Write the repeating decimal as a fraction. .936936936 ______

Identify Repeating Pattern: Let's identify the repeating pattern in the decimal. The digits 936 are repeating.Express as x: Express the repeating decimal as x: x = 0.936936936...Multiply by 1000: To isolate the repeating pattern, multiply x by 1000 (since there are three digits in the repeating pattern): 1000x = 936.936936...Subtract Equations: Now subtract the original equation (x = 0.936936936...) from the new equation (1000x = 936.936936...): 1000x - x = 936.936936... - 0.936936936...Solve for x: Perform the subtraction: 999x = 936Find GCD: Now solve for x by dividing both sides of the equation by 999: x = 936 / 999Simplify Fraction: Simplify the fraction by finding the greatest common divisor (GCD) of 936 and 999. The GCD of 936 and 999 is 9.Perform Division: Divide both the numerator and the denominator by the GCD to simplify the fraction: x = (936 / 9) / (999 / 9)Check Simplification: Perform the division: x = 104 / 111Check the fraction to ensure it is fully simplified. Since there are no common factors between 104 and 111 other than 1, the fraction is 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. $\newline$ $.936936936$

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

.936936936

Identify Repeating Pattern: Let's identify the repeating pattern in the decimal. The digits $936$ are repeating.
Express as $x$ : Express the repeating decimal as $x$ : $x = 0.936936936\ldots$
Multiply by $1000$ : To isolate the repeating pattern, multiply $x$ by $1000$ (since there are three digits in the repeating pattern): $1000x = 936.936936\ldots$
Subtract Equations: Now subtract the original equation $x = 0.936936936\ldots$ from the new equation $1000x = 936.936936\ldots$ : $1000x - x = 936.936936\ldots - 0.936936936\ldots$
Solve for x: Perform the subtraction: $999x = 936$
Find GCD: Now solve for $x$ by dividing both sides of the equation by $999$ : $x = \frac{936}{999}$
Simplify Fraction: Simplify the fraction by finding the greatest common divisor (GCD) of $936$ and $999$ . The GCD of $936$ and $999$ is $9$ .
Perform Division: Divide both the numerator and the denominator by the GCD to simplify the fraction: $x = \frac{936 / 9}{999 / 9}$
Check Simplification: Perform the division: $x = \frac{104}{111}$
Check Simplification: Perform the division: $x = \frac{104}{111}$ Check the fraction to ensure it is fully simplified. Since there are no common factors between $104$ and $111$ other than $1$ , the fraction is in its simplest form.