Question

The sum of 0.3 bar and 0.2 bar is
5/99
5/100
5/10
5/9

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

$\sf{The \: sum \: of \: \: 0. \overline{3} \: \: and \: \: 0.\overline{2} \: \: is }$

$\displaystyle \sf{ \frac{5}{99} }$

$\displaystyle \sf{ \frac{5}{100} }$

$\displaystyle \sf{ \frac{5}{10} }$

$\displaystyle \sf{ \frac{5}{9} }$

EVALUATION

We have to find the sum of

$\sf{ \: 0. \overline{3} \: \: and \: \: 0.\overline{2}}$

Let

$\sf{x = \: 0. \overline{3} }$

$\implies \sf{x = 0.3333........} \: \: \: \: \: - - - - (1)$

Multiplying both sides by 10 we get

$\sf{10x = 3.3333........} \: \: \: \: \: - - - - (2)$

Now Equation (2) - Equation (1) gives

$\displaystyle \sf{9x = 3}$

$\implies \displaystyle \sf{x = \frac{3}{9} }$

$\therefore \: \: \displaystyle \sf{0. \overline{3} = \frac{3}{9} }$

Similarly

$\therefore \: \: \displaystyle \sf{0. \overline{2} = \frac{2}{9} }$

$\therefore \: \: \displaystyle \sf{0. \overline{3} + 0. \overline{2} }$

$\displaystyle \sf{ = \frac{3}{9} + \frac{2}{9} }$

$\displaystyle \sf{ = \frac{3 + 2}{9} }$

$\displaystyle \sf{ = \frac{5}{9} }$

FINAL ANSWER

$\: \displaystyle \sf{0. \overline{3} + 0. \overline{2} = \frac{5}{9} }$

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Answer 2

Answer:

5/9

Step-by-step explanation:

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