Classify the following numbers as rational or irrational :
(i) \(\sqrt23 \)
(ii) \(\sqrt225 \)
(iii) 0.3796
(iv) 7.478478...
(v) 1.101001000100001...
(i) \(\sqrt23\) = 4.79583152331.... As the decimal expansion of this number is non-terminating non-recurring, therefore, it is an irrational number.
(ii) \(\sqrt225\) = 15= \(\frac{15}{1}\)It is a rational number as it can be represented in \(\frac{p}{q}\) form.
(iii) 0.3796 As the decimal expansion of this number is terminating, therefore, it is a rational number.
(iv) 7.478478 … = \(\overline{7.478 }\) As the decimal expansion of this number is non-terminating recurring, therefore, it is a rational number.
(v) 1.10100100010000 … As the decimal expansion of this number is non-terminating non-repeating, therefore, it is an irrational number.
Write the following in decimal form and say what kind of decimal expansion each has :
(i) \(\frac{36}{100}\) (ii) \(\frac{1}{11}\) (iii) \(4\frac{1}{8}\)
(iv) \(\frac{3}{13}\) (v) \(\frac{2}{11}\) (vi) \(\frac{329}{400}\)
Express the following in the form \(\frac{p }{ q}\) , where p and q are integers and q ≠ 0.
(i) 0.6(ii) 0.47 (iii) 0.001.