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  • Show that 0.142857142857 = 1 by 7

Show that 0.142857142857 ……. = \frac{1}{7} 

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Solution.    Let, x = 0.142857142857…         …(i)
Multiply (i) by 1000000, we get
1000000 x = 142857.142857…     …(ii)
Subtracting equation (i) from (ii), we get
1000000 x – x = 142857.142857… - 0.142857…
999999 x = 142857
x= \frac{142857}{999999}= \frac{47619}{333333}= \frac{15873}{111111}= \frac{5291}{37037}
 = \frac{481}{3367}= \frac{1}{7}
Hence, 0.142857 ……. \frac{1}{7}
Hence proved

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infoexpert27

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