How is 3 11 represented in decimal form?

Question

How is        3    11   represented in decimal form?

Hudson Fry · Accepted Answer

The correct option is  A 0.272727Given fraction is 311.311=3×111......(1)Now,111 = 111 × 100100    = (10011) × 1100    = (9111) × 1100    =  (9+111) × 1100    = 9100 + 11100.......(2)Now, 11100 = 111×100               = (111) × 1100.......(3)From (2), 111 = 9100 + 11100; substitute it in eq (3).⇒ 11100 = (9100 + 11100)  × 1100          = 910000 + 1110000Adding this value to equation 1 now, we get111 = 9100 + (910000 + 1110000)    = (9100 + 910000) + 1110000Likewise, determining the value of 1110000=(111×110000)and on solving that will give 91000000 + 111000000⇒ 111 = 9100 + 910000 + (91000000 + 111000000) The continuation of this cycle results in 111 = 9100 + 910000 + 91000000 + ........= 0.09 + 0.0009 + 0.000009 + .....∴ 111 = 0.090909.....Now, substituting 111 in (1) gives311=3×0.090909...      = 0.272727....

How is 3/11 represented in decimal form?

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