Write the repeating decimal as a fraction. .33333333 ______

Identify Repeating Pattern: Identify the repeating pattern in the decimal. The repeating decimal is 0.33333333..., where the digit 3 repeats indefinitely.Set Equal to Decimal: Let x equal the repeating decimal. So, we set x = 0.33333333...Multiply by 10: Multiply x by 10 to shift the decimal point to the right, which will help us set up an equation to solve for x. 10x = 3.33333333...Subtract to Eliminate Decimals: Subtract the original x from 10x to eliminate the repeating decimals. 10x - x = 3.33333333... - 0.33333333... This gives us 9x = 3.Divide by 9: Divide both sides of the equation by 9 to solve for x. x = 3 / 9Simplify Fraction: Simplify the fraction. 3 / 9 can be simplified to 1 / 3, since both the numerator and the denominator are divisible by 3.

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Write the repeating decimal as a fraction. $\newline$ $0.33333333$

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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

0.33333333

Identify Repeating Pattern: Identify the repeating pattern in the decimal. $\newline$ The repeating decimal is $0.33333333\ldots$ , where the digit $3$ repeats indefinitely.
Set Equal to Decimal: Let $x$ equal the repeating decimal. $\newline$ So, we set $x = 0.33333333\ldots$
Multiply by $10$ : Multiply $x$ by $10$ to shift the decimal point to the right, which will help us set up an equation to solve for $x$ . $10x = 3.33333333\ldots$
Subtract to Eliminate Decimals: Subtract the original $x$ from $10x$ to eliminate the repeating decimals. $\newline$ $10x - x = 3.33333333... - 0.33333333...$ $\newline$ This gives us $9x = 3$ .
Divide by $9$ : Divide both sides of the equation by $9$ to solve for $x$ . $x = \frac{3}{9}$
Simplify Fraction: Simplify the fraction. $3 / 9$ can be simplified to $1 / 3$ , since both the numerator and the denominator are divisible by $3$ .