Given:
The decimal number is 15.265.
To find:
The decimals in the form of [tex]\dfrac{p}{q}[/tex] and p,q are co-primes.
Solution:
Let the decimal number be [tex]x=15.265[/tex].
It can be rewritten as
[tex]x=15.265\times \dfrac{1000}{1000}[/tex]
[tex]x=\dfrac{15265}{1000}[/tex]
[tex]x=\dfrac{5\times 3053}{5\times 200}[/tex]
Cancel out the common factors.
[tex]x=\dfrac{3053}{200}[/tex]
Here, p=3053 and q=200 and the HCF of (p,q) is 1. So, p and q are co-primes.
Therefore, the requited fraction form is [tex]\dfrac{3053}{200}[/tex].
