Write the repeating decimal as a fraction. .32323232 ______

Rephrase the Problem: Let's first rephrase the ＂Convert the repeating decimal 0.32323232... to a fraction.＂Identify Repeating Pattern: Identify the repeating pattern in the decimal. The digits ＂32＂ repeat indefinitely, so we can write the decimal as 0.32(32)...Assign Variable: Let x equal the repeating decimal, so x = 0.32323232...Isolate Repeating Pattern: To isolate the repeating pattern, multiply x by 100 (since the pattern is two digits long), which gives us 100x = 32.32323232...Subtract Decimals: Now, subtract the original x from 100x to get rid of the decimal part. This gives us 100x - x = 32.32323232... - 0.32323232...Solve Equation: Perform the subtraction: 100x - x = 99x and 32.32323232... - 0.32323232... = 32. This results in the equation 99x = 32.Divide by 99: To find the value of x, divide both sides of the equation by 99. So, x = 32/99.Check for Simplification: Check the fraction to ensure it cannot be simplified further. Since 32 and 99 have no common factors other than 1, the fraction is in its simplest form.

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Write the repeating decimal as a fraction. $\newline$ $.32323232$

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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

.32323232

Rephrase the Problem: Let's first rephrase the ＂Convert the repeating decimal $0.32323232\ldots$ to a fraction.＂
Identify Repeating Pattern: Identify the repeating pattern in the decimal. The digits ＂ $32$ ＂ repeat indefinitely, so we can write the decimal as $0.32(32)...$
Assign Variable: Let $x$ equal the repeating decimal, so $x = 0.32323232\ldots$
Isolate Repeating Pattern: To isolate the repeating pattern, multiply $x$ by $100$ (since the pattern is two digits long), which gives us $100x = 32.32323232\ldots$
Subtract Decimals: Now, subtract the original $x$ from $100x$ to get rid of the decimal part. This gives us $100x - x = 32.32323232... - 0.32323232...$
Solve Equation: Perform the subtraction: $100x - x = 99x$ and $32.32323232\ldots - 0.32323232\ldots = 32$ . This results in the equation $99x = 32$ .
Divide by $99$ : To find the value of $x$ , divide both sides of the equation by $99$ . So, $x = \frac{32}{99}$ .
Check for Simplification: Check the fraction to ensure it cannot be simplified further. Since $32$ and $99$ have no common factors other than $1$ , the fraction is in its simplest form.