Write the repeating decimal as a fraction. .227227227 ______

Denote Repeating Decimal as x: Let's denote the repeating decimal 0.227227227... as x. x = 0.227227227...Multiply by Power of 10: To convert this repeating decimal into a fraction, we can multiply x by a power of 10 that moves the repeating digits to the left of the decimal point. Since the repeating block is three digits long (227), we multiply by 10^3 (which is 1000). 1000x = 227.227227...Subtract Original Number: Now, we subtract the original number x from this new number 1000x to get rid of the repeating decimals. 1000x - x = 227.227227... - 0.227227227...Perform Subtraction: Perform the subtraction on the left side of the equation: 1000x - x = 999x On the right side, the repeating decimals cancel out, leaving us with: 227.227227... - 0.227227227... = 227 So, we have: 999x = 227Solve for x: To solve for x, we divide both sides of the equation by 999: x = 227 / 999Simplify the Fraction: Now, we can simplify the fraction if possible. However, 227 and 999 do not have any common factors other than 1, so the fraction is already in its simplest form. x = 227 / 999

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Write the repeating decimal as a fraction. $\newline$ $.227227227$

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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

.227227227

Denote Repeating Decimal as $x$ : Let's denote the repeating decimal $0.227227227\ldots$ as $x$ . $\newline$ $x = 0.227227227\ldots$
Multiply by Power of $10$ : To convert this repeating decimal into a fraction, we can multiply $x$ by a power of $10$ that moves the repeating digits to the left of the decimal point. Since the repeating block is three digits long ( $227$ ), we multiply by $10^3$ (which is $1000$ ). $\newline$ $1000x = 227.227227\ldots$
Subtract Original Number: Now, we subtract the original number $x$ from this new number $1000x$ to get rid of the repeating decimals. $1000x - x = 227.227227... - 0.227227227...$
Perform Subtraction: Perform the subtraction on the left side of the equation: $\newline$ $1000x - x = 999x$ $\newline$ On the right side, the repeating decimals cancel out, leaving us with: $\newline$ $227.227227... - 0.227227227... = 227$ $\newline$ So, we have: $\newline$ $999x = 227$
Solve for x: To solve for x, we divide both sides of the equation by $999$ : $x = \frac{227}{999}$
Simplify the Fraction: Now, we can simplify the fraction if possible. However, $227$ and $999$ do not have any common factors other than $1$ , so the fraction is already in its simplest form. $\newline$ $x = \frac{227}{999}$