Every rational number or fraction can
be expressed in terms of decimal numbers by the actual division. And, those
decimal numbers can either be **terminating** or **non-terminating**.

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**What are terminating decimals?**

**Terminating decimal** is a fraction decimal
having a finite number of digits after decimal point. In this case division
ends after a finite number of stages. For example : 1/5, 1/4, 1/8 etc. are terminating decimals
because,

**What are non-terminating decimals?**

**Non-terminating decimal** is a fraction
decimal having infinite number of digits after decimal point. In this case
division never ends but recur the same digit or group of digits again and again.
So they are also called recurring decimals. For example: 1/3, 2/3, 4/7 etc. are
non-terminating decimals because,

Here, a number or group of numbers are
repeated and do not end after a finite number of stages, such number are
denoted by a dot (.) or a bar(–) above it.

**Types of Non-terminating Decimals:**

There are two types of non-terminating (recurring) decimals:

a.
**Simple recurring decimals**: In this
case the recurring starts just after the decinal point. For example, 0.333…

b.
**Mixed recurring decimals**: In this
case the recurring does not start just after the decimal point. For example,
0.5181818…

**Conversion of Decimal into Fraction**

For **terminating
decimal** we can convert a decimal into fraction simply by removing decimal
and dividing by 10 if there is 1 decimal place, by 100 if there is 2 decimal
places and by 1000 if there is 3 decimal places and so on. For example:

For **non-terminating
decimal** we can convert a decimal into fraction by the following method as
given in the example below:

**Do you have any
questions regarding the Terminating and Non-terminating Decimals?**

You can ask your questions or problems in the comment section below.

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