3 numbers whose decimal expansions are non-terminating non-recurring are as follows.
0.505005000500005000005…
0.7207200720007200007200000…
0.080080008000080000080000008…
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) \(\frac{329}{400}\)
You know that \(\frac{1}{7}\) = 0142857_ . . Can you predict what the decimal expansions of \(\frac{2}{7},\frac{3}{7},\frac{4}{7},\frac{5}{7},\frac{6}{7}\) are, without actually doing the long division? If so, how? [Hint : Study the remainders while finding the value of 1/7 carefully.]
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.
(i) The kind of person the doctor is (money, possessions)
(ii) The kind of person he wants to be (appearance, ambition)
ABCD is a quadrilateral in which AD = BC and ∠ DAB = ∠ CBA (see Fig. 7.17). Prove that
(i) ∆ ABD ≅ ∆ BAC
(ii) BD = AC
(iii) ∠ ABD = ∠ BAC.
