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.

In this article, you will learn more about fractions and repeating decimals with solved examples and worksheets to reinforce your learning.

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.

$fractions and repeating decimals$

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.

CHECK POINT

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

$\frac{8}{18}$
$\frac{7}{11}$
$\frac{6}{9}$
$\frac{3}{8}$
$\frac{8}{11}$

Answer Key

$fractions9$

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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