Terminating and Non-terminating Decimals

Terminating and Non-terminating Decimals

Terminating and Non-terminating Decimals

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

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.
non-terminating decimals

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:
Example 2. Convert 0.181818... into fraction.

You can comment your questions or problems regarding terminating and non-terminating decimals here.

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