Question

simplest form of 0.78bar in fraction​

Answer 1

Let x = 0.787878...... ... (1)

100x = 78.787878..... ... (2)

(2) - (1)

100x - x = 78.7878 - 0.7878

99x = 78

x = 78/99

Answer 2

SOLUTION

TO DETERMINE

To express as fraction

$\sf{ 0. \overline{78}}$

EVALUATION

$\sf{ let \: \: x = 0. \overline{78}}$

Then

x = 0.787878. . . . - - - - - - (1)

Multiplying both sides of Equation 1 by 100 we get

100x = 78.787878. . . . - - - - - - (2)

Equation 2 - Equation 1 gives

99x = 78

$\displaystyle \sf{ \implies x = \frac{78}{99} }$

$\displaystyle \sf{ \implies x = \frac{26}{33} }$

FINAL ANSWER

$\displaystyle \sf{ 0. \overline{78}= \frac{26}{33} }$

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