Write the repeating decimal as a fraction. .56565656 ______

Identify Repeating Pattern: Identify the repeating pattern in the decimal. The repeating pattern in the decimal is ＂56＂, which repeats indefinitely.Assign Variable: Let x equal the repeating decimal, so we can write an equation to represent it. Let x = 0.56565656...Multiply by Power of 10: Multiply x by a power of 10 that moves the decimal point to the right so that it aligns with the start of the repeating pattern. If we multiply x by 100 (since the repeating pattern has two digits), we get: 100x = 56.56565656...Subtract Original Number: Subtract the original number x from the result of the multiplication to eliminate the repeating pattern. 100x - x = 56.56565656... - 0.56565656... 99x = 56Solve for x: Solve for x by dividing both sides of the equation by 99. x = 56 / 99Simplify Fraction: Simplify the fraction if possible. Both the numerator and the denominator are divisible by 11. x = (56 ÷ 11) / (99 ÷ 11) x = 56/11 / 99/11 x = 5.09090909... / 9 x = 5/9

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Write the repeating decimal as a fraction. $\newline$ $.56565656$

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Algebra 2

Write a repeating decimal as a fraction

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Q. Write the repeating decimal as a fraction.

\newline

.56565656

Identify Repeating Pattern: Identify the repeating pattern in the decimal. The repeating pattern in the decimal is $56$ , which repeats indefinitely.
Assign Variable: Let $x$ equal the repeating decimal, so we can write an equation to represent it. $\newline$ Let $x = 0.56565656\ldots$
Multiply by Power of $10$ : Multiply $x$ by a power of $10$ that moves the decimal point to the right so that it aligns with the start of the repeating pattern. $\newline$ If we multiply $x$ by $100$ (since the repeating pattern has two digits), we get: $\newline$ $100x = 56.56565656\ldots$
Subtract Original Number: Subtract the original number $x$ from the result of the multiplication to eliminate the repeating pattern. $100x - x = 56.56565656\ldots - 0.56565656\ldots$ $99x = 56$
Solve for x: Solve for x by dividing both sides of the equation by $99$ . $\newline$ $x = \frac{56}{99}$
Simplify Fraction: Simplify the fraction if possible. $\newline$ Both the numerator and the denominator are divisible by $11$ . $\newline$ $x = (56 \div 11) / (99 \div 11)$ $\newline$ $x = \frac{56}{11} / \frac{99}{11}$ $\newline$ $x = 5.09090909\ldots / 9$ $\newline$ $x = \frac{5}{9}$