Question

without performing division, state whether the following rational numbers will
have a terminating decimal form or a non-terminating, repeating decimal form 13/3125,11/12,64/455,15/1600,29/343​

Answer 1

There is a basic rule to get answers for questions of this type.

You have to do the prime factorisation of the denominator of each rational no.

whichever prime factorisation will be in the form of 2^n x 5^m will give you terminating any other type will be non termination.

HOPE I HELPED YOU!!!

Answer 2

Answer:

Step-by-step explanation:

i) 13/3125

Factorize the denominator we get  

3125 =5 x 5 x 5 x 5 x 5 = 55  

So denominator is in form of 5m so 13/3125 is terminating .

(iii) 64/455  

Factorize the denominator we get  

455 =5 x 7 x 13  

There are 7 and 13 also in denominator so denominator is not in form of 2n*5m . hence 64/455 is not terminating.

(iv) 15/1600  

Factorize the denominator we get  

1600 =2 x 2 x 2 x2 x 2 x 2 x 5 x 5 = 26 x 5²  

so denominator is in form of 2n x 5m  

Hence 15/1600 is terminating.

(v) 29/343  

Factorize the denominator we get  

343 = 7 x 7 x 7 = 7³

There are 7 also in denominator so denominator is not in form of 2n x 5m  

Hence it is none - terminating.