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

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Standard IX

Mathematics

Rational Numbers (Definition)

A rational nu...

Question

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.

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

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

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2^{m} \times 3^{n}

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Solution

The correct option is A $2^{m} \times 5^{n}$

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Similar questions

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. 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

Let $x$ be a rational number whose simplest form is expressed as $\frac{p}{q}$ , where $p$ and $q$ are co-prime integers and $q \neq 0$ and also, $x$ is a terminating decimal, then $q$ can be expressed in the form of _____________ (where m and n are non-negative integers).

Let $x = \frac{p}{q}$ be a rational number, such that the prime factorisation of $q$ is not of the form $2^{m} 5^{n}$ , where $n, m$ are non-negative integers. Then, $x$ has a decimal expansion which is

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

The correct option is A 2m×5n

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.

The correct option is A $2^{m} \times 5^{n}$