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Standard IX

Mathematics

Irrational Numbers and Properties of Irrational Numbers

Rational numb...

Question

Rational number p/q, q ≠ 0 will be terminating decimal if the prime factorisation of q is of the form. (m and n are non negative integers):

2^m x 5ⁿ

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3^m x 7ⁿ

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3^m x 5ⁿ

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2^m x 3ⁿ

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Solution

The correct option is A
2^m x 5ⁿ

Rational number p/q, q ≠ 0 will be terminating decimal if the prime factorisation of q is of the form 2^m x 5ⁿ.

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Similar questions

Q. Rational number

\frac{p}{q}, q \neq 0

will be terminating decimal if the prime factorisation of q is of the form (m and n are non negative integers) :

Q. Assertion (A):

\frac{29}{9261}

will have a non-terminating, non-repeating decimal expansion.
Reason (R): Let

a = \frac{p}{q}

be a rational number such that

p

and

q

are co-prime and the prime factorisation of

q

is of the form

2^{n} \times 5^{m}

, where

n

and

m

are non-negative integers. Then

a

has a decimal expansion, which is non-terminating.

Q. A rational number whose decimal expansion is non-terminating can be expressed in the form

\frac{p}{q}

, where

p

and

q

are coprime, and the prime factorisation of

q

is NOT of the form _____ , where

n

and

m

are non-negative integers.

Q. In a rational number of the form

\frac{p}{q}

, the prime factorisation of

q

is of the form

2^{m} \times 5^{n}

, where

m

and

n

are positive integers. The decimal expansion terminates after ____ decimal places if

m > n

Any rational number x in the form p/q (where p and q are co primes), whose decimal expression terminates. Which of the following represents the correct form of prime factorisation of q?

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Rational number p/q, q ≠ 0 will be terminating decimal if the prime factorisation of q is of the form. (m and n are non negative integers):

The correct option is A 2m x 5nRational number p/q, q ≠ 0 will be terminating decimal if the prime factorisation of q is of the form 2m x 5n.

The correct option is A
2^m x 5ⁿ

Rational number p/q, q ≠ 0 will be terminating decimal if the prime factorisation of q is of the form 2^m x 5ⁿ.