Question

1.3 (bar on 3) express as fractions

Answer 1

$\boxed{\boxed{\large\mathbf{\frac{4}{3}}}}$
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$\mathsf{Let \: x = 1. \bar 3 -----(1)}$

Multiplying the equation by 10

[Since, the bar is over 1 digit only]

=> $\mathsf{ 10x = 13. \bar 3 -----(2)}$

$\underline{\textsf{Now, subtracting equation( 2 ) by}} \\ \underline{\textsf{equation ( 1 ) we get,}}$

$\mathsf{(10x - x) = (13. \bar 3 - 1. \bar3)}$

=> $\mathsf{9x = 12}$

=> $\mathsf{x = \frac{12}{9}}$

=> $\boxed{\mathbf{X = \frac{4}{3}}}$
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Hence, $\mathsf{1. \bar 3 = \frac{4}{3}}$