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:

We have,

8

17

=

2

3

×5

0

17

So, the denominator 8 of 17/8 is of the form 2

m

×5

n

, where m,n are non-negative integers.

Hence 17/8 has terminating decimal expansion. the decimal expansion of

8

17

terminates after max(3,0)=3 places of decimals.

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Answer 2

Step-by-step explanation:

ANSWER

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