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  • Without actually performing the long division, state whether the following rational numbers will have terminating decimal expansion or non-terminating repeating decimal expansion. (i)315/16(ii)427/625 (iii)619/325

Without actually performing the long division, state whether the following rational numbers will have terminating decimal expansion or non-terminating repeating decimal expansion. (i)315/16(ii)427/625 (iii)619/325

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Theorem: Letx=fracpq? be a rational number, s.t.  prime factorization of denominator q is in the form of  (2^a imes 5^b), where a, b are non-negative integers. Then, x has a decimal expansion which surely terminates.

1)frac31516=frac3152^4

If u compare denominator with 2^a imes 5^b then a=4, b=0

The denominator is in the form 2^a imes 5^b 

So,frac31516 surely terminate 

 

2)frac427625=frac4275^4

If u compare denominator with 2^a imes 5^b then a=0, b=4

The denominator is in the form 2^a imes 5^b 

So,frac427625 surely terminate 

3)frac619325=frac6195^2 imes13

The denominator is in the form 5^b imes13^c

So,frac619325 is non terminating, repeating  

 

Posted by

Deependra Verma

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