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1. Number System
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Q12 of 131 Page 1

Express 0.6666………in the form of 

Let x = 0.6666……….                          …(i)
∴ 10 x =                  ...(ii)
(ii) – (i), 9x = 6                ∴  x ==
∴ 0.6666 =
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10 Which of the following rational numbers have the terminating decimal representation?
       (i) 3/5              (ii) 7/20                   (iii) 2/13
       (iv) 27/40        (v) 133/125            (vi) 23/7
       [Making use of the result that a rational number p/q where p and q have no common factor(s) will have a terminating representation if and only if the prime factors of q are 2's or 5's or both.]
11 Find the decimal representation of 1/7, 2/7. Deduce from the decimal representation of 1/7, without actual calculation, the decimal representation of 3/7, 4/7, 5/7 and 6/7. 13 If a and b are two rational numbers, prove that a + b, a - b, ab are rational numbers. If b ≠ 0, show that a/b is also a rational number. 14 Express 0.272727………in the form of .
Questions · 131
1. Number System
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