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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 co-prime
- And q is of the form Where n and m are non-negative integers
Checking Co-prime
23 and have no common factors, so, 23 and are co-prime
For denominator
So, denominator is of the form
Where
Thus is terminating decimal
Q (VII)
Is terminating if
- p and q are co-prime
- And q is of the form Where n and m are non-negative integers
Checking Co-prime
129 and have no common factors,
So, 129 and are co-prime
For denominator
So, denominator is not of the form
Thus has a non-terminating repeating decimal
Q (VIII)
Is terminating if
- p and q are co-prime
- And q is of the form Where n and m are non-negative integers
Checking Co-prime
2 and 5 have no common factors,
So, 2 and 5 are co-prime
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 co-prime
- And q is of the form Where n and m are non-negative integers
Checking Co-prime
7 and 10 have no common factors,
So, 7 and 10 are co-prime
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 co-prime
- And q is of the form Where n and m are non-negative integers
Checking Co-prime
11 and 30 have no common factors, so, 11 and 30 are co-prime
For denominator 30
So, denominator is not of the form
Thus i.e.. is a non-terminating repeating decimal