Write the repeating decimal as a fraction. .226226226 ______

Rephrase the Problem: Let's first rephrase the ＂How can the repeating decimal 0.226226226... be expressed as a fraction?＂Identify Repeating Pattern: Identify the repeating pattern in the decimal. The digits ＂226＂ repeat indefinitely, so we can write the decimal as 0.226226226...Set Decimal as Variable: Let's set x equal to the repeating decimal: x = 0.226226226...Multiply by 1000: To isolate the repeating part, we can multiply x by 1000, because there are three digits in the repeating sequence. This gives us 1000x = 226.226226226...Subtract Original Decimal: Now, subtract the original x from 1000x to get rid of the decimal part: 1000x - x = 226.226226226... - 0.226226226...Perform Subtraction: Perform the subtraction: 999x = 226Solve for x: Now, solve for x by dividing both sides of the equation by 999: x = 226/999Check for Simplification: Check if the fraction can be simplified. The numerator and denominator do not have any common factors other than 1, so the fraction is already in its simplest form.

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Write the repeating decimal as a fraction. $\newline$ $.226226226$

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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

.226226226

Rephrase the Problem: Let's first rephrase the ＂How can the repeating decimal $0.226226226\ldots$ be expressed as a fraction?＂
Identify Repeating Pattern: Identify the repeating pattern in the decimal. The digits ＂ $226$ ＂ repeat indefinitely, so we can write the decimal as $0.226226226\ldots$
Set Decimal as Variable: Let's set $x$ equal to the repeating decimal: $x = 0.226226226\ldots$
Multiply by $1000$ : To isolate the repeating part, we can multiply $x$ by $1000$ , because there are three digits in the repeating sequence. This gives us $1000x = 226.226226226\ldots$
Subtract Original Decimal: Now, subtract the original $x$ from $1000x$ to get rid of the decimal part: $1000x - x = 226.226226226\ldots - 0.226226226\ldots$
Perform Subtraction: Perform the subtraction: $999x = 226$
Solve for x: Now, solve for x by dividing both sides of the equation by $999$ : $x = \frac{226}{999}$
Check for Simplification: Check if the fraction can be simplified. The numerator and denominator do not have any common factors other than $1$ , so the fraction is already in its simplest form.