Q. 13.9( 32 Votes )

# Without actual division, find which of the following rationals are terminating decimals.

(i) (ii) (iii)

(iv) (v)

Answer :

First we have to know what is terminating decimal. Terminating decimal is the number which has digits that do not go on forever.

(i)

Denominator 80 has factors = 2 × 2 × 2 × 2 × 5

So, 80 has no prime factors other than 2 and 5, thus is terminating decimal.

(ii)

Denominator 24 has factors = 2 × 2 × 2 × 3

So, 24 has factors other than 2 and 5, thus is not a terminating decimal.

(iii)

Denominator 12 has factors = 2 × 2 × 3

So, 12 has factors other than 2 and 5, thus is not a terminating decimal.

(iv)

Denominator 35 has factors = 5 × 7

So, 35 has factors other than 2 and 5, thus is not a terminating decimal.

(v)

Denominator 24 has factors = 5 × 5 × 5

So, 125 has no prime factors other than 2 and 5, thus is a terminating decimal.

Rate this question :

If x is rational and y is irrational, then show that (x + y) is always irrational.

RS Aggarwal & V Aggarwal - MathematicsIf =1.414, then the value of upto three place of decimal is

RD Sharma - MathematicsIf =1.4142, then is equal to

RD Sharma - MathematicsThe value of is

RD Sharma - MathematicsIf *x* = , then *x*^{2} + -2 =

If , then *a* =

If *x* = 3+, find the value of *x*^{2}+.

The decimal representation of an irrational number is

RS Aggarwal & V Aggarwal - MathematicsAn irrational number between

RS Aggarwal & V Aggarwal - Mathematics