Write the repeating decimal as a fraction. .726726726 ______

Denote x as decimal: Let's denote the repeating decimal 0.726726726... as x. x = 0.726726726... To isolate the repeating part, we multiply x by 1000 because there are three digits in the repeating sequence. 1000x = 726.726726726...Multiply by 1000: Now, we subtract the original x from 1000x to get rid of the decimal part. 1000x - x = 726.726726726... - 0.726726726... This simplifies to: 999x = 726Subtract to eliminate decimal: To find the value of x, we divide both sides of the equation by 999. x = 726 / 999Divide by 999: We can simplify the fraction by finding the greatest common divisor (GCD) of 726 and 999. The GCD of 726 and 999 is 3. x = (726 / 3) / (999 / 3) x = 242 / 333Simplify fraction: We check if the fraction 242/333 can be simplified further. Since there are no common factors between 242 and 333 other than 1, the fraction is already in its simplest form.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Write the repeating decimal as a fraction. $\newline$ $.726726726$

View step-by-step help

Home

Math Problems

Algebra 2

Write a repeating decimal as a fraction

Full solution

Q. Write the repeating decimal as a fraction.

\newline

.726726726

Denote $x$ as decimal: Let's denote the repeating decimal $0.726726726...$ as $x$ . $\newline$ $x = 0.726726726...$ $\newline$ To isolate the repeating part, we multiply $x$ by $1000$ because there are three digits in the repeating sequence. $\newline$ $1000x = 726.726726726...$
Multiply by $1000$ : Now, we subtract the original $x$ from $1000x$ to get rid of the decimal part. $\newline$ $1000x - x = 726.726726726... - 0.726726726...$ $\newline$ This simplifies to: $\newline$ $999x = 726$
Subtract to eliminate decimal: To find the value of $x$ , we divide both sides of the equation by $999$ . $x = \frac{726}{999}$
Divide by $999$ : We can simplify the fraction by finding the greatest common divisor (GCD) of $726$ and $999$ . The GCD of $726$ and $999$ is $3$ . $\newline$ $x = \frac{726 / 3}{999 / 3}$ $\newline$ $x = \frac{242}{333}$
Simplify fraction: We check if the fraction $\frac{242}{333}$ can be simplified further. Since there are no common factors between $242$ and $333$ other than $1$ , the fraction is already in its simplest form.