RECURRING DECIMAL

Definition Of Recurring Decimal

Recurring Decimals are decimals in which a digit or a sequence of digits keeps repeating. For example: 0.666666666… .

More about Recurring Decimal

Recurring decimal is also known as repeating decimal.
The repeating decimal can be represented by putting a bar over the digit or the sequence of digits that repeat. For instance, 0.166666666 can also be written as .

Examples of Recurring Decimal

Here are a few examples of recurring or repeating decimals. 
0.3333333 or  
0.166666666 or  
0.86666666666 or 

Video Examples: Recurring Decimals

Solved Example on Recurring Decimal

Ques: Which of the following is a repeating decimal?.

Choices:

A. 
B.
C.
D. 
Correct Answer: D

Solution:

Step 1: When a digit or sequence of digits keeps repeating in a decimal, it is called a repeating decimal.
Step 2: For  , when 8 is divided by 5, the quotient is 1.6
Step 3:For , when 1 is divided by 4, the quotient is 0.25.
Step 4: For , when 5 is divided by 10, the quotient is 0.5.
Step 5: For , when 1 is divided by 11, the quotient is 0.090909... and the digits 09 are repeating. Step 6: Therefore,  is a repeating decimal.