Terminating and non terminating fractions

Terminating and non terminating fractions:

Terminating fractions:

Some times when we solve a fraction (p/q) and observe the ans. of that fraction in which the number of digits after decimal point is finite (countable) then it is a terminating fractions.

    OR

When we convert a rational number( which can be written in the form of P/Q, where P/Q are the integers which is denoted by Z and Z=.....-3,-2,-1,0,1,2,3.......) into a decimal fraction and the division process ends means in division we obtain a zero as a remainder, then we say it is a terminating fraction or terminating decimal fraction.

If we reverse the process then these fractions can easily be converted or change into rational numbers or in the form of p/q, where p,q are the integers (Z) and q is not equal to zero (0).

مختتم کسر آ عشاریہ

ایسے ناطق اعداد جن کو کسر آ عشاریہ میں تبدیل کرتے ہوئے تقسیم کا عمل رک جائے۔مطلب تقسیم کرتے ہوئے باقی صفر بچے ۔

یا

ایسی کسر آ عشاریہ جس میں نقطہ اعشاریہ کے بعد اعداد کی تعداد محدود ہو۔

Examples of terminating decimal fractions:

0.12 , 0.45 , 5.32 and 0.0625 etc are the examples of terminating decimal fractions.

Now we see some examples and try to convert them into decimal fractions.

1- 3/5

2- 9/4

Note:

In a fraction (p/q), where p is nominator and q is denominator if the denominator of that fraction has no prime factor other than 2 ,5 and 2 and 5 itself, then that fraction ( rational number) is a terminating decimal.

وہ ناطق اعداد جن کے مخرج میں 2 یا 5 ہو یا 2 اور 5 کے اضعاف ہوں۔ تو وہ ناطق اعداد مختتم کسر اعشاریہ کہلاتی ہیں۔

Non Terminating Decimal fractions:

The decimal fraction in which the numbers after decimal point (.) is infinite then that decimal fraction is called Non Terminating decimal fraction.

The definition of non terminating decimal fractions can also be define as " while converting a rational number (p/q) into a decimal fraction, the process of division never ends and the numbers after decimal point came again and again"  means  the number of digits after  the decimal point are infinite then that are called non Terminating decimal fractions.

غیر مختتم کسر اعشاریہ

ایسے ناطق اعداد جن کو کسر آ عشاریہ میں تبدیل کرتے ہوئے تقسیم کا عمل جاری رہے۔مطلب تقسیم کرتے ہوئے باقی صفر نا بچے ۔

یا

ایسی کسر اعشاریہ جس میں نقطہ اعشاریہ کے بعد اعداد کی تعداد لا محدود ہو تو وہ کسر اعشاریہ غیر مختتم کسر اعشاریہ کہلاتی ہیں۔

Examples of non terminating decimal fractions:

0.12323.......  , 4.5657.........  , 0.1111111........  

Now we solve some examples related to non Terminating decimal fractions.

1- 1/3

2-  1/9

3- 9/7 etc

Non Terminating decimal fractions:

Non Terminating decimal fractions are of two types.

1-  Repeating decimal fractions

2-  Non repeating decimal fractions

متوالی کسر اعشاریہ

غیر متوالی کسر اعشاریہ

Such non Terminating decimal fractions in which the number of digits after decimal point (.) Repeat itself again and again then sush fractions are called non terminating with repeating decimal fractions.

ایسی کسر اعشاریہ جس میں نقطہ اعشاریہ کے بعد اعداد اپنے آپکو دہرانا شروع کر دیں۔ تو ایسی کسر اعشاریہ متوالی کسر اعشاریہ کہلاتی ہے۔

Examples:

1/9 = 0.11111111........

1/3 = 0.3333333.........

2.32 32 32 32 ........

1.1234 1234 1234...........

And Such non Terminating decimal fractions in which the number of digits after decimal point (.) does not repeat itself again and again but continue with different digits after decimal point then such fractions are called non terminating with non repeating decimal fractions.

غیر متوالی کسر اعشاریہ

ایسی کسر اعشاریہ جس میں نقطہ اعشاریہ کے بعد مختلف اعداد آ نا شروع کر دیں تو وہ کسر اعشاریہ غیر متوالی کسر اعشاریہ کہلاتی ہے۔

Examples:

9/7 = 1.2857142........

3.48348610637......

0.92637065......... 

Note:

The decimal which are non terminating and non repeating are called Irrational numbers.

ایسی کسر اعشاریہ نو غیر مختتم اور غیر متوالی  ہو تو ایسے غیر ناطق اعداد کے نام سے جانا جاتا ہے۔

What are terminating fractions 
Examples of terminating fractions
Non terminating decimal fractions Examples of non terminating decimal fractions, 
Repeating decimal fractions
Non repeating decimal fractions
Examples of repeating decimal fractions
Examples of non repeating decimal fractions,

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