Question

without actually performing the long division method state whether the following rational number will have a terminating decimal expansion or a non terminating reapeting decimal expansion of 23/2​

Answer 1

Step-by-step explanation:

Theorem: Let x=

q

p

be a rational number, such that the prime factorisation of q is of the form 2

n

5

m

, where n, m are non-negative integers. Then, x has a decimal expansion which terminates

Answer 2

Answer:

23/2 in the form of p/q..

=> p & q are terminating if

1) p & q are co prime

2) q is the form of 2^n 5^m

23 & 2 has no common factors so that 23 & 2 are co-prime.

=> for denominator

=> 2 = 2¹

=> so that 2 is in form of 2^n*5^m

=> so that 23/2 is a repeating decimal expansion.