Question

3. Express decimal expansion 23.3408 in the form a rational number.

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Answer 1

Hello friends!!

Here is your answer :

➡️ 23.3408

=> It has terminating decimal expansion.

$= > \frac{233408} {10000}$

$= > \frac{116704}{5000}$

$= > \frac{29176}{1250}$

$= > \frac{14588}{625}$

$= > \frac{14588}{{2}^{0} \times {5}^{4}}$

Therefore, it will terminates after 4 places of digit.

Hope it helps you..

# Be Brainly

Answer 2

Given Decimal Expansion = 23.3408.

= > It is terminating decimal.

Therefore it would be a rational number.

Method 1:

$= \ \textgreater \ \frac{23408}{10000}$

$= \ \textgreater \ \frac{23408}{10^4}$

$= \ \textgreater \ \frac{23408}{2^4 * 5^4}$


The decimal expansion terminates after 4 decimal places.


Method2:

$= \ \textgreater \ \frac{23408}{10000}$

$= \ \textgreater \ \frac{14588}{625}$

$= \ \textgreater \ \frac{14588}{2^0 * 5^4}$


The decimal expansion terminates after 4 decimal places.



Hence 23.3408 is in the form of p/q.


Hope this helps!