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Question: Please explain terminal and non-terminal numbers

Posted by: Archita K. on 06.05.2020

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Terminating numbers are those numbers which come to an end after few repetitions after decimal point.

Terminating numbers Example: 0.5, 2.456, 123.456, etc. ...1/2, 9/3, 7/5 etc... 

Non terminating numbers are those which keep on continuing after decimal point (i.e. they go on forever).

Non terminating numbers Example: 1/3, 10/9 etc.. 


Terminal Numbers- These are those nubers which have a definite end point.

Eg- 2/5= 0.4 and  4/100=0.04

Non Terminal Numbers- These are those numbers which do not have a definite end point. In order to find their value we usually round off the digits.

Eg-  4/6=0.6666...but to have a value we made it as 0.66667

        2/6=0.3333.... so we made it as 0.33334


Terminal Numbers: Numbers which have a defined end point an terminates after a certain point

Example : (3/4) = 0.75, (7/8) = 0.875

Non Terminal Numbers : Numbers which does not have a defined end point and does not terminate.

Example : Pi seems to be a fraction written in the form (22/7) but it does not terminate and has the value 3.14.....


Terminal number are finite number of decimal digit .for ex-25/5=5 And non terminal number are infinite number of decimal digit. For ex-11/3=3.66666
Terminating numbers are numbers with finite number of decimal part For eg. 25/2=12.5 Nonterminal numbers are numbers with infinite number of decimal part. Non terminal numbers are of two types, recurring and non recurring For eg. 87/7=12.42857142857...... This is recurring non terminal numbers Non repeating digits are nonrecurring nonterminal numbers

Terminating numbers are decimal numbers which have finite number of digits after decimal point

Example 22/5 = 4.4

Non terminating numbers are decimal numbers which have an infinite number of digits after the decimal point. Non terminating numbers are of two types: recurring non-terminating numbers and non-recurring non-terminating numbers

Example: pi= 22/7=  3.142857142857........             This is recurring non-terminating

                355/113 = 3.14159292035.........                This is non-recurring non-terminating


When we divide a number, if we do not get zero as remainder we continue the division by adding zeros to the divident and in the quotient we start writing the numbers after a dot. So when we go on dividing like this if at a point we get zero as remainder then its a terminating decimal. for eg if we divide 27 by 4 first our quotient is 6 which gives us a remainder 3 now we add zero to 3 it becomes 30, th quotient becomes 6.7 which gives us a remainder 2 and again the next step we add 0 the number is 20, which goes by 4 and gives us quotient 6.75 and remainder 0. this kind of division which gives us 0 are terminating decimals whereas in some divisions it do not give us a remainder 0 but it goes on.. for eg 10 divided by 3 the quotient is always 3.33333 it goes on infinity such kinds of divisions which do not give us a remainder 0 are non terminating decimals.  



terminal numbers= numbers which are havinge finite number of digit in the decimal part are called as terminal numbers. for eg: 2.87 , 4.67 etc.

non terminal numbers= numbers which are having infinte number of digit in a decimal part are called as non terminal numbers, for eg: 2.73444....  , 3.677777...



Terminal numbers are the numbers with finite numbers of digit in decimal part. For eg. 2.5, 4.36, 1.0000001. Those fractions which have denominator a multiple of only 2 and 5 are terminating numbers.

Non-terminal numbers are the numbers with infinite numbers of digit in decimal part. For eg. 2.5453244........, 5/3.  Those fractions which have denominator a multiple of number other than 2 or 5 are terminating numbers.

Terminal and nonterminal the name name itself explains the meaning . 1. Terminal number: If a number terminates in its decimal form , it is terminal number. e.g.1/2= 0.5 , 0.0052 etc. 2. Nonterminal number: If a number does not terminate in its decimal form, it is nonterminal number. e.g 1/3 =0.33333... Contd. 1/7= 0.1428571428571.... Contd., π , etc.

Decimal expansion of any rational number of the form p/q will be either terminating or  non –terminating and repeating. The expansion will be terminating if the prime factorization of q is of the form 2^n X 5^m.where n and m are non negative integers. The expansion will be non terminating and repaeting(recurring) if prime factorization of q is not of  the form of

 2^n X 5^m. The following  examples will make the above clear;

1. 32/25 =  1.28.The denominator 25 is of the form 2^0 X5^2..So the decimal expansion  terminates at 1.28

2. 47/20=   2.35   .Here also the denominator is of the form 2^2 X5^1. So the decimal expansion   terminates at 2.35.

Now consider the following:

1. 4/3= 1.333 . The denominator is not of the form 2^n X 5^m. . Hence decimal expansion is non- terminating and  

     repeating. The dot placed above the digit “3” indicates that the expansion  repeats from here  onwards.

2.  29/7=  4.142857142857 .Here also the denominator is not of the form 2^n X 5^m. . Hence decimal    expansion  is

      non terminating and repeating. The dot placed above the digit “7”indicates that the expansion repeats from here


  And finally any number that does not fall into either of the above is not a rational number.



In retional number when numerator divided by denominator it's remainder become zero after certain stage then it's called terminate number ok. Ex _3÷2 And if reminder never become zero then it's called non terminal numbers.ex _22÷7

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