NCERT Class 10 Solutions: Real Numbers (Chapter 1) Exercise 1.4 –Part 3
In the questions below, find the types of decimals.
Q VI)
Is terminating if

p and q are coprime

And q is of the form Where n and m are nonnegative integers
Checking Coprime
23 and have no common factors, so, 23 and are coprime
For denominator
So, denominator is of the form
Where
Thus is terminating decimal
Q VII)
Is terminating if

p and q are coprime

And q is of the form Where n and m are nonnegative integers
Checking Coprime
129 and have no common factors,
So, 129 and are coprime
For denominator
So, denominator is not of the form
Thus has a nonterminating repeating decimal
Q VIII)
Is terminating if

p and q are coprime

And q is of the form Where n and m are nonnegative integers
Checking Coprime
2 and 5 have no common factors,
So, 2 and 5 are coprime
For denominator 5
So, denominator is of the form
Where
Thus i.e. is a terminating decimal
Q IX)
Is terminating if

p and q are coprime

And q is of the form Where n and m are nonnegative integers
Checking Coprime
7 and 10 have no common factors,
So, 7 and 10 are coprime
For denominator 10
So, denominator is of the form
Where
Thus i.e. is a terminating decimal
Q X)
Is terminating if

p and q are coprime

And q is of the form Where n and m are nonnegative integers
Checking Coprime
11 and 30 have no common factors, so, 11 and 30 are coprime
For denominator 30
So, denominator is not of the form
Thus i.e. is a nonterminating repeating decimal