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Learn Exercise 1.4

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Software Engineer with Tutoring Experience

- Since this number has a terminating decimal expansion of the form and q is of the form . Hence, prime factors of q will either be 2 or 5 or both. The decimal expansion is neither terminating nor recurring. Hence, the given number is an irrational number. Since the decimal expansion is non-terminating...
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- Since this number has a terminating decimal expansion of the form and q is of the form . Hence, prime factors of q will either be 2 or 5 or both.
 The decimal expansion is neither terminating nor recurring. Hence, the given number is an irrational number.
Since the decimal expansion is non-terminating yet recurring.Hence the given number is of the form and q will not be of the form . Therefore, the prime factors of q will also have a factor other then 2 or 5.

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(i) Ratinal number prime factors of q are in the form 2^m× 5^n. (ii) Irrational number (iii) Rational number prime factors of q not in the form of 2^m×5^n
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Maths Tutor

The prime factor of 'q' are either multiple of 2 or 5 or both 2 and 5.
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I have 8 year experience in teaching.

Option no.2- is irrational number
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Software Engineer with Tutoring Experience

- Since this number has a terminating decimal expansion of the form and q is of the form . Hence, prime factors of q will either be 2 or 5 or both. The decimal expansion is neither terminating nor recurring. Hence, the given number is an irrational number. Since the decimal expansion is non-terminating...
read more

- Since this number has a terminating decimal expansion of the form and q is of the form . Hence, prime factors of q will either be 2 or 5 or both.
 The decimal expansion is neither terminating nor recurring. Hence, the given number is an irrational number.
Since the decimal expansion is non-terminating yet recurring.Hence the given number is of the form and q will not be of the form . Therefore, the prime factors of q will also have a factor other then 2 or 5.

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Enthusiastic Teacher

1.) RATIONAL NUMBER: A number is called a rational number if the form p/q and q≠ 0 and ‘p ‘and ‘q’ should be integers. The decimal expansion can be:a.) Terminating (i.e. the division will have remainder=0) b.) Non-terminating (i.e. the division will not have remiander=0, it...
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1.) RATIONAL NUMBER: A number is called a rational number if the form p/q and q≠ 0 and ‘p ‘and ‘q’ should be integers. The decimal expansion can be:
a.) Terminating (i.e. the division will have remainder=0)
b.) Non-terminating (i.e. the division will not have remiander=0, it will never end ) but repeating (i.e. the quotient will happen in some pattern)
The number to be terminating, the factors of ‘q’ should be any powers of 2, 5 or both. Therefore ‘q’ can be of the form 2^m or 5^n or both and or 2^m * 5^n.

2.) NON-RATIONAL NUMBER: A number with decimal expansion as non-terminating and non-repeating.

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Online Teacher with over 30 Years Experience

i) It is terminating. Prime factors of q will be 2 and 5 ii) It is non-terminating, non-recurring. Prime factors of q will be other than 2 and 5. iii)It is non-terminating and recurring. Prime factors of q will be 2, 5 and any other number too.
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Maths trainer for my friends with good experience

Option number 2 is irrational because it can't be written as p/q form Option number 1 and 3 can be written as p/q form
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