## Want to practice?

In the fraction 4/9 , the number 4 is

• Numerator
• Denominator
• Decimal
• Fraction

In the fraction 4/9 , the number 9 is

• Numerator
• Denominator
• Decimal
• Fraction

What is the equivalent fraction to 4/9 ?

• 4/18
• 8/18
• 16/45
• 8/27

What is the equivalent fraction to 4/9 ?

• 4/36
• 8/27
• 16/36
• 12/45

## Solution

A recurring decimal is a decimal in which a sequence of digits is repeated. A recurring or repeating decimal number is the result of long division where the division of the number gives the same remainders in the consecutive steps.

Some of the examples of recurring decimals are

0.4444…., 1.363636…., 0.48754875…., 0.7535353….

The digits that are repeated are indicated by placing a bar over the numbers.
The digits above can be written as

The long division method is used to convert the fractions to decimal forms. It can be observed that all the divisions do not give a decimal answer with remainder 0.

Some fractions give a decimal answer that has one or more digits repeating in a sequence and hence are called repeating or recurring decimals.

Let us take the example of a fraction which will give us a simple recurring decimal number.

Here it can be seen that the number 4 is repeating in the steps of division and hence gives the same digits in the quotient.

As mentioned earlier, the recurring digits are written by placing a bar over the digit that is repeated.

Hence the decimal form of the fraction is .

## Remember

Here are some common terms you should be familiar with.

• In the fraction , the number 4 is the dividend (our numerator)
• The number 9 is our divisor (our denominator)

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