# Non-Terminating Decimal – Definition, Examples | How to Identify if it is a Non Terminating Decimal?

A decimal is a number whose decimal part and fractional part are separated using a decimal point. In this article, we have presented all about Non-Terminating Decimals such as Definition How to Identify a Non-Terminating or Recurring Decimal all in one place. Refer to Solved Examples on Non-Terminating Decimals so that you will better understand the concept.

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## Non-Terminating Decimal – Definition

While converting a fraction to decimal we usually perform division operation and obtain a certain remainder. If the division procedure doesn’t end and we get a remainder other than zero, then such decimal is called a non-terminating decimal.

Example: 2.666 is a non-terminating repeating decimal and can be written as 2.$$\overline6$$

### How to Determine if it is a Non-Terminating Decimal?

Follow the simple guidelines listed below to determine whether a given decimal number a non-terminating decimal or not. They are along the lines

• Whenever we perform a division we get a certain block of digits that do repeat in the decimal part.
• Such Decimals are the ones that don’t end and continue and are called as Non-Terminating Decimal or Recurring Decimal.
• You can represent these decimals by placing a bar on the repeated part.

### Examples of Non-Terminating Decimals or Recurring Decimals

1. Express 7/3 in decimal form and determine whether it is a non-terminating decimal or not?

Solution:

Perform division operation and check if the decimal quotient has finite numbers or infinite numbers. If the digits after the decimal part don’t end and continue then they are called Non-Terminating or Recurring Decimals.

Since 7/3 has an infinite number of digits after the decimal point i.e. 2.3333333…. thus it is a non-terminating decimal.

2. Express 125/99 in decimal form and determine whether it is a non-terminating decimal or not?

Solution:

Perform division operation and check if the decimal quotient has finite numbers or infinite numbers. If the digits after the decimal part don’t end and continue then they are called Non-Terminating or Recurring Decimals.

Since 125/99 has an infinite number of digits after the decimal point i.e. 1.2626…… thus it is non-terminating.

### FAQs on Non-Terminating Decimals

1. What is a Non-Terminating Decimal?

A Non-Terminating Decimal is a decimal number that continues endlessly.

2. How do you know if a decimal is Non-Terminating?

After performing division if you get a certain block of digits that repeat in the decimal part then the decimal part is called a Non-Terminating Decimal.

3. Is 0.544444….. a non-terminating decimal?

Yes, 0.54444…. is a non-terminating decimal as it has an infinite number of terms.

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