Write the repeating decimal as a fraction. .37373737 ______

Define x as decimal: Let x be the repeating decimal we want to convert to a fraction. x = 0.37373737...Shift decimal by multiplying: Multiply x by 100 to shift the decimal two places to the right. 100x = 37.37373737...Subtract to remove decimals: Subtract the original number x from 100x to get rid of the repeating decimals. 100x - x = 37.37373737... - 0.37373737... 99x = 37Divide by 99: Divide both sides of the equation by 99 to solve for x. x = 37 / 99Simplify the fraction: Simplify the fraction if possible. Both 37 and 99 are divisible by 1 only, so the fraction is already in its simplest form. x = 37 / 99

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Write the repeating decimal as a fraction. $\newline$ $.37373737$

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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

.37373737

Define $x$ as decimal: Let $x$ be the repeating decimal we want to convert to a fraction. $x = 0.37373737\ldots$
Shift decimal by multiplying: Multiply $x$ by $100$ to shift the decimal two places to the right. $\newline$ $100x = 37.37373737\ldots$
Subtract to remove decimals: Subtract the original number $x$ from $100x$ to get rid of the repeating decimals. $\newline$ $100x - x = 37.37373737... - 0.37373737...$ $\newline$ $99x = 37$
Divide by $99$ : Divide both sides of the equation by $99$ to solve for $x$ . $x = \frac{37}{99}$
Simplify the fraction: Simplify the fraction if possible. $\newline$ Both $37$ and $99$ are divisible by $1$ only, so the fraction is already in its simplest form. $\newline$ $x = \frac{37}{99}$