The distance from the Sun to Mars is an average of 2.1 repeating. 1 times the distance from the Sun to Venus. How can this repeating decimal be expressed as a fraction?

19/9

Step-by-step explanation:

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

-6 is the correct option from the above given options

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