Write the repeating decimal as a fraction. .544544544 ______

Rephrase Problem: Let's first rephrase the problem as a ＂How can the repeating decimal 0.544544544... be expressed as a fraction?＂Identify Repeating Pattern: Identify the repeating pattern in the decimal. The digits ＂544＂ repeat indefinitely, so we can write the decimal as 0.544544544...Assign Variable: Let x equal the repeating decimal, so x = 0.544544544...Shift Decimal Point: Multiply x by 1000 to shift the decimal point three places to the right, since there are three repeating digits. This gives us 1000x = 544.544544544...Subtract Decimals: Subtract the original x from 1000x to get rid of the repeating decimals. This gives us 1000x - x = 544.544544544... - 0.544544544...Perform Subtraction: Perform the subtraction: 1000x - x = 999x and 544.544544544... - 0.544544544... = 544. This results in the equation 999x = 544.Solve for x: Solve for x by dividing both sides of the equation by 999. This gives us x = 544/999.Check Fraction Simplification: Check if the fraction can be simplified. The numbers 544 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. $\newline$ $.544544544$

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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

.544544544

Rephrase Problem: Let's first rephrase the problem as a ＂How can the repeating decimal $0.544544544\ldots$ be expressed as a fraction?＂
Identify Repeating Pattern: Identify the repeating pattern in the decimal. The digits ＂ $544$ ＂ repeat indefinitely, so we can write the decimal as $0.544544544\ldots$
Assign Variable: Let $x$ equal the repeating decimal, so $x = 0.544544544\ldots$
Shift Decimal Point: Multiply $x$ by $1000$ to shift the decimal point three places to the right, since there are three repeating digits. This gives us $1000x = 544.544544544\ldots$
Subtract Decimals: Subtract the original $x$ from $1000x$ to get rid of the repeating decimals. This gives us $1000x - x = 544.544544544... - 0.544544544...$
Perform Subtraction: Perform the subtraction: $1000x - x = 999x$ and $544.544544544... - 0.544544544... = 544$ . This results in the equation $999x = 544$ .
Solve for x: Solve for x by dividing both sides of the equation by $999$ . This gives us $x = \frac{544}{999}$ .
Check Fraction Simplification: Check if the fraction can be simplified. The numbers $544$ and $999$ do not have any common factors other than $1$ , so the fraction is already in its simplest form.