Let x be a rational number whose simplest form is expressed as p-q- where p and q are co-prime integers and q - 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-

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Terminating and Non-Terminating Decimals

Let x be a ra...

Question

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).

$2^{n} 5^{m}$

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$3^{n} 7^{m}$

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$11^{n} 1^{m}$

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$2^{n} 3^{m}$

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Solution

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

Any real number which has a decimal expansion that terminates, can be expressed as a rational number whose denominator is a power of 10.
Also, the only prime factors of 10 are 2 and 5.

Example:
$\frac{13}{125} = \frac{13}{5^{3}} = \frac{13 \times 2^{3}}{5^{3} \times 2^{3}} = \frac{104}{10^{3}} = 0.104$

Therefore, the denominator should be in the form of $2^{n} 5^{m}$ .

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Let x be a rational number whose simplest form is expressed as pq, where p and q are co-prime integers and q≠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 $x$ 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).