Write the repeating decimal as a fraction. .553553553 ______

Rephrase Problem: Let's first rephrase the problem into a single ＂How can the repeating decimal 0.553553553... be expressed as a fraction?＂Identify Repeating Pattern: Identify the repeating pattern in the decimal. The repeating pattern is ＂553＂.Assign Variable x: Let x equal the repeating decimal, so x = 0.553553553...Multiply by 1000: Multiply x by 1000 (since the repeating pattern has three digits) to shift the decimal point three places to the right: 1000x = 553.553553553...Subtract Original Number: Subtract the original number x from the result of the multiplication to get rid of the repeating decimals: 1000x - x = 553.553553553... - 0.553553553...Perform Subtraction: Perform the subtraction: 1000x - x = 553 - 0. This simplifies to 999x = 553.Divide by 999: Divide both sides of the equation by 999 to solve for x: x = 553/999.Check for Simplification: Check if the fraction can be simplified. The numbers 553 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. $\newline$ $.553553553$

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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

.553553553

Rephrase Problem: Let's first rephrase the problem into a single ＂How can the repeating decimal $0.553553553\ldots$ be expressed as a fraction?＂
Identify Repeating Pattern: Identify the repeating pattern in the decimal. The repeating pattern is $553$ .
Assign Variable $x$ : Let $x$ equal the repeating decimal, so $x = 0.553553553\ldots$
Multiply by $1000$ : Multiply $x$ by $1000$ (since the repeating pattern has three digits) to shift the decimal point three places to the right: $1000x = 553.553553553\ldots$
Subtract Original Number: Subtract the original number $x$ from the result of the multiplication to get rid of the repeating decimals: $1000x - x = 553.553553553\ldots - 0.553553553\ldots$
Perform Subtraction: Perform the subtraction: $1000x - x = 553 - 0$ . This simplifies to $999x = 553$ .
Divide by $999$ : Divide both sides of the equation by $999$ to solve for $x$ : $x = \frac{553}{999}$ .
Check for Simplification: Check if the fraction can be simplified. The numbers $553$ and $999$ do not have any common factors other than $1$ , so the fraction is already in its simplest form.