##
**Terminating
and Non-terminating Decimals**

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**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,

1/5 = 0.2

1/4 = 0.25

1/8 = 0.125

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**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,

1/3 = 0.3333333…..

2/3 = 0.6666666…..

2/11 = 0.181818…..

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.

**There are two types of recurring decimals:**

a.

**Simple recurring decimals**: In this case the recurring starts just after the decimal 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:

*Example 1. Convert 2.5, 0.28, 0.125 into fraction.*

*Solution:*

*Here,*

*2.5 = 25/10 = 5/2*

*0.28 = 28/100 = 7/25*

*0.125 = 125/1000 = 1/8*

For

**non-terminating decimal**we can convert a decimal into fraction by the following method as given in the example below:*You can comment your questions or problems regarding terminating and non-terminating decimals here.*

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