Question

23. What type of decimal form will the number
368/1050 show?
(a) Terminating
(b) Non-terminating repeating
(c) Non-terminating non-repeating
(d) None of these
​

Answer 1

Given : number 368/1050  

To Find: type of decimal form

(a) Terminating

(b) Non-terminating repeating

(c) Non-terminating non-repeating

(d) None of these

​

Solution:

Rational numbers are real numbers which can be written in the form p/q where p and q are integers and q≠0

All real numbers which are not rational  are irrationals.

Any number in the form of p/q  where p and q are co primes.

if q has only prime factors of 2 and 5 then it is terminating decimal.

if q has prime factors other than 2 and 5 also then its non terminating recurring decimal  

Irrational numbers are non terminating non-recurring decimals  

368/1050  

= 184/525

184 = 2 * 2 * 2 * 23

525 = 3 * 5 * 5 * 7

184 and 525 are co primes

and 525 has prime factors 3 and 7  also

so  it is  non terminating recurring decimal

368/1050 is  Non-terminating repeating

Correct option is :

(b) Non-terminating repeating

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