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# Fractions and Repeating Decimals

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### Arithemetic & Pre Algebra

The Number System

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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 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.

### Arithemetic & Pre Algebra

The Number System

### Algebra

Expressions and Equations

### Statistics and Probability

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