Write the repeating decimal as a fraction. .801801801 ______

Identify Repeating Pattern: Identify the repeating pattern in the decimal. The digits ＂801＂ repeat indefinitely.Assign Variable x: Let x equal the repeating decimal: x = 0.801801801...Multiply by 1000: Multiply x by 1000 to shift the decimal point three places to the right, since the repeating pattern has three digits: 1000x = 801.801801801...Subtract Equations: Subtract the original equation (x = 0.801801801...) from the new equation (1000x = 801.801801801...) to eliminate the repeating decimals: 1000x - x = 801.801801801... - 0.801801801...Perform Subtraction: Perform the subtraction: 999x = 801Divide by 999: Divide both sides of the equation by 999 to solve for x: x = 801/999Find GCD: Simplify the fraction by finding the greatest common divisor (GCD) of 801 and 999. The GCD of 801 and 999 is 9.Simplify Fraction: Divide both the numerator and the denominator by the GCD to simplify the fraction: x = (801/9) / (999/9) = 89/111

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Write the repeating decimal as a fraction. $\newline$ $.801801801$

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

.801801801

Identify Repeating Pattern: Identify the repeating pattern in the decimal. The digits ＂ $801$ ＂ repeat indefinitely.
Assign Variable $x$ : Let $x$ equal the repeating decimal: $x = 0.801801801\ldots$
Multiply by $1000$ : Multiply $x$ by $1000$ to shift the decimal point three places to the right, since the repeating pattern has three digits: $1000x = 801.801801801\ldots$
Subtract Equations: Subtract the original equation $x = 0.801801801...$ from the new equation $1000x = 801.801801801...$ to eliminate the repeating decimals: $1000x - x = 801.801801801... - 0.801801801...$
Perform Subtraction: Perform the subtraction: $999x = 801$
Divide by $999$ : Divide both sides of the equation by $999$ to solve for $x$ : $x = \frac{801}{999}$
Find GCD: Simplify the fraction by finding the greatest common divisor (GCD) of $801$ and $999$ . The GCD of $801$ and $999$ is $9$ .
Simplify Fraction: Divide both the numerator and the denominator by the GCD to simplify the fraction: $x = \frac{801}{9} / \frac{999}{9} = \frac{89}{111}$