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