Question

Write the following in decimal form and say what kind of decimal expansion each has:
(1.) 3/13? How to find the answer.

Answer 1

The answer of 3/13 will be 0.230769 ( bar on all of them ).
This type of decimal expansion is known as non-terminating repeating.

3/13
= 0.230769230769… = 0.230769 (Non terminating repeating)
On dividing 3 by 13 we get to 230769 again and again and remainder never become zero so 3/13 is a non terminating repeating decimal.



I can give you more examples to clear your doubt

On dividing p by q, if remainder becomes zero then the decimal expansion is terminating and if remainder never become zero and Set of digits repeats periodically then the decimal expansion is non terminating repeating. It is also known as non terminating recurring decimal expansion.

____________________________________________________________________________

Solution:

(i) 36/100
= 0.36 (Terminating)

On dividing 36 by 100 we get the exact value 0.36 and set a reminder become zero so 36/100 has a terminating decimal expansion.

(ii) 1/11
0.09090909… = 0.9 (Non terminating repeating)

On dividing 1/11 we get 09 again and again i.e. remainder never becomes zero and set a digits repeats periodically.
So 1/11 has a non terminating repeating decimal expansion.

(iii) 4⅛
= 33/8 = 4.125 (Terminating)

On dividing 33 by 8 we get the exact value 4.125 and remainder becomes zero. So 4 ⅛ is a terminating decimal..

Hope you understand