Question

"Question 1 Write the following in decimal form and say what kind of decimal expansion each has:
(i) 36/100
(ii) 1/11
(iii) 4.1/8
(iv) 3/13
(v) 2/11
(vi) 329/400

Class 9 - Math - Number Systems Page 14"

Answer 1

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.

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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..



(iv) 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.


(v) 2/11
= 0.181818181818… = 0.18 (Non terminating repeating)
On dividing 2 by 11 we get 18 again and again and remainder never become zero. so 2 /11 is a non terminating repeating decimal


(vi) 329/400
= 0.8225 (Terminating)

On dividing 329 by 400 we get the exact value 0.8225 and remainder never become zero . so 329 / 400 is a terminating decimal

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Hope this will help you...

Answer 2

I) 0.36- terminating
ii) 0.9090909...-non terminating and repeating
iii)0.5125-terminating
IV)0.2307692307-non terminating and repeating
v) 0.1818181818...- non terminating and repeating
vi) 0.8225-terminating