Express following form, where p & q integers & q ≠ 0. (i)0.6.(ii)0.47(iii)0.001

Question

KnowledgeBoat · Accepted Answer

(i) Let x = x = 0.666666........... (1) Here one digit 6 is repeated so we multiply both side by 10 in equation (1) 10x = 6.6666....... we can write 10x = 6.66666....... 10x = 6 + 0.666666........... From equation (1) 10x = 6 + x 10x - x = 6 9x = 6 x = = Hence, = (ii) Let x = 0.47777777........ (1) Here one digit 7 is repeated so we multiply both side by 10 in equation (1) We can write 10x = 4.77777..... (2) On subtracting equation (2) from equation (1) 10x - x = 4.777777........ - 0.477777......... 9x = 4.300000...... x = Multiplying numerator and denominator by 10 we get, x = = Hence, = (iii) Let x = 0.001001001...... (1) Here three digit 001 are repeating so we multiply both side by 1000 in equation (1) 1000x = 0001.001001........ (2) On subtracting equation (2) from equation (1) 1000x - x = 0001.001001...... - 0.001001...... 999x = 1.0000000..... x = Hence, =

Mathematics

Express following form, where p & q integers & q ≠ 0. (i)0.6.(ii)0.47(iii)0.001

Number System

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