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# Fractions and Repeating Decimals Worksheets

Fractions are mathematical expressions that represent a part of a whole or a division of a quantity. They consist of a numerator (the number on top) and a denominator (the number on the bottom), separated by a fraction bar. Repeating decimals, on the other hand, are decimal numbers that have a pattern of digits that repeat indefinitely. A horizontal line or a set of parentheses above the repeating digits usually indicate the repeating part. These decimals can be written as fractions, where the repeating part represents the numerator and a number of nines (9s) in the denominator.

## 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.

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.

##### What is a fraction?

A fraction is a mathematical representation of a part of a whole or a division of a quantity. It consists of a numerator (the number on top) and a denominator (the number on the bottom) separated by a fraction bar.

##### How do I simplify a fraction?

To simplify a fraction, you need to divide both the numerator and the denominator by their greatest common divisor (GCD). This process reduces the fraction to its simplest form.

##### How do I convert a fraction to a decimal?

To convert a fraction to a decimal, divide the numerator by the denominator using long division or a calculator. The result will be a decimal representation of the fraction.

##### How do I convert a repeating decimal to a fraction?

To convert a repeating decimal to a fraction, identify the repeating part and set it as the numerator. In the denominator, write as many nines (9s) as the length of the repeating part. Simplify the fraction if possible.

##### Can fractions and repeating decimals be used in real-life situations?

Absolutely! Fractions and repeating decimals are used in various real-life scenarios, such as cooking measurements, financial calculations, and understanding probabilities. They are fundamental concepts in mathematics with practical applications in everyday life.

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