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NCERT Class 10 Solutions: Real Numbers (Chapter 1) Exercise 1.4 β Part 2
In the questions, below find the types of decimals.
Q. (III)
Is terminating if
- p and q are co-prime
- q is of the form Where n and m are non-negative integers
Checking Co-prime
64 and 455 have no common factors, so, 64 and 455 are co-prime
For denominator 455
Hence
So, denominator is not of the form
Thus has a non-terminating repeating decimal
Q. (IV)
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
3 and 320 have no common factors, so, 3 and 320 are co-prime
For denominator 320
Hence
So, denominator is of the form
Where
Thus i.e.. is terminating decimal
Q. (V)
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
29 and 343 have no common factors, so, 29 and 343 are co-prime
For denominator 343
Hence
So, denominator is not of the form
Thus has a non-terminating repeating decimal