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We are given repeating decimal number 2.1¯.
We know 2.1¯ = 2.1111..... repeating 1's.
Let us assume x is a fraction equals given repating decimal number.
And set it as a first eqaution.
x = 2.1111..... ------------- (equation 1).
Multiplying equation both side by 10 ( because only one digit is repeating after decimal, we multiply by 10).
On multiplying by 10 we get
10*x = 10*2.1111.....
10x = 21.1111...... ----------------- (equation 2)
Subtracting equation 1 from equation 2, we get
10x = 21.1111......
-x = -2.1111.....
_____________
9x = 19.
Now, dividing both sides by 9. we get
Therefore, 2.1¯ repeating decimal be expressed as a fraction .
So, the correct option is option c. 19/9.