3 numbers whose decimal expansions are non-terminating non-recurring are as follows.
0.505005000500005000005…
0.7207200720007200007200000…
0.080080008000080000080000008…
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.
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) \(\frac{329}{400}\)
Classify the following numbers as rational or irrational :
(i) \(\sqrt23 \)
(ii) \(\sqrt225 \)
(iii) 0.3796
(iv) 7.478478...
(v) 1.101001000100001...
Two circles intersect at two points B and C. Through B, two line segments ABD and PBQ are drawn to intersect the circles at A, D and P, Q respectively (see Fig. 9.27). Prove that ∠ACP = ∠ QCD

ABCD is a trapezium in which AB || CD and AD = BC (see Fig. 8.14). Show that
(i) ∠A = ∠B
(ii) ∠C = ∠D
(iii) ∆ABC ≅ ∠∆BAD
(iv) diagonal AC = diagonal BD [Hint : Extend AB and draw a line through C parallel to DA intersecting AB produced at E.]

(i) The kind of person the doctor is (money, possessions)
(ii) The kind of person he wants to be (appearance, ambition)