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# Fractions and Repeating Decimals

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## Fractions and Repeating Decimals

We have already discussed how to convert a given fraction into the decimal form with terminating decimals, https://www.etutorworld.com/fractions-to-decimals.html. Here, we will try to understand how to convert a given fraction to repeating decimal. 1. Now, we consider each of the above cases separately and understand them with examples.

### Terminating and non-repeating decimal

Example 1: = = =0.5 or by long division method 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. #### Example 2: Consider   #### Example 3: Consider  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. So decimal representation of = 0.83333… and this repetition is denoted by putting a bar over the repeated number i.e. = 0.83333… = 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.

### CHECK POINT

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

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Site by Little Red Bird Our mission is to provide high quality online tutoring services, using state of the art Internet technology, to school students worldwide.

Connect with us
+1-269-763-4602
+1-269-763-5024

Online test prep and practice
SCAT
CogAT
SSAT
ISEE
PSAT
SAT
ACT
AP Exam

Science Tutoring
Physics Tutoring
Chemistry Tutoring
Biology Tutoring

English Tutoring
Writing
Grammar