Given: The numbers are provided.
To find: Whether the numbers are rational numbers or not?
Explanation:
A number that can be expressed in the form of p/q is called a rational number.
Let us check the first number 29.64761 , it is a rational number since we can express it as
[tex]\frac{2964761}{100000}[/tex]
The next number is 29.42664, it is also a rational number . Since, it can be expressed as
[tex]\frac{2942664}{100000}[/tex]
The next number is
[tex]\sqrt{169}[/tex]
the value of of which is
[tex]\sqrt{169}=13[/tex]
it is a rational number since 13 can be expressed as
[tex]\frac{13}{1}[/tex]
The next number is 30.760520....
It is not a rational number since it is non-terminating and the non-terminating decimals are not repeating also.
therefore, 30.760520.... is not a rational number.
the last number
[tex]24.955\bar{68}[/tex]
it is a rational number since the decimals are repeating. As we can see the term 68 above it has bar so it will keep on repeating.
Therefore, the number is a rational number.
Final Answer: The rational numbers are 29.64761, 29.42664,
[tex]\sqrt{169}[/tex]
and
[tex]29.955\bar{68}[/tex]
