Write the repeating decimal as a fraction. .626626626 ______

Rephrase the Problem: Let's first rephrase the ＂How can the repeating decimal 0.626626626... be expressed as a fraction?＂Identify Repeating Pattern: Identify the repeating pattern in the decimal. The digits ＂626＂ repeat indefinitely.Assign Variable x: Let x equal the repeating decimal: x = 0.626626626...Isolate Repeating Pattern: To isolate the repeating pattern, multiply x by 1000, because there are three digits in the repeating pattern: 1000x = 626.626626626...Subtract Original x: Now subtract the original x from 1000x to get rid of the decimal part: 1000x - x = 626.626626626... - 0.626626626...Perform Subtraction: Perform the subtraction: 999x = 626Divide by 999: Divide both sides of the equation by 999 to solve for x: x = 626/999Check for Simplification: Check if the fraction can be simplified. The numbers 626 and 999 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. $\newline$ $.626626626$

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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

.626626626

Rephrase the Problem: Let's first rephrase the ＂How can the repeating decimal $0.626626626\ldots$ be expressed as a fraction?＂
Identify Repeating Pattern: Identify the repeating pattern in the decimal. The digits $\text{“626”}$ repeat indefinitely.
Assign Variable $x$ : Let $x$ equal the repeating decimal: $x = 0.626626626\ldots$
Isolate Repeating Pattern: To isolate the repeating pattern, multiply $x$ by $1000$ , because there are three digits in the repeating pattern: $1000x = 626.626626626\ldots$
Subtract Original $x$ : Now subtract the original $x$ from $1000x$ to get rid of the decimal part: $1000x - x = 626.626626626\ldots - 0.626626626\ldots$
Perform Subtraction: Perform the subtraction: $999x = 626$
Divide by $999$ : Divide both sides of the equation by $999$ to solve for $x$ : $x = \frac{626}{999}$
Check for Simplification: Check if the fraction can be simplified. The numbers $626$ and $999$ do not have any common factors other than $1$ , so the fraction is already in its simplest form.