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Is $0.\overline{3} = \frac{1}{3}$ a true statement?
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Let the left hand side be:     x = 0.3333333……        (i)

Multiplying (i) by 10 gives:    10x = (10)(0.3333333……) = 3.333333......       (ii)

(ii) - (i) gives:    10x - x = 3.333333...... - 0.3333333……

9x = 3

x = 3/9 = (1/3)

Therefore the initial statement is true

by Silver Status (30,559 points)