Classify the following number as rational or irrational with justification:
$0.5918$ .

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Solution

Rational number is a number which can be written in form $\frac{p}{q}$ , where $p, q$ are both integers.
$0.5918 = \frac{0.5918 \times 10000}{1 \times 10000} = \frac{5918}{10000}$
So, $0.5918$ can be written in a form $\frac{p}{q}$ , with $p, q$ both integers.
So, it is a rational number.

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Question 4
Classify the following numbers as rational or irrational with justification.
$(i) \sqrt{196}$
(ii) $3 \sqrt{18}$
(iii) $\sqrt{\frac{9}{27}}$
(iv) $\frac{\sqrt{28}}{343}$
(v) $- \sqrt{0.4}$
(vi) $\frac{\sqrt{12}}{\sqrt{75}}$
(vii) 0.5918
(viii) $(1 + \sqrt{5}) - (4 + \sqrt{5})$
(ix) 10.124124 ....
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To classify, use the definition a rational number is in the form of $\frac{p}{q}$ , where p and q are integers and $q \neq 0$ and otherwise it is an irrational number.

Q. Question 4
Classify the following numbers as rational or irrational with justification.

(i) \sqrt{196} (i i) 3 \sqrt{18} (i i i) \sqrt{\frac{9}{27}} (i v) \frac{\sqrt{28}}{343} (v) - \sqrt{0.4} (v i) \frac{\sqrt{12}}{\sqrt{75}}

(vii) 0.5918
(viii)

(1 + \sqrt{5}) - (4 + \sqrt{5})

(ix) 10.124124 ....
(x) 1.010010001....
To classify, use the definition a rational number is in the form of

\frac{p}{q}

, where p and q are integers and

q \neq 0

and otherwise it is an irrational number.

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Classify the following number as rational or irrational with justification:0.5918.

Rational number is a number which can be written in form pq, where p,q are both integers.0.5918=0.5918×100001×10000=591810000So, 0.5918 can be written in a form pq, with p,q both integers.So, it is a rational number.

Classify the following number as rational or irrational with justification:
$0.5918$ .

Rational number is a number which can be written in form $\frac{p}{q}$ , where $p, q$ are both integers.
$0.5918 = \frac{0.5918 \times 10000}{1 \times 10000} = \frac{5918}{10000}$
So, $0.5918$ can be written in a form $\frac{p}{q}$ , with $p, q$ both integers.
So, it is a rational number.