Question

without actually performing the long division state whether the following rational number will have a terminating decimal expansion or a non terminating repeating decimal expansion 7/8​

Answer 1

Answer:

Without actually performing the long division, state whether the following rational number will have terminating decimal expansion or a non-terminating repeating decimal expansion. Also, find the numbers of places of decimals after which the decimal expansion terminates.

8

17

​  

 

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ANSWER

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.

Step-by-step explanation: