Write the repeating decimal as a fraction. .967967967 ______

Assign x value: Let x equal the repeating decimal we want to convert to a fraction. x = 0.967967967...Multiply by 1000: Multiply x by 1000 to shift the decimal point three places to the right, since the repeating block has three digits (967). 1000x = 967.967967...Subtract original x: Subtract the original number x from 1000x to get rid of the repeating part. 1000x - x = 967.967967... - 0.967967967...Isolate non-repeating part: Perform the subtraction to isolate the non-repeating part. 999x = 967Divide by 999: Divide both sides of the equation by 999 to solve for x. x = 967 / 999Check for simplification: Check if the fraction can be simplified. In this case, 967 and 999 have no 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. $\newline$ $.967967967$

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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

.967967967

Assign $x$ value: Let $x$ equal the repeating decimal we want to convert to a fraction. $x = 0.967967967...$
Multiply by $1000$ : Multiply $x$ by $1000$ to shift the decimal point three places to the right, since the repeating block has three digits ( $967$ ). $\newline$ $1000x = 967.967967\ldots$
Subtract original x: Subtract the original number $x$ from $1000x$ to get rid of the repeating part. $\newline$ $1000x - x = 967.967967... - 0.967967967...$
Isolate non-repeating part: Perform the subtraction to isolate the non-repeating part. $999x = 967$
Divide by $999$ : Divide both sides of the equation by $999$ to solve for $x$ . $x = \frac{967}{999}$
Check for simplification: Check if the fraction can be simplified. In this case, $967$ and $999$ have no common factors other than $1$ , so the fraction is already in its simplest form.