Fractions and Repeating Decimals

Fractions and Repeating Decimals

We have already discussed how to convert a given fraction into the decimal form with terminating decimals, Here, we will try to understand how to convert a given fraction to repeating decimal.

fractions and repeating decimals
  1. Now, we consider each of the above cases separately and understand them with examples.

Terminating and non-repeating decimal

Example 1:    \frac{1}{2}=\frac{1\times5}{2\times5}=\frac{5}{10}=0.5 or by long division method

fractions and repeating decimals

So, we observe that in this case the remainder is zero and hence the long division terminates and given fraction has a terminating & non-repeating decimal representation.

Non-terminating and repeating decimal.

fractions and repeating decimals

 Example 2: Consider \frac{1}{3}

fractions and repeating decimals

Example 3: Consider \frac{5}{6}


So, we observe in this case the remainder is 2 from second step onwards and hence the long division does not terminate and the given fraction has a non-terminating & repeating decimal representation.
fractions and repeating decimals


So decimal representation of = 0.83333… and this repetition is denoted by putting a bar over the repeated number i.e. = 0.83333… = fractions11

From the above examples, we see that the decimal representation of a fraction is non-terminating and repeating if its long division does not terminate & we have the same remainder, which cannot be exactly divided by the divisor.


Convert the following fractions to their decimal form and identify whether it is a repeating decimal  or not.

  1. \frac{8}{18}
  2. \frac{7}{11}
  3. \frac{6}{9}
  4. \frac{3}{8}
  5. \frac{8}{11}
Answer Key


Personalized Online Tutoring

eTutorWorld offers affordable one-on-one live tutoring over the web for Grades 2-12, Test Prep help for Standardized tests like SCAT, CogAT, SSAT, SAT, ACT, ISEE and AP. You may schedule online tutoring lessons at your personal scheduled times, all with a Money-Back Guarantee. The first one-on-one online tutoring lesson is always FREE, no purchase obligation, no credit card required.

For answers/solutions to any question or to learn concepts, take a FREE Demo Session.

No credit card required, no obligation to purchase.
Just schedule a FREE Sessions to meet a tutor and get help on any topic you want!

Pricing for Personalized Online Tutoring

Tutoring Package Validity Grade (1-12), College
5 sessions 21 Days $114
1 session 21 Days $24
10 sessions 2 months $219
15 sessions 3 months $319
20 sessions 3 months $409
50 sessions 6 months $949
100 sessions 10 months $1849


©2021 eTutorWorld           Terms of use            Privacy Policy            Site by Little Red Bird          

©2021 eTutorWorld
Terms of use
Privacy Policy
Site by Little Red Bird



♦ Coupon JAN10 for a 10% Discount on all Tutoring Packs

♦ Coupon TEST20 for a 20% Discount on all SCAT, SSAT, CogAT & Enrichment Online Practice Packs

You have Successfully Subscribed!