What can you say about the prime factorization of the denominators of the following rational:
43.123456789

Given:

The given rational number is 43.123456789.

To do: 

Here, we have to determine the nature of the prime factorisation of the denominator of the given rational number when expressed in $\frac{p}{q}$ form.

Solution:

$43.123456789$ has a terminating decimal expansion. 

This implies, it is a rational number of the form $\frac{p}{q}$ and $q$ is of the form $2^m \times 5^n$, where $p$ and $q$ are non-negative integers. The prime factors of the denominator of the given rational number are $2$ and $5$.

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Updated on: 10-Oct-2022

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