Rational numbers can be represented as ternimating , and which as non-terimating decimals ?Give answer without actually dividing .(1) 3 / 16 (2) 17 /64

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1) 3/16 =3/2^4 has terminating  decimal form.

2)17/64 =17/2^6 Has a terminating decimal form.

Reason:

Any rational fraction of the form  p/2^n or p/5^n   or  p/[(2^m)(5^n)]   has a terminating decimal form. Where, p,m,n are integers or zero. Otherwise it(=rational fraction) has a nonterminating recurring form.

Example for non terminating form: 1/3 = 0.33333....

1/7 =0.142857 142857 142857.....

1/9=0.11111...

 

 

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