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  • Express the recurring decimal $0.\overline{026}$ in the form of a fraction.Option: 1 26/999Option:

Express the recurring decimal $0.\overline{026}$ in the form of a fraction.

Option: 1

26/999


Option: 2

1/5


Option: 3

2/5


Option: 4

2/9


Answers (1)

best_answer

$0.026=0.026026026 \quad \Rightarrow(1)

As the period is containing 2 digits, we multiply by $10^3$, i.e. 1000 , therefore

$1000 \times 0.026=26.026026 \Rightarrow(2)$

(2) - (1) gives

$999 \times 0.026=26 \quad \Rightarrow 0.026=26 / 999$

Posted by

Pankaj

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