$ . Therefore, the fraction is already in its simplest form.