Write the repeating decimal as a fraction. .98989898 ______

Rephrase Problem: Let's first rephrase the problem into a single ＂How can the repeating decimal 0.989898... be expressed as a fraction?＂Identify Repeating Pattern: Identify the repeating pattern in the decimal. The pattern is ＂98＂ which repeats indefinitely.Assign Variable: Let x be the repeating decimal, so x = 0.989898....Shift Decimal: Multiply x by 100 to shift the decimal two places to the right, since the repeating pattern has two digits. This gives us 100x = 98.989898....Subtract Decimals: Subtract the original x from 100x to get rid of the repeating decimals. This gives us 100x - x = 98.989898... - 0.989898.... Perform Subtraction: Perform the subtraction: 100x - x = 99x and 98.989898... - 0.989898... = 98. This results in the equation 99x = 98.Divide by 99: Divide both sides of the equation by 99 to solve for x. This gives us x = 98/99.Check Result: Check the result by converting the fraction back to a decimal to ensure it matches the original repeating decimal. 98 divided by 99 gives 0.989898..., which is the original decimal.

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Write the repeating decimal as a fraction. $\newline$ $.98989898$

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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

.98989898

Rephrase Problem: Let's first rephrase the problem into a single ＂How can the repeating decimal $0.989898\ldots$ be expressed as a fraction?＂
Identify Repeating Pattern: Identify the repeating pattern in the decimal. The pattern is $＂98＂$ which repeats indefinitely.
Assign Variable: Let $x$ be the repeating decimal, so $x = 0.989898\ldots$
Shift Decimal: Multiply $x$ by $100$ to shift the decimal two places to the right, since the repeating pattern has two digits. This gives us $100x = 98.989898\ldots$ .
Subtract Decimals: Subtract the original $x$ from $100x$ to get rid of the repeating decimals. This gives us $100x - x = 98.989898... - 0.989898....$
Perform Subtraction: Perform the subtraction: $100x - x = 99x$ and $98.989898\ldots - 0.989898\ldots = 98$ . This results in the equation $99x = 98$ .
Divide by $99$ : Divide both sides of the equation by $99$ to solve for $x$ . This gives us $x = \frac{98}{99}$ .
Check Result: Check the result by converting the fraction back to a decimal to ensure it matches the original repeating decimal. $98$ divided by $99$ gives $0.989898\ldots$ , which is the original decimal.