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Standard X

Mathematics

Rational Numbers

If p/q is a r...

Question

If $\frac{p}{q}$ is a rational number with terminating decimal expansion where $p$ and $q$ are coprimes, then $q$ can be represented as:
(Here, n and m are non-negative integers.)

2 or 5 or both

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2 or 3 or both

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3 or 5 or both

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2,3 or 5

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Solution

The correct option is A
2 or 5 or both

If $\frac{p}{q}$ is a rational number with terminating decimal expansion where $p$ and $q$ are coprimes, then the prime factorisation of $q$ will be in the form of $2^{n} 5^{m}$ .

Example:
Consider rational number $\frac{1}{8}$ .
Here, denominator $8 = 2^{3} \times 5^{0}$
Therefore, the rational number $\frac{1}{8}$ will have terminating decimal expansion.
$\frac{1}{8} = 0.125$ which is terminating.
Hence verified.

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Similar questions

Q. The decimal expansion of rational number

\frac{p}{q}

is terminating if q is in the form

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

. My question is, if q is only in the form

2^{n} o r 5^{m}

then will it be a terminating rational number?

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. If

x = \frac{p}{q}

be a rational number such that the prime factorization of

q

is not of the form

2^{n} 5^{m}

, where

n, m

are non-negative integers. Then

x

has a decimal expansion which is terminating.

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

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

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are co-prime and the prime factorisation of

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

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n

and

m

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If pq is a rational number with terminating decimal expansion where p and q are coprimes, then q can be represented as: (Here, n and m are non-negative integers.)

If $\frac{p}{q}$ is a rational number with terminating decimal expansion where $p$ and $q$ are coprimes, then $q$ can be represented as:
(Here, n and m are non-negative integers.)