Question

What kind of decimal representation does 23
/2³3³ have?​

Answer 1

$\large\underline{\sf{Solution-}}$

Given rational number is

$\rm :\longmapsto\:\dfrac{23}{ {3}^{3} \times {2}^{3}}$

We know that decimal representation of rational number is terminating if its denominator can be factorized in the form of 2^m 5^n, where m and n are whole numbers, otherwise its decimal representation is non terminating but repeating.

Now, for the given rational number, the decimal representation is non terminating as its denominator contains other factors than 2 or 5.

So, decimal representation is non terminating.

More to know :

Fundamental theorem of arithmetic :- Every composite number can be factorized as the product of their primes, and this prime factorization is unique irrespective of their places.

4 is the smallest composite number.