Question
upstudy study bank question image url

2.) (2 pts) in lowest terms, give the fraction for the repeating decimal \( 0.321321321321 . \mathrm{n}=0.321 \)

Ask by Whittaker Simmons. in the United States
Mar 17,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The repeating decimal \(0.\overline{321}\) is equal to the fraction \(\frac{107}{333}\) in its lowest terms.

Solution

Sign in to Unlock Answers for Free!

A Learning Platform Trusted by Millions of Real Students and Teachers.

star-icon Unlock

Answered by UpStudy AI and reviewed by a Professional Tutor

Extra Insights

To convert the repeating decimal \( 0.321321321... \) into a fraction, we can denote it as \( x \). Thus, \( x = 0.321321321... \). To eliminate the repeating part, we can multiply both sides by \( 1000 \) (since there are three digits in the repeat): \[ 1000x = 321.321321321... \] Now, subtract the original equation from this new one: \[ 1000x - x = 321.321321321... - 0.321321321... \] This simplifies to: \[ 999x = 321 \] Now, divide both sides by 999: \[ x = \frac{321}{999} \] To express this fraction in its lowest terms, we can find the greatest common divisor (GCD) of 321 and 999. The GCD is 3. Therefore, we can divide both the numerator and denominator by 3: \[ x = \frac{321 \div 3}{999 \div 3} = \frac{107}{333} \] So, the repeating decimal \( 0.321321321... \) can be expressed as the fraction \( \frac{107}{333} \) in its lowest terms.

Latest Pre Algebra Questions

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy