Write the repeating decimal as a fraction. .80808080 ______

Denote Repeating Decimal: Let's denote the repeating decimal 0.80808080... by x. x = 0.80808080... To convert this repeating decimal into a fraction, we can use the following strategy: multiply x by a power of 10 that shifts the decimal point to the right so that the repeating part lines up with the original decimal. In this case, since the repeating part is two digits long (80), we will multiply by 100.Multiply by 100: Now, let's multiply x by 100. 100x = 80.80808080... Notice that the decimal part of 100x is the same as the original x, which allows us to set up an equation to solve for x.Subtract and Simplify: Next, we subtract x from 100x to get rid of the repeating decimal part. 100x - x = 80.80808080... - 0.80808080... This simplifies to: 99x = 80Solve for x: Now, we solve for x by dividing both sides of the equation by 99. x = 80 / 99Check for Simplification: We check to see if the fraction can be simplified. Since 80 and 99 have no common factors 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. $\newline$ $.80808080$

View step-by-step help

Home

Math Problems

Precalculus

Write a repeating decimal as a fraction

Full solution

Q. Write the repeating decimal as a fraction.

\newline

.80808080

Denote Repeating Decimal: Let's denote the repeating decimal $0.80808080\ldots$ by $x$ . $\newline$ $x = 0.80808080\ldots$ $\newline$ To convert this repeating decimal into a fraction, we can use the following strategy: multiply $x$ by a power of $10$ that shifts the decimal point to the right so that the repeating part lines up with the original decimal. In this case, since the repeating part is two digits long ( $80$ ), we will multiply by $100$ .
Multiply by $100$ : Now, let's multiply $x$ by $100$ . $100x = 80.80808080...$ Notice that the decimal part of $100x$ is the same as the original $x$ , which allows us to set up an equation to solve for $x$ .
Subtract and Simplify: Next, we subtract $x$ from $100x$ to get rid of the repeating decimal part. $\newline$ $100x - x = 80.80808080... - 0.80808080...$ $\newline$ This simplifies to: $\newline$ $99x = 80$
Solve for x: Now, we solve for $x$ by dividing both sides of the equation by $99$ . $x = \frac{80}{99}$
Check for Simplification: We check to see if the fraction can be simplified. Since $80$ and $99$ have no common factors other than $1$ , the fraction is already in its simplest form.