Write the repeating decimal as a fraction. .23232323 ______

Denote Decimal as x: Let's denote the repeating decimal 0.232323... as x. x = 0.232323... To convert this repeating decimal into a fraction, we can use algebraic manipulation. We will multiply x by a power of 10 that matches the length of the repeating pattern to shift the decimal point to the right so that the repeating digits align. Since the repeating pattern is two digits long (23), we multiply x by 100. 100x = 23.232323...Multiply by 100: Now, we subtract the original x from 100x to get rid of the repeating decimal part. 100x - x = 23.232323... - 0.232323... This simplifies to: 99x = 23Subtract and Simplify: Next, we solve for x by dividing both sides of the equation by 99. x = 23 / 99Solve for x: We check to ensure that the fraction is in its simplest form. Since 23 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. $\newline$ $.23232323$

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

.23232323

Denote Decimal as $x$ : Let's denote the repeating decimal $0.232323...$ as $x$ .
$x = 0.232323...$
To convert this repeating decimal into a fraction, we can use algebraic manipulation. We will multiply $x$ by a power of $10$ that matches the length of the repeating pattern to shift the decimal point to the right so that the repeating digits align.
Since the repeating pattern is two digits long ( $23$ ), we multiply $x$ by $100$ .
$100x = 23.232323...$
Multiply by $100$ : Now, we subtract the original $x$ from $100x$ to get rid of the repeating decimal part. $\newline$ $100x - x = 23.232323... - 0.232323...$ $\newline$ This simplifies to: $\newline$ $99x = 23$
Subtract and Simplify: Next, we solve for $x$ by dividing both sides of the equation by $99$ . $\newline$ $x = \frac{23}{99}$
Solve for $x$ : We check to ensure that the fraction is in its simplest form. Since $23$ and $99$ have no common factors other than $1$ , the fraction is already in its simplest form.