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$Convert the following repeating decimal to a fraction in simplest form. . bar(43) Answer:$

Convert the following repeating decimal to a fraction in simplest form. $\newline$ $. \overline{43}$ $\newline$ Answer:

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Roots of integers

Full solution

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

\newline

. \overline{43}

\newline

Answer:

Assign $x$ as decimal: Let $x$ equal the repeating decimal $0.43$ with $43$ repeating. $x = 0.434343\ldots$
Multiply by $100$ : Multiply $x$ by $100$ , since there are two digits in the repeating sequence, to shift the decimal two places to the right. $\newline$ $100x = 43.434343\ldots$
Subtract original $x$ : Subtract the original $x$ from the $100x$ to get rid of the repeating part. $\newline$ $100x - x = 43.434343... - 0.434343...$ $\newline$ $99x = 43$
Divide by $99$ : Divide both sides of the equation by $99$ to solve for $x$ . $x = \frac{43}{99}$
Check for simplification: Check if the fraction can be simplified. $\newline$ The numbers $43$ and $99$ have no common factors other than $1$ , so the fraction is already in simplest form.

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