(i) Classify the given number as rational or irrational with justification..
(ii) Classify the given number as rational or irrational with justification
(iii) Classify the given number as rational or irrational with justification.
(iv) Classify the given number as rational or irrational with justification.
(v) Classify the given number as rational or irrational with justification.
(vi) Classify the given number as rational or irrational with justification.
(vii) Classify the given number as rational or irrational with justification.0.5918
(viii) Classify the given number as rational or irrational with justification.
(ix) Classify the given number as rational or irrational with justification.10.124124 ………..
(x) Classify the given number as rational or irrational with justification.1.010010001 ………….
.
(i)Answer. [Rational]
Solution.
We have,
= 14 = which follows rule of rational number.
Any number which can be represented in the form of p/q where q is not equal to zero is a rational number. Also, both p and q should be rational when the fraction is expressed in the simplest form.
So, is a rational number.
(ii)Answer. [Irrational]
Solution.
Any number which can be represented in the form of p/q where q is not equal to zero is a rational number. Also, both p and q should be rational when the fraction is expressed in the simplest form.
We have,
So, it can be written in the form of as
But we know that is irrational
(Irrational numbers are real numbers which cannot be represented as simple fractions.)
Hence, is an irrational number
(iii)Answer. [Irrational]
Solution.
Any number which can be represented in the form of p/q where q is not equal to zero is a rational number. Also, both p and q should be rational when the fraction is expressed in the simplest form.
We have,
So this can be written in the form of as but we can see that (denominator) is irrational.
(Irrational numbers are real numbers which cannot be represented as simple fractions.)
Hence is irrational
(iv)Answer. [Rational]
Solution.
We have,
Any number which can be represented in the form of p/q where q is not equal to zero is a rational number. Also, both p and q should be rational when the fraction is expressed in the simplest form.
Hence is a rational number.
(v)Answer. [Irrational]
Solution.
Any number which can be represented in the form of p/q where q is not equal to zero is a rational number. Also, both p and q should be rational when the fraction is expressed in the simplest form.
We have,
So, it can be written in the form of as
But we know that both are irrational
(Irrational numbers are real numbers which cannot be represented as simple fractions.)
Hence, is an irrational number
(vi)Answer. [Rational]
Solution.
We have,
Any number which can be represented in the form of p/q where q is not equal to zero is a rational number. Also, both p and q
should be rational when the fraction is expressed in the simplest form.
So, is a rational number.
(vii)Answer. [Rational]
Solution.
We have,
Any number which can be represented in the form of p/q where q is not equal to zero is a rational number. Also, both p and q should be rational when the fraction is expressed in the simplest form.
Also we can see that 0.5918 is a terminating decimal number hence it must be rational.
So, 0.5918 is a rational number.
(viii)Answer. [Rational]
Solution.
We have,
Any number which can be represented in the form of p/q where q is not equal to zero is a rational number. Also, both p and q should be rational when the fraction is expressed in the simplest form.
So, is a rational number.
(ix)Answer. [Rational]
Solution.
Any number which can be represented in the form of p/q where q is not equal to zero is a rational number. Also, both p and q should be rational when the fraction is expressed in the simplest form.
All non-terminating recurring decimal numbers are rational numbers.
Non terminating Recurring decimals are those decimals which have a particular pattern/sequence that keeps on repeating
itself after the decimal point. They are also called repeating decimals.
Examples: 1/3 = 0.33333…, 4/11 = 0.363636…
Now, 10.124124 ………. is a decimal expansion which is a non-terminating recurring.
So, it is a rational number.
(x)Answer. [Irrational]
Solution.
Non terminating Recurring decimals are those decimals which have a particular pattern/sequence that keeps on repeating itself after the decimal point.
All non-terminating recurring decimal numbers are rational numbers.
Non terminating Non Recurring decimals are those decimals which do not have a particular pattern/sequence after the decimal point and it does not end.
All non-terminating non-recurring decimal numbers are irrational numbers.
1.010010001 ………. is non-terminating non-recurring decimal number, therefore it cannot be written in the form ,with p,q both as integers.
Thus, 1.010010001 ……….. is an irrational number.