# Rational numbers can be represented as terminating and which as non-teminating decimals ?Give the answer without actually dividing .(1)9/16 (2)17/64

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Student Comments

neela | Student

1) 9/16 =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 terminating form:

1/2=0.5

1/2^3 = 0.125

1/2^7=0.78125.

1/100=1/(2*5)^2=0.01

1/(2^2*5^3) = 1/500 = 0.002

Example for **non terminating **form: 1/6 = 0.166666....

1/11=0.09090909......

1/99=0.010101....